The Kinetics and Mechanisms of Some Fundamental Organic Reactions of Nitro Compounds

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5-2012

Zhao Li Utah State University

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This Dissertation is brought to you for free and open access by the Graduate Studies at [email protected] It has been accepted for inclusion in All Graduate Theses and Dissertations by an authorized administrator of [email protected] For more information, please contact [email protected] THE KINETICS AND MECHANISMS OF SOME FUNDAMENTAL

ORGANIC REACTIONS OF NITRO COMPOUNDS

Zhao Li

A dissertation submitted in partial fulfillment of the requirements for the degree

DOCTOR OF PHILOSOPHY

Chemistry

Approved:

______Vernon D. Parker, Ph.D. Lance C. Seefeldt, Ph.D. Major Professor Committee Member

______Alvan C. Hengge, Ph.D. Roger A. Coulombe, Jr, Ph.D. Committee Member Committee Member

______Cheng-Wei Tom Chang, Ph.D. Mark R. McLellan, Ph.D. Committee Member Vice President for Research and Dean of the School of Graduate Studies

UTAH STATE UNIVERSITY Logan, Utah

2012 ii

iii

ABSTRACT

The Kinetics and Mechanisms of Some Fundamental Organic Reactions

of Nitro Compounds

Zhao Li, Doctor of Philosophy

Utah State University, 2012

Major Professor: Dr. Vernon D. Parker Department: Chemistry and Biochemistry

The central topic of this dissertation is to seek the answer to the question: Is the single transition state model appropriate for (1) the proton transfer reactions of nitroalkanes and (2) the aromatic nucleophilic reactions of trinitroarenes? If not, what are the real mechanisms? This objective has been accomplished by careful kinetic and mechanistic studies which take advantage of modern digital acquisition of absorbance – time data, combined with extensive new data analysis of results from pseudo-first-order kinetic measurements.

Several new analysis procedures for pseudo-first-order kinetics that are capable of distinguishing between single-step and multi-step mechanisms have been introduced and intensively confirmed during the application in the kinetic study of the target reactions. The procedures include (1) half-life dependence of apparent rate constant, (2) sequential linear pseudo-first-order correlation, (3) approximate instantaneous rate constant analysis, and (4) time-dependent apparent kinetic isotope effects. iv

Various conventional and nonconventional pseudo-first-order kinetic analyses of

the reactions of nitroalkanes in aqueous solutions revealed that the reactions are complex

and involve kinetically significant intermediates. The spectral evidence for the formation

of reactive intermediates was obtained by carrying out the kinetic experiments at the

isosbestic points where changes in reactant and product absorbance cancel. The apparent

deuterium kinetic isotope effects studies indicated that the deuterium kinetic isotope

effects are not associated with the formation of the intermediates. The observations of

anomalous Brønsted exponents previously found for this reaction series could be

rationalized well with the complex mechanisms proposed in this work, which indicate

that the nitroalkane anomaly does not exist, but arises from an interpretation based upon the incorrect assumption that the reactions follow a simple one-step mechanism.

Simulations revealed that the generally accepted competitive mechanism was not appropriate to describe the Meisenheimer complex formation during the reaction of

2,4,6-trinitroanisole with methoxide ion in methanol. This conclusion is supported by the conventional pseudo-first-order kinetic analysis. A reversible consecutive mechanism that accounts for the kinetic behavior has been proposed, which involves an intermediate dianion complex that is formed reversibly from the initial 1,3-σ-complex, and then

eliminates methoxide ion to form the 1,1-σ-complex product.

(296 pages)

PUBLIC ABSTRACT

The Kinetics and Mechanisms of Some Fundamental Organic Reactions

of Nitro Compounds

Zhao Li, Ph.D.

Department of Chemistry and Biochemistry

Utah State University, 2012

In chemistry, kinetics is the study of the rates of chemical reactions. A reaction mechanism describes in detail exactly what takes place at each stage of an overall chemical reaction from reactants to products. The work outlined in this dissertation was carried out in order to find out the true mechanisms of some fundamental organic reactions of nitro compounds by means of a series of novel kinetic techniques and analysis methods.

The target reactions include (1) the proton transfer reactions of nitroalkanes and

(2) the aromatic nucleophilic reactions of trinitroarenes, both of which are undeniably among the most elementary and significant processes in organic chemistry and biochemistry.

Rigorous kinetic investigations have found that both reactions actually take place by multi-step mechanisms involving kinetically significant intermediates. This result challenges the long-held assumption that the reactions follow a simple one-step mechanism. Although the assumption of the one-step mechanism can be applied to evaluate the magnitude of the rate of the overall reaction, it fails to provide a detailed vi description of chemical reactions, especially those behaving abnormally. This is obvious in the conundrum found in the description of the proton transfer reactions of nitroalkanes which is commonly known as the nitroalkane anomaly. However, adopting the multi-step mechanisms proposed in this dissertation should end this chapter of organic chemistry.

Reaction mechanism is a primary topic for organic chemical studies that provides a framework for appropriate application in the chemical and pharmaceutical industry, and in agricultural applications. An essential objective of this work is to point out that more attention should be paid to the importance of reaction mechanism in the field of organic chemistry. A broad impact of this work on academic studies may be achieved via promoting a revision of the mechanisms believed to be established over the past seventy years. It will have a broad effect in other branches of chemistry as well as in biochemistry.

This work is a sub-project of the three-year $665,000 international cooperative project of “Is the single transition state model appropriate for the fundamental reactions of organic chemistry?” initiated by Professor Vernon D. Parker at USU, collaborating with Professors Jin-Pei Cheng and Xiao-Qing Zhu in China’s Nankai University. This international project, supported by both NSF (National Science Foundation) and NSFC

(National Natural Science Foundation of China), has been fostering cooperation and good will between the scientific communities of the United States and China.

Contact: [email protected] vii

ACKNOWLEDGMENTS

The primary acknowledgment goes to my advisor, Dr. Vernon D. Parker, for his

consistent guidance, support, and help during my time at Utah State University. His

breadth and depth of knowledge in physical organic chemistry was a constant source of

support to encourage my independent and original thought, and to provide me a model of

what a successful scientist should be. I am honored that I could have an opportunity to

study in his group. What I have learned from him is invaluable for me and my future

career development.

I would also like to express my appreciation to the other professors in my

supervisory committee, Dr. Alvan C. Hengge, Dr. Cheng-Wei Tom Chang, Dr. Lance C.

Seefeldt, and Dr. Roger A. Coulombe, Jr, for their support, guidance, and helpful

suggestions. I am grateful for their experience in their respective fields.

I especially thank Dr. Jin-Pei Cheng, our collaborator and my former advisor at

Nankai University, for providing me the opportunity to join the USU-Nankai

International Cooperative Graduate Program, as well as for his extensive help and encouragement over the past five years.

I am also grateful to the other collaborator at Nankai University, Prof. Xiao-Qing

Zhu, for his efforts in the funding application and helpful suggestions in my research.

Great thanks to Dr. Donald Bethell, professor at the University of Liverpool, for his help in the study of isosbestic point.

I wish to express my appreciation to my colleagues, Dr. Weifang Hao for her numerous helps throughout my educational experience at USU; Xiaosong Xue for his viii cooperation in calculations; Chad Jacobs for helping with the kinetic study of SNAr reactions; Dr. Rui Cao, Xiaozhen Han, and Russell Scow for their helpful discussion and friendship.

I am profoundly grateful to the Parker couple (Vernon and Monica) and the

Zhang couple (Tao and Weifang). Their friendship and considerate help made me feel part of a large family.

Deep gratitude also belongs to my parents, Lanlin Li and Xueping Wang, for their constant strength, love, and faith in me. I also owe many thanks to all my friends and relatives, whose names are not mentioned here. Your love and support mean a lot to me.

Last but not least, I would express my appreciation to my wife, Kun Liu, for her love, support, and understanding. She is a doctoral student in analytic chemistry at

Brigham Young University. It was very challenging for both of us to pursue graduate studies in different places and bear the life of less time together. Without her excellent work at home and without her personal sacrifice, it would have been impossible for me to finish this project. It is to her, my parents, and my parents-in-law, that this dissertation is dedicated.

Zhao Li

CONTENTS

Page

ABSTRACT ...... iii

PUBLIC ABSTRACT ...... v

ACKNOWLEDGMENTS ...... vii

LIST OF TABLES ...... xi

LIST OF FIGURES ...... xvi

LIST OF SCHEMES ...... xxiii

CHAPTER

1. INTRODUCTION ...... 1

Background ...... 1 Steady-State vs. Non-Steady-State ...... 4 Previous Work on the Proton Transfer Reactions of Nitroalkanes ...... 12 Previous Work on the Nucleophilic Aromatic Substitution of Trinitroarenes 33

2. THEORETICAL DIFFERENTIATION BETWEEN THE SINGLE-STEP AND THE PRE-ASSOCIATION MECHANISMS IN ORGANIC CHEMICAL REACTIONS ...... 58

3. NEW METHODOLOGY FOR DIFFERENTIATING BETWEEN SINGLE-STEP AND MULTI-STEP MECHANISMS ...... 82

4. REACTIONS OF THE SIMPLE NITROALKANES WITH HYDROXIDE ION IN WATER. EVIDENCE FOR A COMPLEX MECHANISM ...... 95

5. KINETICS AND MECHANISMS OF THE PROTON TRNASFER REACTIONS OF 1-NOTROPROPANE AND NITROCYCLOALKANES WITH HYDROXIDE ION IN WATER ...... 117

6. ISOSBESTIC POINTS STUDY OF THE PROTON TRANSFER REACTIONS OF ALIPHATIC NITROALKANES WITH HYDROXIDE ION IN AQUEOUS SOLUTIONS. A METHOD TO VERIFY THE PRESENCEOF AN INTERMEDIATE...... 137

7. PROTON TRANSFER REACTIONS OF 1-ARYLNITROETHANES WITH HYDOXIDE ION IN AQUEOUS SOLUTIONS. A RATIONAL EXPLANATION OF THE NITROALKANE ANOMALY ...... 163

8. THE REVERSIBLE CONSECUTIVE MECHANISM FOR THE REACTION OF TRINITROANISOLE WITH METHOXIDE ION ...... 190

9. CONCLUSIONS...... 210

APPENDICES ...... 214

Appendix A. Supplementary Table for Theoretical Differentiation Between Mechanisms ...... 215 Appendix B. Supplementary Information for Reactions of the Simple Nitroalkanes with Hydroxide Ion in Water ...... 217 Appendix C. Supplementary Information for Reactions of 1-NP and nitrocycloalkanes with Hydroxide Ion in Water ...... 228 Appendix D. Supplementary Information for Reactions of the 1-Arylnitroethanes with Hydroxide Ion in Aqueous Solutions ...... 236 Appendix E. Supplementary Information for Reactions of Trinitroanisole with Methoxide Ion in Methanol ...... 247 Appendix F. Copyright Permissions...... 257

CURRICULUM VITAE ...... 269

LIST OF TABLES

Table Page

1-1. Mechanism Probes………..………………………………………………… 7

1-2. Mechanism Probe Values…….……………...……………………………… 9

1-3. pKa Values of Three Simple Aliphatic Nitroalkanes…………...…………… 15

1-4. pKa Values of β-Methyl Substituted Nitroethanes………...……………… 16

1-5. Equilibrium and Rate Constants for the Proton Transfer Reactions of Three - Simple Nitroalkanes with OH in H2O…….……...………………………… 19

1-6. The Anomalous Brønsted Relations (α > 1) in the Proton Transfer Reactions of Aryl Nitroalkanes…………………………………………… 20

1-7. Brønsted β Values for the Proton Transfer Reactions of Nitroalkanes…… 20

1-8. Normal Brønsted α Values (0 ≤ α ≤ 1) for the Proton Transfer Reactions of 1-Arylnitroethanes with Various Nitrogen Bases in H2O at 298 K………… 24

1-9. KIE Values for the Proton Transfer Reaction Between p-NPNM and TMG in Aprotic Solvents………………………………………………………… 26

1-10. KIE Values for Reactions Between p-NPNM and Amine Bases in Toluene.. 27

1-11. Proton Transfer Reactions of Nitroalkanes Involving Proton Tunneling…… 28

1-12. Isotope Effects and Arrhenius Parameters for Proton Transfer Reactions of 1-(4-Nitrophenyl)-1-nitroalkanes with DBU……………………………… 29

1-13. Isotope Effects and Arrhenius Parameters for Proton Transfer Reaction of 1-(4-Nitrophenyl)-1-nitroethane with OH- in Aqueous Acetonitrile……… 30

1-14. Solvent Isotope Effects in the Deprotonations of Nitroalkanes by Lyate Ion in H2O and D2O…………………………………………………………… 32

1-15. Thermodynamic and Kinetic Parameters for the SNAr Reactions of TNB with Lyate Ions in H2O, MeOH and EtOH………………………………… 36

1-16. Kinetic and Thermodynamic Data for the Reaction of TNA with MeO- in MeOH……………………………………………………………………… 39 xii

Table Page

1-17. Buncel’s Classification of SNAr Reactions of 1-X-2,4,6-Trinitroarenes…… 41

2-1. Rate Constant Matrix for the KSPAM……………………………………… 66

2-2. Time Ratio (t0.50/t0.05) Matrix for the KSPAM When Reactant Decay Is Monitored…………………………………………………………………… 67

3-1. Changes in the Slopes and the Intercepts with the Extent of Reaction during Conventional Pseudo-First-Order Analysis of the KSPAM with kapp -1 -1 -1 -1 = 1.0 s , kf’ = 1.1 s , kb = 0.5 s , kp = 5.0 s ……………………………… 85

3-2. Point Segment Set for KCONT Analysis…………………………………… 86

3-3. A Theoretical Model of Pre-Association Mechanism for Apparent KIE Analysis…………………………………………………………………… 89

3-4. A Theoretical Model of Pre-Association Mechanism for Apparent KCE Analysis…………………………………………………………………… 92

4-1. Equilibrium and Rate Data Often Cited in Support of the “Nitroalkane Anomaly”………………………………………………………………… 96

4-2. Variations of the Apparent Pseudo-First-Order Rate Constants for the - Reactions of Nitroalkanes with OH in H2O over Several Half-Lives (5 Half-Lives for NM, 4 Half-Lives for NE, 3 Half-Lives for 2-NP)………… 100

4-3. Apparent Rate Constants for the Reactions of Nitroalkanes with OH- in H2O over the First Half-Life at 298 K……………………………………… 101

5-1. Equilibrium and Kinetic Acidities of Simple Aliphatic Nitroalkanes……… 118

5-2. Equilibrium and Kinetic Acidities of Nitrocycloalkanes…………………… 119

- 5-3 pKa’s and Rates with OH of Simple Nitroalkanes in H2O at 298 K……… 121

- 5-4. pKa’s and Rates with OH of Nitrocycloalkanes in H2O at 298 K………… 122

5-5. Changes in the Slopes and the Intercepts with the Extent of Reaction During Conventional Pseudo-First-Order Analysis of the Reactions of 0.1 - mM 1-NP, NC4 and NC5 with OH in H2O at 298 K (240 nm)…………… `123 xiii

Table Page

5-6. Changes in the Slopes and the Intercepts with the Extent of Reaction During Conventional Pseudo-First-Order Analysis of the Reactions of 0.1 - mM NC6, NC7 and NC8 with 100.0 mM OH in H2O at 298 K (240 nm)………………………………………………………………………… 123

5-7. Time Ratios (t0.50/t0.05) for the Reactions of 0.1 mM 1-NP and - Nitrocycloalkanes with OH in H2O at Various Wavelengths, When Product Evolution Is Monitored at 298 K…………………………………………… 124

5-8 Apparent Rate Constants Obtained by the 24-Point Sequential Analysis of - the Reactions of 0.1 mM 1-NP and Nitrocycloalkanes with OH in H2O at 298 K (240nm)……………………………………………………………… 125

5-9. KIE and Arrhenius Parameters for Proton and Deuterium Transfer - Reactions of Five Aliphatic Nitroalkanes with OH in H2O……………… 128

7-1. Half-Life Dependence of Conventional Pseudo-First-Order Rate Constants and the Intercepts of Linear Correlations for the Reactions of p-NPNE with OH- in Various Solvents at 298 K………………………………………… 168

7-2. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of p-MePNE (0.1 mM) with - OH (50.0 mM) in H2O-Dioxane (50/50 vol %) at 298 K, 320 nm………… 172

7-3. Brønsted α Values for the Reactions of ArNE with OH- in Aqueous Solutions at 298 K………………………………………………………… 180

7-4. Equilibrium and Rate Constants for the Reactions of ArNE with OH- in H2O at 298 K……………………………………………………………… 182

8-1. Rate and Equilibrium Constants for the Formation of 1,3-Dimethoxy and 1,1-Dimethoxy Complexes During the Reaction of TNA with MeO- in MeOH at 298 K, According to the Competitive Mechanism Shown in Scheme 5-1………………………………………………………………… 192

8-2. Simulation of the Kinetics of the Reaction of TNA with MeO- in MeOH According to Scheme 5-1 Applying Input Data from Table 5-1…………… 194

8-3. Test for Linearity of ln (1 – E.R.) from the 10000 Point Simulation with - [MeO ]0 Equal to 120 mM………………………………………………… 195

8-4. Experimental Rate Constants for the Reaction of TNA (0.0001 M) MeO- in MeOH at 293 K…………………………………………………………… 196 xiv

Table Page

8-5. Apparent Rate Constants as a Function of Degree of Conversion and - [MeO ]0…………………………………………………………………… 200

8-6. The Effect of K1 Magnitude on the Value of the Apparent Second-Order Rate Constants (k2’) Obtained from Simulated Data for the Mechanism in Scheme 5-1………………………………………………………………… 201

8-7. Simulated Values of the Ratios of Rates of Formation and Decay of Complex II………………………………………………………………… 201

A.1. Time Ratio (t0.50/t0.05) Matrix for the KSPAM when Product Evolution is Monitored…………………………………………………………………… 216

B.1. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments on the Reaction of NM (0.10 mM) with NaOH (20.0 mM) in H2O at 298 K……………………………………………………………… 218

B.2. Apparent Rate Constants and Standard Deviations for 4 Sets of Experiments on the Reaction of NE (0.10 mM) with NaOH (50.0 mM) in H2O at 298 K……………………………………………………………… 219

B.3. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments on the Reaction of 2-NP (0.10 mM) with NaOH (50.0 mM) in H2O at 298 K……………………………………………………………… 222

C.1. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of 1-NP (0.1 mM) with OH- (50.0 mM) in H2O at 298 K (240 nm)……………………………………… 230

C.2. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC4 (0.1 mM) with OH- (50.0 mM) in H2O at 298 K (240 nm)……………………………………… 231

C.3. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC5 (0.1 mM) with OH- (100.0 mM) in H2O at 298 K (240 nm)…………………………………… 232

C.4. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC6 (0.1 mM) with OH- (100.0 mM) in H2O at 298 K (240 nm)…………………………………… 233 xv

Table Page

C.5. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC7 (0.1 mM) with OH- (100.0 mM) in H2O at 298 K (240 nm)…………………………………… 234

C.6. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC8 (0.1 mM) with OH- (100.0 mM) in H2O at 298 K (240 nm)…………………………………… 235

D.1. Equilibrium and Kinetic Acidities of ArNE in H2O………………………… 245

D.2. Equilibrium and Kinetic Acidities of ArNE in H2O-MeOH (50/50 vol %)… 245

D.3. Equilibrium and Kinetic Acidities of ArNE in H2O-Dioxane (50/50 vol %). 246

E.1. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (15 mM) in MeOH at 293 K……………………………… 248

E.2. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (30 mM) in MeOH at 293 K……………………………… 249

E.3. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (60 mM) in MeOH at 293 K……………………………… 250

E.4. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (120 mM) in MeOH at 293 K…………………………… 251

xvi

LIST OF FIGURES

Figure Page

1-1. Some current theories of physical organic chemistry relationships……… 2

1-2. (a) Theoretical ln[Reactant] – time and (b) extent of reaction – time profiles for Diels–Alder reaction between ANTH and TCNE in -1 -1 acetonitrile, [Reactant]0 = 0.2 mM, kf’ = 0.874 s , kb = 14.8 s and kp = 12.4 s-1…………………………………………………………………… 8

1-3. Instantaneous rate constant – time profiles for (a) simple one-step irreversible mechanism and (b) two-step reversible consecutive mechanism………………………………………………………………… 11

1-4. Reactions of nitroalkanes………………………………………………… 12

1-5. Acidities of some carbon acids…………………………………………… 13

1-6. Relation of Brønsted exponent to transition state………………………… 17

1-7. Brønsted plot curvature (a) predicted by Brønsted and Pedersen in 1924, and (b) confirmed by Eigen in 1964……………………………………… 18

1-8. Ideal (dash curve) and the proposed (solid curve) free energy vs. reaction coordinate profiles for the deprotonation of aryl nitromethanes as viewed by Bernasconi…………………………………………………………… 22

1-9. Relation between kinetic isotope effects and ΔpK of the reacting system... 31

1-10. Variation of kH/kD with ΔpK for nitroalkanes proton transfer system…… 31

1-11. Energy vs. reaction coordinate profiles for reaction of TNA with MeO-…38

1-12. Qualitative free energy profiles detailing the different patterns of regioselectivity: K3T1, K1T1, K3T3 and K1T3………………………… 41

2-1. Calculated concentration – time profiles for (a) reactant and product, and (b) intermediate according to the reversible consecutive mechanism…….. 63

2-2. (a) (1 – E.R.) – time, and (b) (1 – E.R.) – t/t0.5 profiles for kapp equal to 1 (kf’ = kp = kb = 2), to 10 (kf’ = kp = kb = 20), to 100 (kf’ = kp = kb = 200), respectively……………………………………………………………… 65 xvii

Figure Page

-1 2-3. Plots of calculated kinst – time profiles for kf’ equal to 1 s , kp and kb equal -1 to (a) 1, or to (b) 16 s . The value of kapp was equal to 0.50 in both (a) and (b)…………………………………………………………………… 69

2-4. kinst – time profiles (left hand column) and conventional kinetic analysis -1 -1 (right hand column) for the KSPAM with kf’ = 1.1 s , kapp = 1.0 s and kp = 0.125, 4.0, and 128 s-1 from top to bottom, respectively……………… 70

2-5. kinst – time profiles (left hand column) and conventional kinetic analysis -1 -1 (right hand column) for the KSPAM with kf’ = 2.0 s , kapp = 1.0 s and kp = 0.125, 4.0, and 128 s-1 from top to bottom, respectively……………… 71

2-6. kinst – time profiles (left hand column) and conventional kinetic analysis -1 -1 (right hand column) for the KSPAM with kf’ = 4.0 s , kapp = 1.0 s and kp = 0.125, 4.0, and 128 s-1 from top to bottom, respectively……………… 72

2-7. Reaction coordinate diagrams (a) for the SN2 reaction in the gas phase, and (b) for the reactions of methyl iodide or m-nitrobenzyl bromide and p-nitrophenoxide in AN/DMSO (75/25 vol %)…………………………… 76

-1 -1 2-8. Concentration profiles for the KSPAM kf’ = 4 s , kb = 0.50 s and kp = 0.125 s-1…………………………………………………………………… 77

-1 -1 3-1. (a) kapp – time and (b) kIRC – time profiles for kapp = 1.0 s , kf’ = 2.0 s , kb -1 = kp = 16 s ……………………………………………………………… 86

-1 3-2. Comparison between kIRC – time and kinst – time profiles, kapp = 1.0 s , kf’ -1 -1 -1 -1 -1 = 2.0 s , kb = kp = (a) 16 s , (b) 2.0 s , (c) 0.5 s , (d) 0.25 s …………… 87

E.R. 3-3. Calculated KIEapp – E.R. profiles for (a) reactant decay and (b) product evolution………………………………………………………………… 89

3-4. KIEapp – time profiles calculated in (a) 10 s and (b) 100 s……………… 91

E.R. 3-5. Calculated (a) KCEapp – E.R. and (b) KCEapp – time profiles………… 92

4-1. Absorbance – time profiles (a, b, c) and ln (1 – E.R.) – time profiles (a’, b’, c’) for the reactions of nitroalkanes (a, a’ NM; b, b’ NE; c, c’ 2-NP) - with OH in H2O at 298 K………………………………………………… 99

4-2 Apparent KIE for the reactions of NE and NE-d2 as a function of degree of conversion under the conditions shown……………………………… 103 xviii

Figure Page

4-3. Simulated concentration – time (a, c) and kinst – time (b, d) profiles for the reversible consecutive mechanism with the rate constants shown, kf’ = kf[Excess Reactant]0……………………………………………………… 105

4-4. Diode-array UV absorption spectra of the reaction between NE-d2 (20.37 - mM) and OH (100.0 mM) in H2O at 298 K: start time, 0 s; cycle time, 10 s; total run time, 300 s…………………………………………………… 106

4-5. Abs – time profiles at the isosbestic points for the reactions of (a) NE, (b) - NE-d2 with OH in H2O at 298 K………………………………………… 107

- 4-6. ΔAbs – time profiles for the reaction of NE-d2 (20.37 mM) with OH (50.0 mM) in H2O at 298 K near the isosbestic point, 267.5 nm (a: from 266.0 nm to 269.0 nm with the increment of 1.0 nm; b: from 267.3 nm to 267.7 nm with the increment of 0.1 nm). ΔAbs = Abst – Abs0…………… 113

5-1. Approximate instantaneous rate constant (kIRC) – time profiles for the - reactions of 1-NP (a) and nitrocycloalkanes (b – f) with OH in H2O at 298 K……………………………………………………………………… 126

E.R. 5-2. KIEapp – E.R. profiles (a, b, c) and KIEapp – time profiles (a’, b’, c’) for the reactions of 1-NP (a, a’), NC5 (b, b’), and NC6 (c, c’) with OH- in H2O under the conditions as shown……………………………………… 129

E.R. - 5-3. KIEapp – E.R. profiles for the reaction of 1-NP (0.1 mM) with OH (50.0 mM) in H2O at various temperatures……………………………… 130

5-4. Abs – time profiles at the isosbestic points for the reactions of (a) NC7, - (b) NC8 with OH in H2O………………………………………………… 131

6-1. Correlation between the concentrations of product and reactant during the reactions following (a) simple one-step and (b) reversible consecutive mechanisms……………………………………………………………… 140

6-2. Calculated ΔAbs – time profiles at the isosbestic point of reactant and product for the two-step reversible consecutive mechanism……………… 141

6-3. Diode-array UV absorption spectra of the reactions of (a) NE-d2 (20.4 - mM), (b) 2-NP-d1 (19.5 mM) with OH (100.0 mM) in H2O at 298 K…… 143 xix

Figure Page

- 6-4. ΔAbs – time profiles for the reaction of NE-d2 (20.4 mM) with OH (50.0 mM) in H2O at 298 K near the isosbestic point, 267.5 nm (a: from 266.0 nm to 269.0 nm with the increment of 1.0 nm; b: from 267.3 nm to 267.7 nm with the increment of 0.1 nm). ΔAbst = Abst – Abs0………………… 144

6-5. Abs – time profiles at the isosbestic points for the reactions of (a) NE, (b) - NE-d2, (c) 2-NP-d1, (d) 1-NP-d2, (e) NC7 and (f) NC8 with OH in H2O… 145

6-6. (a) ΔAbs – time profiles near the isosbestic point 271.2 nm, and (b) Abs – time profile at the isosbestic points for the reaction of 2-NP-d1 (40.0 mM) - with OH (100.0 mM) in H2O at 298 K, measured by SF-61 stopped-flow spectrophotometer………………………………………………………… 146

6-7. Abs – time profiles at the isosbestic points for the reactions of (a) NE, (b) - 2-NP, (c) 1-NP, (d) NC4, (e) NC5 and (f) NC6 with OH in H2O, measured by SF-61 stopped-flow spectrophotometer…………………… 147

6-8 Abs – time profiles at the isosbestic points for the reactions of (a) - NC5-d1, and (b) NC6-d1 with OH in H2O-MeOH (50/50 vol %) at 303 K. 148

6-9. (a) UV absorption spectra and (b) Abs – time profile at 282.8 nm for the - reactions between NM (19.9 mM) and with OH in H2O at 298 K……… 149

-1 6-10. Calculated [I] – time profiles based on two kf’ values (0.1 and 0.2 s ), kb -1 -1 = 0.5 s , kp = 0.25 s ……………………………………………………… 151

6-11. ΔAbs – time profiles at the isosbestic points for the reactions of (a) NE-d2 - and (b) 2-NP-d1 with OH of two concentrations in H2O at 298 K……… 151

6-12. ΔAbs – time profiles at the isosbestic points for the reaction of 2-NP-d1 - (39.8 mM) with OH (100.0 mM) in H2O at 288, 298 and 308 K………… 152

6-13. UV absorption spectra for the acyl transfer reaction between PNPA and - OH in (a) H2O and (b) AN-H2O (80/20 vol %) at 298K………………… 154

6-14. Abs – time profiles near the isosbestic points (a) 248.0 nm and (b) 319.8 - nm for the reaction of PNPA with OH in H2O at 298K under the conditions as shown……………………………………………………… 155 xx

Figure Page

6-15. Calculated Abs – time profiles near the isosbestic point (274.5 nm) for (a) the single one-step mechanism and (b) the reversible consecutive mechanism when εI = εP. Curve b: 274.1 nm, c: 274.2 nm, d: 274.3 nm, e: 274.4 nm, f: 274.5 nm isosbestic point, g: 274.6 nm, h: 274.7 nm, i: 274.8, j: 274.9 nm. The εP and εR values at various wavelengths are from - the reaction between 2-NP and OH in H2O at 298K…………………… 155

6-16 Abs – time profiles near the isosbestic points (a) 247.0 nm and (b) 318.8 - nm for the reaction of PNPA with OH in AN-H2O (80/20 vol %) at 298K under the conditions as shown…………………………………………… 156

7-1. Long-time (over about 5 HL) –ln(1 – E.R.) – time profile and corresponding least squares correlation line for the reaction of p-NPNE - with OH in H2O-dioxane (50/50 vol %) at 298 K……………………… 169

7-2. Long-time –ln(1 – E.R.) – time profiles for the reactions of ArNE with OH- in various solutions under the conditions shown…………………… 170

7-3. Apparent rate constants (kapp) – time plots for the reaction between p-NPNE and OH- in various solvents at 298 K under the condition shown. 171

- 7-4. kIRC – time profiles for the reactions of ArNE with OH in various 174 solvents…………………………………………………………………… 1

7-5. Simulated kapp – time profiles for (a) the reversible consecutive mechanism, and (b) a series of product profiles under the influence of the intermediate absorption over a wide range of degree…………………… 176

E.R. 7-6. KIEapp – E.R. profiles for the reactions of p-NPNE (left) and m-NPNE (right) with OH- under the conditions shown…………………………… 178

7-7. KIEapp – time profiles for the reactions of p-NPNE (left) and m-NPNE (right) with OH- under the conditions shown…………………………… 178

7-8. Brønsted correlation of kp with pKa and αreal for the reactions of ArNE - with OH in H2O………………………………………………………… 182

7-9. Conventional Brønsted correlations of apparent rate constants with pKa for the proton transfer reactions of arylnitromethanes with benzoate anion in (a) DMSO and (b) acetonitrile………………………………………… 183

- 8-1. Pseudo-first-order plots for the reaction of TNA with [MeO ]0 equal to 15 mM……………………………………………………………………… 197 xxi

Figure Page

- 8-2. Pseudo-first-order plots for the reaction of TNA with [MeO ]0 equal to 60 mM……………………………………………………………………… 198

- 8-3. Pseudo-first-order plots for the reaction of TNA with [MeO ]0 equal to 120 mM…………………………………………………………………… 199

8-4. Simulated concentration – time plots for the reaction of TNA (0.1 mM) - with [MeO ]0 equal to 15 and 120 mM…………………………………… 204

B.1. Apparent KIE for the reactions of NM and NM-d3 in H2O at 298 K as a function of degree of conversion………………………………………… 221

B.2. Apparent KIE for the reactions of NE and NE-d2 in H2O at 298 K as a function of degree of conversion………………………………………… 221

B.3. Apparent KIE for the reactions of 2-NP and 2-NP-d1 in H2O at 298 K as a function of degree of conversion………………………………………… 222

B.4. UV absorption spectra for the reactions of NM (a, a’), NE (b, b’), 2-NP - (c, c’) with OH in H2O under the conditions as shown………………… 223

B.5. Absorbance – time profile at the isosbestic point near 269.6 nm for the - reaction of NE (21.1 mM) with OH (50.0 mM) in H2O at 298 K……… 224

B.6. Absorbance – time profile at the isosbestic point near 267.5 nm for the - reaction of NE-d2 (20.37 mM) with OH (100.0 mM) in H2O at 298 K… 224

B.7. Absorbance – time profile at the isosbestic point near 268.4 nm for the - reaction of 2-NP (20.9 mM) with OH (100.0 mM) in H2O at 298 K…… 225

B.8. Absorbance – time profile at the isosbestic point near 269.4 nm for the - reaction of 2-NP-d1 (19.5 mM) with OH (100.0 mM) in H2O at 298 K… 225

B.9. Apparent KIE for the reactions of NM and NM-d3 in H2O at 298 K as a function of reaction time………………………………………………… 226

B.10. Apparent KIE for the reactions of NE and NE-d2 in H2O at 298 K as a function of reaction time………………………………………………… 226

B.11. Apparent KIE for the reactions of 2-NP and 2-NP-d1 in H2O at 298 K as a function of reaction time………………………………………………….. 227 xxii

Figure Page

C.1. UV absorption spectra for the reactions of (a) 1-NP, (b) NC4, (c) NC5, (d) - NC6, (e) NC7, and (f) NC8 with OH in H2O under the conditions as shown……………………………………………………………………… 229

D.1. Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE with OH- in H2O at 298 K…………………………………………………………… 237

D.2. Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE with OH- in H2O-MeOH (50/50 vol %) at 298 K…………………………………… 238

D.3. Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE with OH- in H2O-dioxane (50/50 vol %) at 298 K………………………………… 240

- D.4. kIRC – time profiles for the reactions of ArNE with OH in H2O at 298 K... 241

- D.5. kIRC – time profiles for the reactions of ArNE with OH in H2O-MeOH (50/50 vol %) at 298 K…………………………………………………… 242

- D.6. kIRC – time profiles for the reactions of ArNE with OH in H2O-dioxane (50/50 vol %) at 298 K…………………………………………………… 244

E.1. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (15 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots………………………………………………………… 252

E.2. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (30 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots………………………………………………………… 253

E.3. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (60 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots………………………………………………………… 254

E.4. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (120 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots………………………………………………………… 255

xxiii

LIST OF SCHEMES

Scheme Page

1-1. Simple Mechanism with Encounter Complex…………………………… 2

1-2. (a) Simple One-Step Mechanism, and (b) Reversible Consecutive Mechanism……………………………………………………………… 3

1-3. Deprotonation of Nitroalkanes…………………………………………… 14

1-4. Hyperconjugation Effect on Ethyl Nitronate Anion……………………… 15

1-5. The Transition State for the Proton Transfer Reactions Between Nitroalkanes and OH- Supposed by Kresge……………………………… 21

1-6. The Multi-Step Mechanism for Proton Transfer Reactions of Nitroalkanes Supposed by Bordwell…………………………………… 23

1-7. Reversible Consecutive Mechanism for the Proton Transfer Reaction between p-NPNE and OH- in Aqueous Acetonitrile Supposed by Parker... 25

2-1. Reversible Consecutive Mechanism……………………………………… 59

2-2. The 3-Step Mechanism for Reaction Between 4,4’,4”-Trimethoxytrityl Ion and Acetate Ion in Acetic Acid……………………………………… 61

2-3. The SN2 Reaction………………………………………………………… 73

2-4. KSPAM for SN2 Reaction of MeI with p-Nitrophenoxide……………… 75

4-1. Proposed Mechanism for the Reaction of TNA with MeO- in MeOH…… 97

- 4-2. Reactions of Nitroalkanes with OH in H2O……………………………… 98

4-3. The 2-Step Reversible Consecutive Mechanism Applied to the Proton - Transfer Reactions Between the Nitroalkanes and OH in H2O (Mechanism 1)…………………………………………………………… 103

4-4. The 3-Step Reversible Consecutive Mechanism Applied to the Reactions - Between the Nitroalkanes and OH in H2O (Mechanism 2)……………… 108

4-5. The Intra-Complex Hydrogen Atom Coupled Electron Transfer from a “Reactant Complex”……………………………………………………… 109 xxiv

Scheme Page

5-1. The Three-Step Reversible Consecutive Mechanism Applied to the - Reactions between the Aliphatic Nitroalkanes and OH in H2O………… 132

6-1. The Reversible Consecutive Mechanism for Acyl Transfer Reaction - Between PNPA and OH in H2O………………………………………… 153

7-1. Simple One-Step Mechanism for the Proton Transfer Reactions of Nitroalkanes……………………………………………………………… 165

7-2. Reversible Consecutive Mechanism for the Proton Transfer Reaction Between p-NPNE and OH- in Aqueous Acetonitrile…………………… 166

7-3. Proton Transfer Reactions Between ArNE and OH-……………………… 167

7-4. The Two-Step Reversible Consecutive Mechanism for the Proton Transfer Reactions Between ArNE and OH- in Aqueous Solutions……… 179

8-1. Assumed Mechanism for the Formation of 1,3 (I)- and 1,1 (II)- Dimethoxy Complexes in MeOH Containing MeO-…………………… 191

8-2. Reversible Consecutive Mechanism for the Formation of Complex II During the Reaction of TNA with MeO- in MeOH……………………… 202

8-3. Possible Reaction of Complex I with MeO- to Form the Dianion Complex III (“Reactant Complex” = III) Which Eliminates MeO- to Produce Complex II……………………………………………………… 203

CHAPTER 1

INTRODUCTION

1.1

Background

A reaction mechanism is a detailed description of a reacting system as it

progresses from reactants to products. In the ideal case it includes identification of all of

the intermediates that are involved, assessment of the characteristics of the transition

state(s) through which the reaction progresses, and recognition of the factors that affect

reactivity, such as solvent effects. The rate constant(s) and the order of a reaction with

respect to all reactants can be directly evaluated from the kinetic data. The latter can also

reveal important evidence concerning the reaction steps and the intermediate(s) that may be involved.

According to the development of experimental technology, physical organic chemists in the 20th century have made rapid progress in the theoretical exploration of

reactions based upon a series of empirical and semi-empirical correlations of reactivity.

Many current theories of physical organic chemistry center on the quantitative structure reactivity relationships, such as those shown in Figure 1-1, which are often used to describe an approach to the reaction mechanisms, from kinetic and thermodynamic study through the prediction of the structures of transition states.

What all of these relationships have in common is that they are only appropriate for the description of reactions that take place in a simple one step. For reactions involving more than a single transition state, parameters derived from these relationships necessarily become less reliable, or even absurd, in describing transition-state structure. 2

 Hammett equation  Brønsted equation  Marcus theory  Variational transition state theory  Configuration mixing model  Kinetic isotope effect  Principle of non‐perfect synchronization

FIGURE 1-1. Some current theories of physical organic chemistry relationships

Eigen1 assumed that all bimolecular reactions in solution pass through an

encounter complex (Scheme 1-1), and this has been generally accepted by the entire physical chemistry community. However, the encounter complex is always excluded from the rate laws during the kinetic analysis, because it is formed at near diffusion-controlled rates and is not considered to be kinetically significant for reactions taking place on the millisecond or second time scale. Thus, all of the mechanistic analysis in this dissertation is referring to the reaction mechanisms without specifically involving the encounter complexes.

SCHEME 1-1. Simple Mechanism with Encounter Complex

In his classic monograph on physical organic chemistry, Hammett2 pointed out

that the kinetic response to the reversible consecutive mechanism (Scheme 1-2b), more

commonly known as the pre-association mechanism, differs from that of the simple

irreversible one-step mechanism (Scheme 1-2a). However, he concluded that the 3 deviations between the kinetic responses of the two mechanisms are too small to be differentiated due to the low precision in kinetic measurements at that time. Digital technology was not available at that time (about 70 years ago) but has developed enormously since then providing the tools necessary to undertake this task.

SCHEME 1-2. (a) Simple One-Step Mechanism, and (b) Reversible Consecutive Mechanism

In fact, the digital revolution during the last half of the 20th century did have a

great influence on the work of the physical chemists studying rapid kinetics. In the

meantime, there were no serious attempts to subject the fundamental slower reactions of

organic chemistry, which are assumed to take place by a simple mechanism, to a rigorous

mechanistic analysis designed to detect a more complex mechanism.

The objective of the work in this dissertation is to fill this gap by introducing

methods for the careful kinetic and mechanistic studies of some fundamental organic

reactions of nitro compounds which take advantage of modern digital acquisition of

absorbance – time data. The latter, combined with extensive new data analysis of results

from pseudo-first-order kinetic measurements (Chapter 2, 3). The reactions relating to

nitro compounds discussed in the text include the proton transfer reactions of nitroalkanes

(Chapter 4 – 7), and the aromatic nucleophilic reactions of trinitroarenes (Chapter 8).

1.2

Steady-State vs. Non-Steady-State

Application and Limitation of the Steady-State Approximation

For simple mechanisms, the corresponding kinetic expression can be written directly as the product of the microscopic rate constant and a concentration term.

However, the kinetic expressions appropriate for complex mechanisms are not immediately obvious. Many of them can be derived by means of the steady-state approximation first used by Bodenstein,3 which assumes that the concentration of each

intermediate remains very small and constant during the course of the reaction.

For example, applying the steady-state approximation to deal with the reversible

consecutive mechanism (Scheme 1-2b), the kinetic expression can be simplified by

defining an apparent rate constant (kapp) (eq 1.2) obtained using the assumptions in the

previous paragraph.

-d[A]/dt = d[P]/dt = [A][B]kapp (1.1)

kapp = kfkp/(kb + kp) (1.2)

Therefore, the steady-state approximation provides a shortcut to study the

complex mechanisms in kinetic terms appropriate for simple mechanisms. The

approximation is supposed to be more rigorously correct the lower the concentration of

the intermediate that prevails in the steady state.4 If an intermediate accumulates to an 5 appreciable extent during a reaction, the steady-state approximation cannot legitimately be used.

For a complex mechanism, the apparent rate constant, kapp, derived from the

steady-state approximation, can only be used to evaluate the magnitude of the rate of the

overall reaction. In the event that the first step in the complex reaction is rate determining,

first order analysis provides the microscopic rate constant for that step. However even in this case, the steady-state approximation cannot be used as a guide to determine the other rate constants (for example, kp and kb). This results in an incomplete and somewhat

unsatisfactory kinetic analysis of the reaction.

It is noticeable that none of the complex mechanisms can be distinguished from

the simple one-step mechanism, once the hypothetical steady state is achieved. Thus this

work must be carried out under the conditions that correspond to pre- or non-steady-state.

The Discovery of the Occurrence of Complex Mechanisms under Non-Steady-State Conditions

In 1998, during the studies of the proton transfer reactions of methylanthracene radical cations with nitrogen-centered bases, Parker et al.5 found that the reactions do not

quickly reach a steady state and that in the pre-steady-state time period, the kinetic

response deviates significantly from that expected for the simple one-step mechanism.

This observation made it possible to kinetically distinguish between the simple and

complex mechanisms shown in Scheme 1-2. Subsequently, it was found that kinetic data

for a number of fundamental organic reactions including a nitroalkane proton transfer,6,7

8 9 an E2 elimination, an SN2 reaction, a hydride transfer reaction between NADH

models,10 a Diels-Alder reaction,11 an acyl-transfer reaction,12 a carbocation-anion 6

13 14 combination as well as an SNAr reaction, are inconsistent with the simple one-step

mechanism and that the corresponding kinetic data can be fit to calculated data for the

pre-association mechanism.

The work of Parker suggests that the bimolecular reactions, which have been

long believed to follow the simple one-step mechanism, actually take place in more than

one step via a kinetically significant intermediate, “reactant complex,” on the reaction coordinate toward product formation. The reactant complex is formed without any covalent bond changes and only involves changes in geometry and solvation around the reactive sites. This mechanism was defined as the kinetically significant pre-association mechanism (KSPAM), in order to differentiate it from the pre-association mechanism15 based upon encounter complexes. The latter mechanism was thoroughly discussed by

Jencks16 in the 1980s.

Methodology for Distinguishing Simple and Complex Mechanisms

For a complex reaction (assuming 1/1 stoichiometry between reactant and product) at steady state, the decay in reactant concentration is equal to the rise in product concentration (-d[R]/dt = d[P]/dt) at all times, while the decay in reactant concentration

leads the rise in product concentration (-d[R]/dt > d[P]/dt) under non-steady-state

conditions, in particular during the pre-steady-state period. These relationships suggest a

number of mechanism probes to distinguish between the simple mechanism and the

complex mechanism under non-steady-state conditions (Table 1-1).

TABLE 1-1. Mechanism Probes (1) Extent of reaction – time profiles (2) Rate constant ratios – kinit/kpro (3) Time ratios – t0.50/t0.05 (times to reach 50 and 5% completion) (4) Extent of reaction-dependent deuterium KIE (5) Wavelength-dependent kinetic response (6) Instantaneous rate constant – time profiles

Practical Aspects of the Mechanism Analysis

In 1974, Bunnett17 expressed the general belief that rate constants obtained by

spectrophotometric methods are reliable to about ±5 %. Such a precision of kinetic

measurements does not allow the differentiation of the (sometimes) small deviations in

the kinetic response exhibited by complex and simple mechanisms. Another important

factor relating to the precision in kinetic measurements is the number of replicate

experiments (N) that are carried out. The standard deviation of the mean (Xbest) is defined

18 in eq 1.3, where Xmean is the mean value and σ is the standard deviation. Obviously, the reliability of kinetic measurements can be greatly increased by carrying out a sufficiently large number of replicate experiments.

0.5 Xbest = Xmean ± σ/N (1.3)

The necessity of gathering large quantities of kinetic data in order to take

advantage of this fact is readily accommodated when using modern stopped-flow

spectrophotometry as the measurement technique. Parker19 found that the precision in

rate constant measurements of first-order reactions can be of the order of 0.5 % using that

method. It indicates that when the numerical probes values differ from those expected for

the simple mechanism by as much as 5 %, the observed deviations are significantly large

to confirm that the data are inconsistent with the simple mechanism. 8

Extent of Reaction – Time Profiles19

The most common method used to evaluate absorbance – time profiles is to fit

the experimental data to an exponential function in order to evaluate the resulting rate

constant. However, this conventional method has the very serious drawback that small

deviations from first-order kinetics are masked and can go unnoticed. This situation is

clearly illustrated by the two different graphical treatments of the same data shown in

Figure 1-2. The kinetic data are for the Diels–Alder reaction between anthracene (ANTH)

and tetracyanoethylene (TCNE) in acetonitrile,11 which follows the complex mechanism.

-8.5 0.0 a b -8.6 Complex Mechanism Data 0.1 Complex Mechanism Data -8.7 0.2 -8.8

-8.9 0.3 ln[Reactant] -9.0 0.4

-9.1 Simple Mechanism Line ExtentReaction of Simple Mechanism Line -9.2 0.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 time/s time/s

FIGURE 1-2. (a) Theoretical ln[Reactant] – time and (b) extent of reaction – time profiles for Diels–Alder reaction between ANTH and TCNE in acetonitrile, [Reactant]0 = -1 -1 -1 0.2 mM, kf’ = 0.874 s , kb = 14.8 s and kp = 12.4 s

In Figure 1-2a, the complex mechanism data points seem to fit well to the

conventional first-order plot, however, in the theoretical analysis, at short times there

really is a slight deviation, which would be buried in noise and go undetected. Figure

1-2b is for the same theoretical data plotted as an extent of the reaction – time profile.

The simple mechanism line is normalized to the theoretical data (solid circles) at extent 9 of reaction equal to 0.05. The deviation of the simple mechanism line from the data points is obvious and can only lead to the conclusion that the data are inconsistent with the simple mechanism.

19 Numerical Mechanism Probes (kinit/kpfo and t0.5/t0.05)

For the simple one-step mechanism, the rate constant ratio, kinit/kpfo (the ratio of

pseudo-first-order rate constants measured in the extent of reaction ranges from 0 to 0.05 and 0.05 to 0.50, respectively), and time ratio, t0.50/t0.05 (the half-life divided by the time

necessary to reach the extent of reaction equal to 0.05) are equal to 1 and 13.5,

respectively. But for the complex mechanism, these values are dependent upon whether reactant or product is monitored (Table 1-2).

TABLE 1-2. Mechanism Probe Values Reversible Consecutive Mechanism Simple Mechanism Monitor reactant Monitor product t0.50/t0.05 = 13.5 t0.50/t0.05 ≥ 13.5 t0.50/t0.05 ≤ 13.5 kinit/kpfo = 1.00 kinit/kpfo ≥ 1.00 kinit/kpfo ≤ 1.00

Extent of Reaction-Dependent Deuterium KIE19

Consider a reaction involving hydrogen atom, hydride or proton transfer, which

follows a complex mechanism in which the H transfer only takes place in the product formation step.

Because of the fact that the intermediate in the complex mechanism partitions 10 between return to reactants and irreversible product formation, the apparent deuterium kinetic isotope effect, KIEapp, is extent of reaction dependent during the pre-steady-state time period and can be considerably smaller than the real value, KIEreal, which is equal to

H D kp /kp . This has the important consequence that possible hydrogen atom, hydride or proton tunneling may be masked when evaluating KIEapp. Of course, the simple mechanism predicts that the KIE will be independent of extent of reaction at all times.

Wavelength-Dependent Kinetic Response19

For reactions following the simple mechanism, the kinetic response is expected

to be independent on whether reactant or product is monitored and on the wavelength

(that is appropriate for monitoring either reactant decay or product evolution) at which

measurements are made. It is obvious from the mechanism probe values shown in Table

1-2 that this is not the case for reactions following the complex mechanism. The

observation that mechanism probe values are dependent upon the wavelength at which

measurements are made is convincing evidence that the kinetics of the reaction are

inconsistent with the simple mechanism.

Instantaneous Rate Constant – Time Profiles12

Instantaneous rate constant analysis provides more detailed data to distinguish

between the two mechanisms. For the simple one-step mechanism, the instantaneous rate

constant – time profiles (Figure 1-3a) are straight lines with zero slopes no matter

whether reactant decay or product evolution is monitored. For the reactions following

complex mechanism, two particular curves are obtained, depending upon whether

reactant decay or product evolution is monitored. In Figure 1-3b, the upper profile is for 11 reactant decay and the lower one is for product evolution. The zero-time intercept for the reactant profile is equal to kf, and it is equal to 0 for the product profile, since there is no

intermediate presence at zero time. During the pre-steady-state time period, the

instantaneous rate constants vary continuously until the steady state is reached. Under

steady-state conditions, the profiles for both the simple mechanism and the complex

mechanism are straight lines with zero slopes, so the two mechanisms become kinetically

indistinguishable.

1.0 a 0.8 -1 -1

/ s 0.6 k1 = 0.50 s inst k 0.4

kreactant = kproduct = k1 0.2

0.0 0.0 0.2 0.4 0.6 0.8 1.0 time/s 1.0

-1 b kf' = 1 s 0.8 kreactant -1 -1 kb = kp = 10 s

/ s 0.6 k inst s.s. k 0.4

0.2 kproduct

0.0 0.0 0.2 0.4 0.6 0.8 1.0 time/s

FIGURE 1-3. Instantaneous rate constant – time profiles for (a) simple one-step irreversible mechanism and (b) two-step reversible consecutive mechanism 12

1.3

Previous Work on the Proton Transfer Reactions of Nitroalkanes

Recently, the remarkable synthetic importance of nitroalkanes has been receiving more and more attentions from both synthetic chemists and pharmaceutical industry. The usefulness of nitroalkanes in organic synthesis lies in their easy availability and transformation into a variety of diverse functionalities20 (Figure 1-4). Nitroalkanes,

specifically nitromethane, nitroethane, 1-nitopropane and 2-nitropropane, are often treated as extremely versatile and inexpensive synthetic feedstocks, which offer the pharmaceutical industry a strategic tool21 for success in cost reduction.

FIGURE 1-4. Reactions of nitroalkanes

Proton transfer reactions have received considerable attention, since they are

undeniably among the most elementary and significant processes in both chemistry22-29 and biochemistry.22 These reactions are the central model for the development of the

Brønsted-Lowry acid-base theory,30 the Brønsted relationship,26 the Hammett equation,31 the Hammond postulate,32 and the Principle of Non-perfect Synchronization, which have 13 been proven to be the guiding theories of current physical organic chemistry and are widely applied in research.

The kinetic study of proton transfer reactions of nitroalkanes can be traced back to the 1930s.33,34 With the development of linear free energy relationships, the study of the proton transfer reactions of nitroalkanes became an active area for physical organic chemical research,35-67 especially in regard to what is known as the “nitroalkane anomaly”.47

Acidities of Nitroalkanes

Nitroalkanes possess moderate acidity properties, for example, their pKa values in H2O are 7 – 10 for aliphatic and 6 – 9 for aromatic substituted substrates, which are

found to be much lower than most other carbon acids. As seen in Figure 1-5,33 a nitro group is greater than ten orders of magnitude more effective than a single carbonyl or cyano group, and 10 – 1000 times more effective than two cyano or ester groups in stabilizing a carbanion.

25 24.5 O

2 25

H 20

20 13.3 a 15 11.2 K

acids 10.2

p 8.6 10 7.7

carbon 5

of 0

FIGURE 1-5. Acidities of some carbon acids 14

The unique feature of nitroalkanes in acidity provides two significant advantages for detailed kinetic analysis of nitroalkane proton transfer. First, nitroalkanes can react with a number of common bases with high equilibrium constants, a fact which eliminates complications due to the reverse reaction. Second, the anionic products are stable and readily monitored by spectrophotometry.

As shown in Scheme 1-3, the ionization of a nitroalkane will not produce the stable corresponding carbanion. Due to the inductive and resonance effect of the neighboring nitro group, the negative charge will delocalize to the nitro group, until a nitronate anion is formed which is accompanied by a hybridization transformation from sp3 to sp2.

SCHEME 1-3. Deprotonation of Nitroalkanes

It is well known that methyl is classified as an electron-donating group, and

exhibits acid-weakening behavior when it is introduced into molecules at sites in

proximity to the acidic center. However, methyl substitution at the α position of aliphatic

nitroalkanes has quite the opposite effect. For example, in the simple series consisting of

nitromethane (pKa = 10.22 in H2O), nitroethane (pKa = 8.60 in H2O) and 2-nitropropane

(pKa = 7.74 in H2O), a marked increase in acidity accompanies successive methyl

substitution. This unusual behavior was generally attributed to hyperconjugative

stabilization48 of the C=N double bond in nitronate ions (Scheme 1-4). This effect might 15 be important here because the nitrogen is positively charged resulting in the electron deficient characters.68

SCHEME 1-4. Hyperconjugation Effect on Ethyl Nitronate Anion

The hyperconjugative effect on the nitroalkane ionization presents a strong

dependence on solvent. As shown in Table 1-3, the pKa values of the three simple

nitroalkanes distribute over a range of about 2.5 pKa units in protic solvents (H2O and

aqueous MeOH), which is quite wider than that (~ 0.5 units) in DMSO. It indicates that

the hydrogen bonding effect in protic solvents could stabilize the charges dispersed on the

alkyl groups attaching to C=N bond in nitronate anions.

TABLE 1-3. pKa Values of Three Simple Aliphatic Nitroalkanes Solvent CH3NO2 CH3CH2NO2 (CH3)2CHNO2 a a b H2O 10.22 8.60 7.74 c H2O-MeOH (50/50 vol %) 11.11 9.63 8.85 DMSO 17.20d 16.72d 16.89e a Ref. 33. b Ref. 34. c Ref. 41. d Ref. 35, 40. e Ref. 36, 42.

Introducing a methyl group will decrease acidity through the inductive effect and

raise acidity by hyperconjugative stabilization of the nitronate ion. The latter effect predominates in the series of nitromethane, nitroethane and 2-nitropropane, but this is not always true. Table 1-4 shows that the methyl groups successively introduced on β

position have a normal acid-weakening effect, which indicates that the inductive effect is

predominant in this series. 16

TABLE 1-4. pKa Values of β-Methyl Substituted Nitroethanes CH3CH2NO2 CH3CH2CH2NO2 (CH3)2CHCH2NO2 (CH3)3CCH2NO2

H2O-MeOH 9.63 9.99 10.38 11.40 (50/50 vol %)a DMSOb 16.72 17.01 17.10 18.13 a Ref. 41. b Ref. 40.

The Nitroalkane Anomaly

The nitroalkane anomaly47 denotes the anomalous relationship between rates and

equilibria for the proton transfer reactions of nitroalkanes, which is accompanied by the

Brønsted exponent, α, falling outside the normal range from zero to unity. This

phenomenon has perplexed physical organic chemists ever since its birth more than a

half-century ago and a number of papers have been published on this topic.

A General Introduction to the Brønsted Relationship

The Brønsted relationship26 is considered to be the earliest linear free energy

relationship, that it antedates the Hammett equation31 by more than ten years. The

Brønsted equation (eq 1.4, 1.5) has been applied most often to general acid-base catalysis,

where there is a linear log-log relationship between the rate constants and the

appropriate equilibrium constants of acids or bases. In eq 1.4 and 1.5, α and β are called

Brønsted exponents. Each of them should lie between the limits zero and one, the sum of

the exponents for a reaction and its reverse should be equal to unity.

Acid catalysis: lgka = αlgKHA + ca (1.4)

+ Base catalusis: lgkb = βlgKB + cb = -βlgKBH + cb’ (1.5) 17

In a proton transfer process, the Brønsted exponent is generally thought to be a measure of the position of the transition state along the reaction coordinate.27 The

exponent α is considered to be numerically equal to the fractional extent of transferred

proton in the transition state, which can be represented graphically in Figure 1-6. In curve

(1), the transition state appears at the midpoint of the diagram, which means that the

proton is half transferred in the transition state, and then α is equal to 0.5. In curve (2),

the transition state is closer to reactant; the extent of proton transfer is less than 0.5 and

the corresponding α is less than 0.5. In curve (3), the transition state is nearer to product

and α is larger than 0.5.

FIGURE 1-6. Relation of Brønsted exponent to transition state

In 1924, Brønsted and Pedersen26 pointed out that the linearity of the Brønsted

relation would only hold over a limited range, and logka would, in the general situation,

be a curved rather than a linear function of pKa. As the chosen acid is stronger and 18 stronger relative to the base, the reaction rate of the proton transfer will become faster and faster until eventually reaction occurs at every encounter between the acid and base molecules. Once this limit is reached, further increases in acid strength will have no effect on the rate, ka will then be constant and independent of KHA, and α will therefore be

equal to zero (Figure 1-7a). Forty years later, their prediction was strikingly confirmed by

Eigen’s kinetic study of the proton transfer reactions to ammonia from a series of oxygen

acids (Figure 1-7b).

(a) (b)

FIGURE 1-7. Brønsted plot curvature (a) predicted by Brønsted and Pedersen in 1924, and (b) confirmed by Eigen in 1964

Kresge29 suggested that the curved Brønsted relations should attribute to the

rapid proton transfer reactions (k > 107 s-1M-1), and the slow proton transfers would give

linear relationships. Since the second-order rate constants for most proton transfer reactions of nitroalkanes are of the order of 10-2 ~ 102 s-1M-1, Brønsted relations for

nitroalkanes proton transfer are dominated by linear relationships.

Although, Brønsted and Pedersen predicted the existence of the curved Brønsted

relations, they, as well as the other chemists had never expected that the Brønsted 19 exponent would less than zero nor greater than one before the discovery of the nitroalkane anomaly.

Discovery of the Nitroalkane Anomaly

The first example of the nitroalkane anomaly,69 observed more than a

half-century ago, is about the unusual inverse order of kinetic and thermodynamic

acidities of the simple aliphatic nitroalkanes, nitromethane, nitroethane and

2-nitropropane, during their reactions with hydroxide ion in water, which results in a

negative Brønsted exponent (α = -0.76). The data for this novel relationship is reproduced

in Table 1-5.

TABLE 1-5. Equilibrium and Rate Constants for the Proton Transfer Reactions of - Three Simple Nitroalkanes with OH in H2O CH3NO2 CH3CH2NO2 (CH3)2CHNO2 a a a,b pKa 10.22 8.60 7.74 -1 -1 c k2 (s M ) 27.6 5.19 0.316 a Ref. 33. bRef. 34. cRef. 69.

Another example of the nitroalkane anomaly was observed in a more extensive series of aryl nitroalkanes, which gave the Brønsted relationships with exponents greater

than one (Table 1-6). The first of these were found almost simultaneously by Shechter46 and Bordwell.37

Since the sum of α and β is normally equal to unity, according to the anomalous

α, the corresponding β values should also be greater than one or less than zero. In fact, up

to now, no anomalous β has been found in the proton transfer reactions of nitroalkanes.

All β values shown in Table 1-7 are normal and show only variations. 20

TABLE 1-6. The Anomalous Brønsted Relations (α > 1) in the Proton Transfer Reactions of Aryl Nitroalkanes Base Solvent Brønsted α a ArCH2NO2 NaOH H2O (298 K) 1.54 a 2,4-lutidine H2O (298 K) 1.30 a morpholine H2O (298 K) 1.29 - b HOCH2CH2S H2O (298 K) 1.30 PhCOOK MeOH (298 K)c 1.31 a ArCH(CH3)NO2 NaOH H2O (288 K) 1.14 d H2O (298 K) 1.15 H O-MeOH 1.37 (288 K) 2 (50/50 vol %) a 1.40 (298 K) H O-dioxane 2 1.17 (50/50 vol %) e H O-MeOH ArCH CH(CH )NO NaOH 2 1.61 (288 K) 2 3 2 (50/50 vol %) f a Ref. 38. b Ref. 57. c Ref. 65. d Ref. 50. e Ref. 46. f Ref. 37.

TABLE 1-7. Brønsted β Values for the Proton Transfer Reactions of Nitroalkanes Base Solvent Brønsted β ArCH(CH3)NO2 m-CH3O 0.56 m-CH 0.55 3 piperidine, H 0.55 piperazine and H O (298 K)a m-Cl 2 0.55 morpholine m-NO3 0.55 p-NO3 0.52 b amine bases H2O (303 K) 0.50 ~ 0.55 CH3CH2NO2 c pyridine bases H2O (303 K) 0.65 d PhCH2NO2 0.65 a Ref. 38. b Ref. 68. c Ref. 33.d Calculation datat. Belikov, V. M.; Korehemnays, Ts. B.; Faleev, N. G. Izv. Akad. Nauk SSSR, Ser. Khim. 1969, 1383; a variety of bases type was used.

Kresge47 was first to use the term of “the nitroalkane anomaly” to represent the

unusual properties and anomalous Brønsted relations observed in proton transfer

reactions of nitroalkanes. In the past half century, the Brønsted relationship has been

subject to a serious challenge, with regard to whether or not it is an appropriate measure

of the position of the transition state along the reaction coordinate of a proton transfer 21 process.

How the Nitroalkane Anomaly Has Been Rationalized

Kresge47 suggested that the unusual Brønsted exponents may be due to some

particular molecular interactions, which are absent from the initial or final states and are

only present in the transition state. For instance, in Scheme 1-5, the interaction between R

and the partly charged hydroxide ion only exists in the transition state. If this interaction

is significant in comparison of the other interactions that can affect the overall process of

the reaction, the Brønsted exponent may go out of the normal range from 0 to 1. He

believed that the Brønsted exponent cannot reflect the extent of proton transfer at the

transition state, regardless of whether the exponent is anomalous or normal.

SCHEME 1-5. The Transition State for the Proton Transfer Reactions Between Nitroalkanes and OH- Supposed by Kresge

Marcus50 has applied his theoretical equation,51 primarily derived for electron

transfer reactions, to explain the anomalous Brønsted exponents for proton transfer

reactions of nitroalkanes. He suggested that the substituent effect on the reorganization energy, λ0, is the crucial factor to determine the validity of the Brønsted relationship. If

the substitution effect makes a small or negligible contribution to λ0 (such is the case

when the base varied), the Brønsted exponent does indeed reflect the position of the

transition state along the reaction coordinate. If the structural reorganization is influenced

by the substituted group (such as in the case of variations in the structure of the 22 nitroalkane), λ0 for the reaction will vary significantly and the resulting Brønsted exponent will no longer reflects the position of the transition state. More detailed numerical analysis according to Marcus’s hypothesis referring to the nitroalkane anomaly can be found in Murdoch’s papers.52

Bernasconi54-60 has used the proton transfer reactions of arylnitromethanes as

prime examples in the development of his Principle of Non-perfect Synchronization

(PNS). He proposed that in the transition state the delocalization of the negative charge

into nitro group lags behind the proton transfer, and that this is able to enhance the

activation energy barrier and make the transition state more sensitive to substituent

effects than that observed in the product ion (α > 1).

FIGURE 1-8. Ideal (dash curve) and the proposed (solid curve) free energy vs. reaction coordinate profiles for the deprotonation of arylnitromethanes as viewed by Bernasconi

The reaction coordinate profiles shown in Figure 1-8, where the dashed curve is

the hypothetical ideal case in which charge delocalization develops synchronously with 23 proton transfer, and the upper solid curve is the situation where charge delocalization lags behind proton transfer according to Bernasconi’s proposal.

Bordwell37-44 regarded as a forerunner in the exploration of the nitroalkane anomaly, had led a group which was the first to carry out systematic thermodynamic and kinetic studies on the proton transfer reactions of organic acids including nitroalkanes in various solvents. Bordwell’s nitroalkane work was originally centered on how to rationalize the anomalous Brønsted relationships in the scope of the simple one-step mechanism. However, the result was always to let him attend to one experimental finding and loose the support of another for his mechanism. Finally, he assumed that the deprotonation of nitroalkanes might take place by a multi-step mechanism.39-43 According to Scheme 1-6, in the rate determining step, deprotonation results in a pyramidal intermediate, the nitro carbanion, followed by a rapid rehybridization to a planar nitronate ion. With this mechanism, the experimental Brønsted α calculated based on a one-step mechanism is insufficient to provide an accurate analysis of the multi-step mechanism.

However, Bordwell never presented any unambiguous experimental evidence to support his hypothesis of multi-step mechanism

SCHEME 1-6. The Multi-Step Mechanism for Proton Transfer Reactions of Nitroalkanes Supposed by Bordwell

Bordwell’s unconventional mechanism, especially the structure of the intermediate proposed, as anticipated suffered severe criticism from the physical organic chemistry community on this topic and was consequentially rejected. Bernasconi55 pointed out that hydrogen bonding to oxygen of the nitronate product by the conjugate acid of the base is more likely than the formation of an intermediate. This is also supported by Saunders’s 14C kinetic isotope effect study,65 which indicated that the

rehybridization at α-C has occurred in the transition state, it is strongly against the

proposed reaction intermediate.

The nitroalkane anomaly was always observed for the reactions of nitroalkanes

in protic solvents. It does not mean that all reactions in protic solvents will result in

anomalous Brønsted exponents, such as the examples in Table 1-8.38 However, the

preponderance of normal Brønsted exponents still seem meaningless for mechanistic

investigation in these cases where the simple mechanism has not been confirmed.

TABLE 1-8. Normal Brønsted α Values (0 ≤ α ≤ 1) for the Proton Transfer Reactions of 1-Arylnitroethanes with Various Nitrogen Bases in H2O at 298 K Base Brønsted α ArCH(CH3)NO2 piperidine 0.99 diethylamine 0.96 in H O (298 K) 2 morpholine 0.94 piperazine 0.91

Keeffe61 and Agmon53 suggested that observance of the nitroalkane anomaly is

confined to protic solvents, in which the acidity of nitroalkane was assumed to be

enhanced by hydrogen bonding stabilization of the nitronate anions. As a consequence of

this hypothesis, the use of an aprotic solvent is expected to accelerate the reaction and 25 likely to diminish the value of α. Later, the reactions of arylnitromethanes with PhCOO- were carried out in DMSO61 and acetonitrile,56 and no obvious anomalous Brønsted

behavior was observed.

With the development of computational chemistry, quantum calculation62-64 has

begun to supplement experimental measurements since the 1990s, and is playing a more and more important role in the discussion on the nitroalkane anomaly. The recent computational studies by Keeffe,62 Bernasconi63 and Yamataka64 led to the conclusions

that “the nitroalkane anomaly, well established in solution, does not exist in the gas

phase.” The strong specific intermolecular forces such as hydrogen bonding between

solvent and anions play an important role in the nitroalkane anomaly existence in

solution.

A new possibility has been raised, for example, whether or not the nitroalkane

anomaly exists even in protic solvents. Parker6 found that the proton transfer reaction

between 1-(p-nitrophenyl)-nitroethane (p-NPNE) and hydroxide ion in aqueous acetonitrile12 actually takes place by a reversible consecutive mechanism (Scheme 1-7), involving a kinetically significant intermediate.

SCHEME 1-7. Reversible Consecutive Mechanism for the Proton Transfer Reaction Between p-NPNE and OH- in Aqueous Acetonitrile Supposed by Parker

The latter work offered a chance to reopen the discussion and argument on the

origin of the nitroalkane anomaly by means of mechanistic analysis. In contrast to the 26 mechanism proposed by Bordwell, in this case the complex mechanism was proposed based on a series of reliable kinetic experiments, which were made possible by the availability of advanced technology to improve the accuracy kinetic measurements along with the development of more appropriate data analysis.

The Study of Deuterium Kinetic Isotope Effects

The proton transfer reaction is the fundamental model for the investigation of deuterium kinetic isotope effects (KIE) .69-72 These reactions are often subject to quantum

mechanical proton tunneling.73,74 Moreover, the magnitude of the KIE is frequently used

to imply the structure of the transition state. As the typical carbon acids, nitroalkane

proton transfer kinetic isotope effects have been extensively studied in the past half

century by many chemists, exemplified by the studies of Bell,69,72,73 Bordwell,39

74-84 85-96 87-92,94,95 48,97 Caldin, Jarczewski, Leffek, and Kresge.

Solvent Dependent KIE

Caldin and Mateo76,77 reported a series of very large kinetic isotope effects

H D (k /k > 30) obtained during the study of the reaction between 4-nitrophenylnitromethane

(p-NPNM), and a strong organic base with an exchangeable N-H (tetramethylguanidine

(TMG)) in low polarity solvents such as toluene and chlorobenzene.

TABLE 1-9. KIE Values for the Proton Transfer Reaction Between p-NPNM and TMG in Aprotic Solvents Cl Solvent (n-Bu) O CH Cl CH CN 2 O 2 2 3 kH/kD (298 K) 32.6 31 41.3 45 50 12.7 11.4 11.8 N ET 0.046 0.068 0.071 0.099 0.188 0.207 0.309 0.460

Later, the controversy98-107 on the reliability of this large KIE resulted in continuous stream publications. Rogne98 found that the results reported for the D-reaction were

unreliable due to the H-D exchange between TMG and p-NPNM-d2 and that the KIE

value was lowered to about 11 when the base was changed to (Me2N)2C=ND.

Kresge studied the tritium kinetic isotope effects (kH/kT) of the reactions between

p-NPNM with amine bases and estimated the values of kH/kD by Swain-Schaad relationship108 (eq 1.6). In Table 1-10, the KIE value for the reaction between p-NPNM

and TMG is adjusted to 14.2.

H T H D 1.442 k /k = (k /k ) (1.6)

TABLE 1-10. KIE Values for Reactions Between p-NPNM and Amine Bases in Toluene Base kH/kD (lit.) kH/kT (kH/kT)1/1.442 TMG 45 a 45.8 14.2 quinuclidine 15.6 b 17.2 7.2 tri-n-butylamine 14 b 31.7 11.0 pentamethylguanidine 13.7 e 44.1 13.8 DBU 13 d 54.5 16.0 diethyl-n-butylamine 11.7 c 27.1 9.84 triethylamine 11.0 b 24.3 9.14 diethyl-n-nonylamine 8.0 c 11.4 5.39 a Ref. 77. b Ref. 78. c Ref. 79. d Ref. 80. e Ref. 99.

However the suspicion on the large KIE still exists, it is clear that the magnitude

of the KIE presents a strong dependence on the solvent polarity. Caldin and Mateo77,78

deduced that the difference between the isotope effects in low polarity and polar solvents

could be attributed to the coupling of the proton transfer with the motions of the more polar solvent molecules, which could raise the effective mass of transferred proton and reduce the mass ratio of mH/mD. As a result, the contribution of tunneling to the overall 28 process is less109 in polar solvents and yields a small or moderate isotopic rate ratio. This

coupling effect was not believed to be appreciable in solvents of low polarity, such as

toluene.

Tunneling Effect

Bell73 suggested the following values of parameters to be characteristic of

processes involving significant proton tunneling: (a) the values of the deuterium kinetic

isotope effect at around room temperature is greater than 10, (kH/kD >10); (b) the isotopic

D H difference in Arrhenius activation energies is greater than 1.41 kcal/mol, (Ea – Ea >

1.41 kcal/mol); (c) the ratio of the pre-exponential factors is greater than unity, (AD/AH >

1). These criteria have been extensively used over the past 40 years. A number of proton transfer reactions of nitroalkanes (Table 1-11) have been confirmed to follow Bell’s criteria and to involve proton tunneling.

TABLE 1-11. Proton Transfer Reactions of Nitroalkanes Involving Proton Tunneling H D D H k /k D H Ea – Ea Nitroalkanes Bases Solvents A /A Ref. 298 K (kcal/mol) CH3CH2NO2 2-t-Bu-pyridine EtOH-H2O 10.4 11 2.8 110 2,6-lutidine EtOH-H2O 10.1 14 2.9 110 (CH3)2CHNO2 2,4,6-collidine BuOH-H2O 24.8 7 3.0 111 - OH H2O 7.4 2.4 1.7 112 morpholine H2O 9.3 10 2.6 112 PhCH2NO2 imidazole H2O 11.5 2.1 1.8 112 2- HPO H2O 9.3 5.2 2.3 112 t-Bu3N toluene 14 2.2 2.0 76

Et3N toluene 11.0 2.4 2.0 76 cyclohexene 32.6 260 5.4 77 mesitylene 31 87 4.7 77 toluene 45 32 4.3 77 4-NO2PhCH2NO2 Bu O 41.3 32 4.2 77 TMG 2 PhCl 50 11 3.7 77 THF 12.7 1.6 1.8 77 CH2Cl2 11.4 1.2 1.9 77 CH3CN 11.8 1.0 1.5 77 29

Leffek and Jarczewski85,86 studied the kinetic effects for the proton transfer

reactions of three 1-(4-nitrophenyl)-1-nitroalkanes (p-NPNE, p-NPNP and p-NPMNP)

with DBU in acetonitrile, THF and chlorobenzene (Table 1-12). Consistent with Bell’s

criteria, significant proton tunneling effects were detected in most of the reactions, except for the reactions of p-NPNP and p-NPMNP in THF, in which the large kH/kD and small

D H D H Ea – Ea and A /A cannot provide clear evidence for tunneling.

TABLE 1-12. Isotope Effects and Arrhenius Parameters for Proton Transfer Reactions of 1-(4-Nitrophenyl)-1-nitroalkanes with DBU

H D D H D H R k /k (298 K) A /A Ea – Ea (kcal/mol) Me 12.5 1.43 1.67 CH3CN Et 12.4 1.67 1.77 i-Pr 12.8 1.67 1.82 Me 11.4 2.5 1.98 THF Et 12.4 0.56 1.15 i-Pr 9.9 0.56 1.00 Me 12.0 2.0 1.84 PhCl Et 11.6 2.0 1.84 i-Pr 9.5 2.0 1.72

Parker met the same problematic facts during the kinetic study on the reaction of p-NPNE and OH- in aqueous acetonitrile. As shown in Table 1-13, activation parameters

H D derived from the apparent rate constants (kapp , kapp ) are close to the semi-classical limits of Bell’s criteria and do not provide evidence for tunneling. On the other hand, Arrhenius

D H activation energy difference (Ea – Ea = 2.80 kcal/mol) and the ratio of pre-exponential

factors (AD/AH = 4.95), derived from the temperature dependence of the microscopic rate

H D constants (kp , kp ) for the proton/deuteron transfer step in the complex mechanisms, are 30 clearly in the range expected for significant proton tunneling. Thus it can be seen that an accurate reaction mechanism is crucial for the determination of tunneling effect.

TABLE 1-13. Isotope Effects and Arrhenius Parameters for Proton Transfer Reaction of 1-(4-Nitrophenyl)-1-nitroethane with OH- in Aqueous Acetonitrile

H D D H D H k /k (298 K) A /A Ea – Ea (kcal/mol) H D Derived by kapp , kapp 7.2 1.26 1.30 H D Derived by kp , kp 22.9 4.95 2.80

Relationship Between the KIE of Proton Transfer Reactions and the Acidity Difference of Reactants

Westheimer71 has presented theoretical arguments to show that, for a series of

related proton transfers, the kinetic isotope effect is expected to be a maximum value

when the transition state is symmetrical. Bell and Goodall69 have further suggested that

for a simple proton transfer, HA + B- → A- + HB, the most symmetrical transition state

should occur when HA and HB have equal acidities. Generally speaking, deuterium

kinetic isotope effects will reach a maximum value when the ΔpK (= pKHA – pKHB) is zero.

Longridge and Long113 have found an apparent maximum in base-catalyzed exchange of protonated aromatic hydrocarbons in acidic solution for a plot of kH/kD vs.

ΔpK. Kresge, et al49 have observed an apparently similar maximum for proton transfer to

C=C but have pointed out that the relationship breaks down when proton transfers to other types of substrates are included. 31

Figure 1-9 is the Bell-Goodall curve69 for a series of carbon acids deprotonations

by different bases (20 points in all). It is obvious that there is a maximum kinetic isotope

effect near ΔpK = 0, although the plot was not smooth, and the slope of ascending and

descending lines to the left and right of the maximum are small.

FIGURE 1-9. Relation between kinetic isotope effects and ΔpK of the reacting system

FIGURE 1-10. Variation of kH/kD with ΔpK for nitroalkanes proton transfer system

Among the 30 points in Figure 1-9, Bordwell39 only selected the points for nitroalkanes and replotted the data after the corrections for α-secondary isotope 32 effects,39,69 set equal to 1.15. In Figure 1-10, the scatter is sharply reduced. According to

the relationship between kH/kD and ΔpK, if the proton transfer from nitroalkanes to

hydroxide ion occurs in one step, the reaction would be highly exoenergetic (very

H D negative ΔpK). However, this is not consistent with the large k /k observed for

nitroalkane deprotonations. Therefore, Bordwell assumed this to be consistent with his

proposal that the proton transfer reactions of nitroalkanes with hydroxide ion might take

place by a multi-step mechanism, in which the step involving proton transfer should have

a small ΔGo.

Application of Solvent Kinetic Isotope Effects

H O D O Solvent kinetic isotope effects (k 2 /k 2 ) provide another experimental probe to evaluate the position of the transition state on the reaction coordinate using the magnitude of the Swain α value calculated by eq 1.7.114,115 Similar to the Brønsted exponent, the

Swain α will also lie between 0 and 1. Bordwell9 found that the Swain α values for proton

transfer reactions of nitroalkanes are in the neighborhood of 0.4 (Table 1-14), which

indicates that the reaction passes through a reactant-like transition state.

α DO- HO- (Kn) = k /k (1.7)

TABLE 1-14. Solvent Isotope Effects in the Deprotonations of Nitroalkanes by Lyate Ion in H2O and D2O temperature ΔpK kDO-/kHO- a Swain α b o CH3CH2NO2 5 C -7.1 1.39 0.44 b o (CH3)2CHNO2 5C -8.3 1.36 0.41 c o m-CH3PhCH(CH3)NO2 25 C -8.6 1.37 0.42 c o PhCH(CH3)NO2 25 C -8.7 1.42 0.47 c o m-ClPhCH(CH3)NO2 25 C -9.0 1.34 0.39 a b c Kn = 2.1. Ref. 33. Ref. 39.

It is obvious in eq 1.7 that the size of the Swain α strongly depends on the value

114 116 39,117 47,118 of Kn, various values of which have been used, such as 1.79, 2.0, 2.1, 2.4 and 2.47,119 however, none of them have been generally accepted. This is perhaps the

main disadvantage that retards the progress of the research on solvent kinetic isotope

effects.

1.4

Previous Work on the Nucleophilic Aromatic Substitution of Trinitroarenes

Introduction

Reactions of trinitroarenes with bases have long been known for the formation of highly colored solutions,120 and solid products can sometimes be isolated.121,122 Mayer123 assumed that the colored species were formed by removal a proton from the aromatic ring.

Hantzsch and Kissel122 suggested that the color is a result of the addition of the base at a

nitro group. Jackson and Gazzolo124 thought that the colors produced from alkyl picrates

and alkoxides could be best described by the quinonoidal structure 1.

In 1902, Meisenheimer125 isolated identical compounds by the addition of MeO- to 2,4,6-trinitrophenetole and EtO- to 2,4,6-trinitroanisole; in each case the adduct

decomposed to give the same mixture of trinitroanisole and trinitrophenetole, which

indicated that the alkoxides were added at C1 to produce 1 (R = Me, R’ = Et), instead of 34

C3 to give 2. Similar confirmatory measurements were reported by Jackson and Earle126 who prepared 1 (R = Et, R’ = isoamyl) from the two parent ethers.

In 1950s, Meisenheimer’s assumption was largely confirmed by spectroscopic and crystallographic methods. The current representation of quinonoidal structure 1 would be 3, in which the negative charge delocalizes throughout the ring and in the nitro groups. Compounds of similar types as 3 are now commonly referred to as Meisenheimer complexes. Reactions of electron-deficient aromatic compounds with nucleophiles have come to be known as “nucleophilic aromatic substitution (SNAr),” which has become an important class of fundamental organic reactions127-129 and has received considerable

attention from a great many research groups, such as those of Caldin,130-132 Foster,133-141

Fyfe,138-143 Gold,144-152 Crampton,150-160 Fendler,161-166 Bernasconi,167-172 Servis,173,174

Norris,175-179 and Buncel.180-185 Reactions of trinitroarenes, exemplified by

1,3,5-trinitrobenzene (TNB) and 1,3,5-trinitroanisole (TNA), with both anionic and

neutral nucleophiles have been studied extensively.

Reactions of TNB

Solutions of TNB in methanol containing MeO- are orange-colored. Foster134 suggested that the colored product (4) had a structure analogous to the Meisenheimer complex. Norris175 also believed Meisenheimer complex 5 was formed during the

reaction between TNB and CN- in non-aqueous solutions. The above two predictions

were strongly supported by NMR measurements.153,176 In the 1H NMR spectra, the 4,6-H

atoms are equivalent and give only a single resonance.

In polar solvents, the reactions between TNB and aliphatic amines186 involve 35 two steps,159 an initial loose attachment of an amine to give a species such as 6, probably by passing through a π-complex,136f followed by a proton transfer to a second amine to

form the ion-pair 7.

TNB can also react with carbanions generated from ketones. The reaction of

TNB with acetone or acetophenone in the presence of alkali187 gives dark crystalline

needles 8, which can be oxidized to corresponding picryl ketone 9 by H2O2 under acid

conditions. Foster and Fyfe139 had found the 1H NMR signals for 8 when they studied the

reaction between TNB and MeO- in ketone.

In fact, the SNAr reactions referring to TNB are not always as simple as to form

a Meisenheimer complex. The reaction of TNB and MeO- is able to go further, after the

Meisenhiemer complex is formed, to eventually produce 3,5-dinitroanisole via an

intermediate (or transition state) of 10.146

During their 1H NMR determination in DMSO, Foster and Fyfe139 actually found

the specific characteristic signals for di-adduct 11. A comparative NMR study with EtS- and PhS- ions indicated the formation of adducts analogous to 11. Gold and Rochester’s

study145 of the reaction between TNB and OH- in water indicated the presence of at least 36 two reversible equilibrium steps. The first involving a 1:1 reaction was thought to give the Meisenheimer complex and the second one is likely that which results in the di-adduct.

2- In aqueous solutions, TNB is able react with SO3 with a stoichiometry of 1:1 or

2- 1:2, depending on the concentration of SO3 . At low concentration, a 1:1 Meisenheimer

2- complex is formed, while the di-adduct is favored for the higher concentrations of SO3 .

TABLE 1-15. Thermodynamic and Kinetic Parameters for the SNAr Reactions of a TNB with Lyate Ions in H2O, MeOH and EtOH

-1 -1 b h k1 (M S ) 37.5 7050 33400, 27500 -1 b k-1 (S ) 9.8 305 27.5 -1 b c,d c h j i K = k1/k-1 (M ) 3.73 , 2.7 23.1, 15.4 1210, 2400 , 1600 , 2070 e f g pKa 13.43, 14.40 , 13.19 15.58, 15.71 15.82 ≠ -1 h ΔH1 (kcal mo1 ) 15.6 ± 0.8 10.2 ± 0.8 8.7 ± 1.0, 11.7 ± 0.1 ≠ h ΔS1 (eu) 1.1 ± 2.7 - 6.7 ± 2.7 - 8.6 ± 3.4, 2.2 ± 0.6 ≠ -1 h ΔH-1 (kcal mo1 ) 7.3 ± 0.8 9.2 ± 0.8 10.4 ± 1.2, 11.4 ± 0.2 ≠ h ΔS-1 (eu) - 29.4 ± 2.7 - 16.3 ± 2.7 - 16.9 ± 4.0, -14.3 ± 0.6 ΔH (kcal mo1-1) 8.3 ± 1.6 1.0 ± 1.6 - 1.4 ± 2.2, 0.3 ± 0.3h ΔS (eu) 30.5 ± 5.4 9.5 ± 5.4 8.3 ± 7.4, 16.5 ± 1.5h a Ref. 169. b Ref. 168. c Ref. 148. d Ref. 188. e Ref. 190. f Ref. 191. g Ref. 192. h Ref. 130. i Ref. 128. j Ref. 189.

The thermodynamic study of the reactions of TNB began in the 1960’s. The

equilibrium constants for the reactions with OH-,148,188 MeO- 145 and EtO- 128,130,189 were

reported more early than the corresponding rate constants, since the SNAr reactions of

TNB often take place rapidly. Caldin130 had studied the kinetics of the reaction of TNB

with EtO- at low temperatures. However, he mistook the Meisenheimer complex to be a

charge transfer (CT) complex. In 1970, Bernasconi169 was first to apply stopped-flow 37 spectrophotometry to the kinetic study of the SNAr reactions of TNB in H2O, MeOH and

EtOH at room temperature. The related thermodynamic and kinetic parameters are

summarized in Table 1-15.

Reactions of TNA

125 135 Since Meisenheimer's classical work on the SNAr reactions of TNA, IR and

visible133 spectroscopic techniques have been employed to confirm the basic formulation

of the reactions. The 1H NMR spectrum150 for reaction between TNA and MeO- shows two singlet bands attributed respectively to the ring and methoxyl protons, which convincingly demonstrates that the structure of the adducts is indeed 12. Other evidence to support this structure came from the crystal structure determinations193,194 of the complex derived from TNA and MeO-, which shows that the two methyl groups are indeed identical in the complex and that the plane defined by their oxygen atoms and C1 is orthogonal to the ring. The C6-C1-C2 bond angle is 109°, very close to the tetrahedral

angle required for an sp3-hybridized carbon.

In 1956, Caldin131 observed two color-producing steps in the reaction between

TNA and EtO- in EtOH at low temperature. The slow reaction produced the

Meisenheimer complex with a similar structure to 12; Caldin suggested that the product

for the fast reaction was a CT complex. However, in the NMR experiments in DMSO,

Servis173 found that the reaction of TNA and MeO- initially formed a C3 adduct 13 38

(1,3-complex) rapidly, which gradually changed to C1 adduct 12 (1,1-complex) as the reaction went to completion. Latter, Crampton and Gold152 found the 1H NMR signal for

13 in EtOH-DMSO (30/70 vol. %). Many visible spectra of 1,3-complexes have been

collected by Terrier.195

Crampton and Gold152 suggested that the conversion of 1,3-complex to

1,1-complex could be catalyzed by MeO- or MeOH, and an inter-conversion was more

likely than an intramolecular transfer of methoxide ion. If excess MeO- was added during

the NMR measurement, Foster and Fyfe,139,141 as well as Servis,174 observed some new

signals, which were attributed to the dianionic adduct 14 (1,1,3-complex).

FIGURE 1-11. Energy vs. reaction coordinate profiles for reaction of TNA with MeO-

The characteristic behavior such as rapid formation of the 1,3-complex and the final product 1,1-complex, led to the assumption of the competitive mechanism for the SNAr

reactions of TNA with alkoxides illustrated in Figure 1-11, where 1,3-complex and

1,1-complex are known respectively as the kinetically and thermodynamically controlled 39 products. The corresponding kinetic and equilibrium data are summarized in Table 1-16.

TABLE 1-16. Kinetic and Thermodynamic Data for the Reaction of TNA with MeO- in MeOH

-1 -1 a b k1 (M S ) 950 17.3 -1 a b k-1 (S ) 350 0.00103 -1 a b K = k1/k-1 (M ) 2.71 17000 ≠ -1 a b ΔH1 (kcal mo1 ) 10.4 ± 1.0 12.9 ± 1.0 ≠ a b ΔS1 (eu) - 10.8 ± 3.4 - 9.4 ± 3.4 ≠ -1 a b ΔH-1 (kcal mo1 ) 8.2 ± 0.5 18.4 ± 1.0 ≠ a b ΔS-1 (eu) - 19.3 ± 1.7 - 4.8 ± 3.4 ΔH (kcal mo1-1) 2.2 ± 1.5 a - 5.5 ± 2.0 b ΔS (eu) 8.5 ± 5.1 a - 4.6 ± 4.0 c a Ref 170. b Ref 163. c Ref 166.

At temperatures below -10° in aprotic solvents, azide ions react with TNA to

196 174 give a 1,1-complex. Similarly, Servis found the NMR evidence that Et2NH was added at C1 of TNA in DMSO to form a zwitterion 15. However, addition of Et3N to

TNA in acetone is reported to result in an acetonate adduct at C3 (16).140

158 2- Crampton found that reaction of TNA with SO3 resulted only in the

formation of 1,3-complex 17 in aqueous DMSO, accompanied by the formation of the

additional di-adduct 1,3,5-complex 18 in water. For other 1-X-2,4,6-trinitroarenes (X =

- 2- NH2, NHMe, SO3 ), their reactions with SO3 were also observed to only give 40

1,3-complexes.158,197 The reaction between TNA and CN- in isopropanol was observed to

occur in the same way.178

It is known that the negative charge in PhO- is distributed throughout the ring,

and consequently, it would react with TNA in two ways (O-attack and C-attack) resulting

in two 1,1-complexes (19, 21) and the 1,3-complexes (20, 22). Actually, only 19 and 22

were observed in Buncel’s NMR measurements.182 If the nucleophile was replaced by

2,4,6-trimethylphenoxide (mesitoxide, MesO-), only O-attack was observed to be

effective and produce unstable 1,1-complex and stable 1,3-complex.183

OMe OMe MeO OPh MeO O N NO O2N NO2 O2N NO2 O2N NO2 2 2 H H H H H H H H OPh NO NO2 NO2 NO2 2 (19) (20) (21) (22) OH

Regioselectivity in SNAr Reactions of Trinitroarenes

The SNAr reactions of 1-X-2,4,6-trinitroarenes always show a strong regioselectivity, inasmuch as both C1 and C3 attacks are possible to be attacked by different nucleophiles. In some cases, only one carbon is selected as the target of nucleophilic attack. Alternatively, both 1,1- and 1,3-complexes would be formed and classified to thermodynamic and kinetic control Meisenheimer complexes. Besides the X group and nucleophiles, the other reaction variables such as solvents and temperature were found to have an impact on the regioselectivity.

180-183 Buncel classified the SNAr reactions of 1-X-2,4,6-trinitroarenes as K1T1,

K3T3, K1T3 and K3T1, where K and T respectively represent kinetic and 41 thermodynamic control, numbers of 1 and 3 indicate the position where nucleophilic attack takes place. For example, K3T1 means kinetic control by attack at the C3 position and thermodynamic control by attack at the C1 position. In the reactions of KIT1, the

1,3-complex may be too unstable to be observed. The classical reaction of TNA and

MeO- should belong to K3T1 pattern. The qualitative free energy profiles corresponding

to the four patterns of regioselectivity are shown in Figure 1-12. Some SNAr reactions of

trinitroarenes are classified in Table 1-17 according to Buncel’s method.

FIGURE 1-12. Qualitative free energy profiles detailing the different patterns of regioselectivity: K3T1, K1T1, K3T3 and K1T3

TABLE 1-17 Buncel’s Classification of SNAr Reactions of 1-X-2,4,6-Trinitroarenes X Nucleophile 1,3-complex 1,1-complex MeO MeO- K T MeO OH- K T MeO HNE2 K/T MeO CN- K/T MeO PhO- (O-attack) K/T MeO PhO- (C-attack) K/T MeO MesO- T K 2- MeO SO3 K/T 2- NH2 SO3 K/T 2- NHMe SO3 K/T 2- 2- SO3 SO3 K/T CHO CN- K/T Me CN- K/T Ph MeO- K T Ph PhO- (C-attack) K/T 42

Reaction of Other Trinitroarenes

2,4,6-Trinitroanilines

In addition to formation of 1,1- and 1,3- Meisenheimer complexes 24 and 25,

reactions of 2,4,6-trinitroanilines with bases may also involve a proton transfer from the

amino group and produce Brønsted bases 23.

Gold and Rochester147,148 have recorded the visible spectra for both 23 and 25

formed in the reactions of trinitroaniline and MeO-. These results were later confirmed by

Crampton and Gold’s NMR measurements,153 in which they also found the formation of

di-adduct 26 and di-anion 27 in the solution containing excess MeO-. Additionally, it was

observed that the proportion of the conjugate bases 23, to the 1,3-complex 25, depends on the R groups of the amide, and increases in the series R = H, Me, Ph.152,154,173,174 The

latter is a consequence of the fact that the phenyl group is able to strengthen the acidity of

the adjacent amino proton.

Crampton158,159 suggested that the reactions of 2,4,6-trinitroanilines with EtS-

2- and SO3 only produce 1,3-complexes, not the conjugate bases, and that a di-adduct

- 1,3,5-complex could be formed in the presence of excess EtS . Therefore the SNAr

reactions of 2,4,6-trinitroanilines belong to K3T3. 43

Picric Acid

The addition of picric acid into concentrated NaOH solution results in an intense

absorption band at 390 nm, which was attributed to a 1,1- Meisenheimer complex 28 by

Abe.198 However, Gold and Rochester149 suggested that one more OH- ion was also

involved and the product should be di-adduct 29. The latter was confirmed by the NMR

160 measurements. In aqueous Na2SO3 solutions, the visible spectra indicate the presence

2- 160 of two SO3 species in addition to the picrate ion including di-adduct 30. This anion

would be unusual as carrying five negative charges. These studies indicate that the SNAr

reactions of picric acid also have the K3T3 regioselectivity.

2,4,6-Trinitrotoluene

It is well known that the strong or moderate bases, such as OH-, RO- and PhO-, would deprotonate the methyl group of 2,4,6-trinitrobenzene (TNT),75-81,130-132 rather than

attack the ring carbon atoms to initiate a nucleophilic substitution. Therefore, SNAr

reactions of TNT can only go with the nucleophiles of low basicity. The fist example179

2- 158 was found in the reaction of TNT with SO3 . Crampton suggested that this reaction

produces the 1,3-complex, as well as di-adduct 1,3,5-complex. Later, the 1H NMR

spectra for 1,3-complex formed in the reaction between TNT and CN- was observed by

176 Buncel. These results suggest that the SNAr reactions of TNT always process in K3T3

pattern. 44

1.5

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CHAPTER 2

THEORETICAL DIFFERENTIATION BETWEEN THE SINGLE-STEP

AND THE PRE-ASSOCIATION MECHANISMS

IN ORGANIC CHEMICAL REACTIONS

Abstract

It is pointed out that the mechanisms of a number of fundamental organic reactions which have long been believed to take place by a single-step mechanism have been challenged in favor of the kinetically significant pre-association mechanism. This development makes it necessary to determine the scope of the possible combinations of microscopic rate constants which allow for the differentiation of the two mechanisms.

In order to limit the number of combinations of microscopic rate constants necessary to calculate and still provide coverage over all of those which can be differentiated from the single step mechanism, it was necessary to devise a presentation of the data in terms of dimensionless parameters. This was readily accomplished by expressing the changes in concentration in terms of the extent of reaction (E.R.) and the time in terms of t/t0.50 where t0.50 is the half-life of the reaction. The range of dimensionless microscopic rate

constants over which calculations are necessary could then be assembled in a single table

(Table 2-1). The kinetic response was calculated over the entire applicable range of rate constants which were varied by a factor of 2 from one series to the next. The most pertinent finding of this study is that the two mechanisms can be differentiated effectively by the instantaneous rate constant procedure. Another important fact that emerged from the study is that the conventional method of establishing first-order (or pseudo-first-order) 59 kinetics, the correlation of ln(1 – E.R.) – time profiles, does in no applicable case differentiate between the single-step and the pre-association mechanism. The SN2 mechanism which has recently been suggested to follow the kinetically significant pre-association mechanism rather than the single-step mechanism was discussed in terms of the consequences of adopting this view of the mechanism.

Introduction

Hammett1 has recognized that the kinetic response to the reversible consecutive pseudo-first-order mechanism (Scheme 2-1), more commonly known as the pre-association mechanism, differs from that of the single-step irreversible pseudo-first- order mechanism. In the meantime, there has been a great deal of discussion of the pre-association mechanism and it has been invoked in numerous cases.2

SCHEME 2-1. Reversible Consecutive Mechanism

Hammett1 concluded that the deviations between the kinetic responses of the two mechanisms are small and could not be differentiated due to the low precision in kinetic measurements at that time. Since digital technology was not available at that time but has developed enormously since then, Hammett’s conclusions1 on this question are no longer

valid. Another important factor relating to precision in kinetic measurements is the

number of duplicate experiments (N) that are carried out. The standard deviation of the

0.5 mean (Xbest) is defined in equation of Xbest = Xmean ± σ/N , where Xmean is the mean value 60 and σ is the standard deviation.2 Obviously, the reliability of kinetic measurements can be greatly increased by carrying out a sufficiently large number of experiments. Modern stopped-flow spectrophotometers provide the ideal vehicle for accomplishing this goal.

The publication of Hammett’s monograph1 triggered an increase in activity in

the new science of physical organic chemistry. This was accompanied by the realization

of the usefulness of linear free energy relationships (LFER) in organic chemistry.3

Perhaps the best known LFER are represented by the Brønsted4 and the Hammett5 equations. The latter were developed in the first half of the twentieth century and have survived to this day.

Very many physical organic chemists were preoccupied with the study of LFER during the second half of the twentieth century.6 This preoccupation contributed to the

experimental philosophy that if kinetic data can be fit to an exponential, that this is

adequate evidence that the data obey first-order or pseudo-first-order kinetics and can be

discussed in terms of the single transition state model. Thus, the main use of digital

technology, which was developing rapidly during that time period, was to fit the digital data available from digital spectrophotometers to exponentials often using software provided by the instrument manufacturers. This phenomenon had another very general effect on the further development of the art of determining reaction mechanisms and to the general acceptance as fact that the fundamental reactions of organic chemistry are adequately described by the single transition state model.

Early in the present century the question as to the practicality of differentiating between the single-step and the pre-association mechanisms in homogenous solution was 61 addressed once again using modern instrumentation and digital methods.7-15 It was found

that kinetic data for a number of fundamental organic reactions including an SN2

11 10 8 reaction, an E2 elimination, a nitroalkane proton transfer, a hydride transfer reaction

between NADH models,12 as well as a Diels-Alder reaction,13 are inconsistent with the

single-step mechanism and were fit to calculated data for the pre-association mechanism.

More recently, an instantaneous rate constant (IRC) method was developed14 and it was

applied to acyl transfer from p-nitrophenyl acetate to hydroxide ion. The latter reaction

was previously believed to take place by a concerted single-step pathway.16 Kinetic data

for all of the reactions mentioned in this paragraph have been found to be consistent with

the pre-association mechanism. The reaction between 4,4’,4”-trimethoxytrityl ion and

acetate ion in acetic acid to give the acetate ester was observed to take place by a 3-step mechanism (Scheme 2-2) 15 The reaction takes place with pre-association as the first step.

But in this case the pre-association is very fast, and the intra-molecular collapse of the ion

pair is an activation process that takes place in two steps via a “reactant complex” on the reaction coordinate toward product formation.

SCHEME 2-2. The 3-Step Mechanism for Reaction Between 4,4’,4”-Trimethoxy- trityl Ion and Acetate Ion in Acetic Acid

It must be pointed out that since all bimolecular reactions in solution pass through encounter complexes,17 pre-association is involved in all such reactions. Jenks18 62 has thoroughly discussed the pre-association mechanism in that context. In order to be clear of the meaning of the mechanism in the context of this chapter we define the kinetically significant pre-association mechanism (KSPAM) as the mechanism where the formation, the dissociation and the further reaction of the association complex are all kinetically significant. Kinetic data for reactions which follow the KSPAM should not be used to make conclusions about the nature of a single transition state. Such data necessarily require analysis according to the consecutive transition state model.

The recent work7-15 suggests that KSPAM, involving a kinetically significant

intermediate, must be considered as a possibility for very many of the reactions which

were treated according to the single transition state model during the twentieth century.

The purpose of this chapter is to show the limitations of the experimental differentiation

between the two mechanisms. This was done primarily with calculated data to eliminate

the effects of experimental error upon our conclusions.

Calculations and Results

Calculations of concentration – time profiles

For a bimolecular reversible consecutive mechanism, pseudo-first-order

conditions were set up when [B]0 >> [A]0, and then kf’ = kf [B]0.

The calculation of concentration – time profiles for reactant (A), intermediate (I)

and product (P) were carried out using eq 2.1 to 2.3, respectively, where λ1 + λ2 = kf’ + kp

19 + kb, and λ1λ2 = kf’kp. The calculations were carried out with [A]0 equal to 1.0 with [I]0 63 and [P]0 equal to 0 on personal computers with processor speeds of 3.2 GHz. The [A] –

time profiles could be equated directly to (1 – E.R.) – time profiles when following decay

of reactant.

[]A []Akeke0 [('' )12tt ( ) ]  ff21 12 (2.1)

' []Ak0 f []Iee (12tt  )  12 (2.2)

  []PA [](121 e12tt  e ) 0   12 12 (2.3)

0.006 0.20 a (0.156, 0.00594) b 0.005 0.15 [A]0 = 0.2 mM [A] = 0.2 mM Reactant 0.004 0 M k ' = 0.874 s-1 -1 f m 0.10 kf' = 0.874 s / 0.003 -1 c /mM c k = 14.8 s -1 b kb = 14.8 s 0.002 -1 kp = 12.4 s 0.05 k = 12.4 s-1 Product p 0.001 Intermediate 0.00 0.000 0.0 0.5 1.0 1.5 2.0 0 5 10 15 20 time/s time/s

FIGURE 2-1. Calculated concentration – time profiles for (a) reactant and product, and (b) intermediate according to the reversible consecutive mechanism

An example is shown in Figure 2-1, which includes the calculated concentration

– time profiles for reactant, product and intermediate. It is noticeable that the curve due to intermediate rises from zero rapidly and gradually decreases towards zero after going through a maximum. The corresponding time is referred to as “steady-state time” (ts.s.), expressing the time required for the intermediate concentration to build up to a steady-state value. 64

Dimensionless Extent of Reaction – Time Profiles

Obviously there are an infinite number of combinations of microscopic rate

constants for the pre-association mechanism. The steady state treatment of the

mechanism results in eq 2.4 for the apparent rate constant (kapp). In order to show data for

a significant cross-section of the kinetic response for the KSPAM it is necessary to reduce

the number of calculations needed.

kapp = kf’kp/(kp + kb) (2.4)

In order to do this it is necessary to convert the kinetic response due to the mechanism to a dimensionless form. The integrated first-order (or pseudo-first-order) rate

equation expressed in terms of the extent of reaction (E.R.) is shown in eq 2.5. Since (1 –

E.R.) is dimensionless, it is only necessary to convert the X-axis in the (1 – E.R.) – time

profile to units of t/t0.50, where t0.50 is the half-life of the reaction, in order to have the

dimensionless form of the profile.

ln (1 – E.R.) = -kt (2.5)

Figure 2-2a includes three different (1 – E.R.) – time curves, in which kapp are

equal to 1 (kf’ = kp = kb = 2), to 10 (kf’ = kp = kb = 20) and to 100 (kf’ = kp = kb = 200),

respectively. Figure 2-2b illustrate the use of the dimensionless (1 – E.R.) – t/t0.50 profiles to represent the same parameters as used in the three different curves shown in Figure

2-2a. It is obvious that the three curves in Figure 2-2a are superimposed upon each other in Figure 2-2b. A direct comparison of the three profiles indicates that they are identical out to the sixth decimal. This confirms that transforming the X-axis to t/t0.50 suffices to make the profiles dimensionless and independent of kapp as long as the relative values of 65 the microscopic rate constants remain constant.

1.0 a 1.0 b -1 (1) kf' = kp = kb = 2 s 0.8 -1 0.8 (2) kf' = kp = kb = 20 s -1 (3) kf' = kp = kb = 200 s 1- E.R. 1 - E.R. 0.6 0.6

0.4 0.4 (3) (2) Reactant Decay (1) Reactant Decay 0.2 0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 time/s t / t0.50

FIGURE 2-2. (a) (1 – E.R.) – time, and (b) (1 – E.R.) – t/t0.50 profiles for kapp equal to 1 (kf’ = kp = kb = 2), to 10 (kf’ = kp = kb = 20), to 100 (kf’ = kp = kb = 200), respectively

The value of kf’ (eq 2.4) cannot be less than of kapp. Should this be the case, the

kinetic response is that of a simple mechanism with kapp equal to kf. We have previously

proposed that the kf’/kapp values over which it is experimentally feasible to resolve the

kinetics of the pre-association mechanism is with kf’/kapp ratios in the range from about

8 1.05 to about 100. This specifies the appropriate range of kf’ for the calculations, keeping

kapp equal to 1.00. The range of kp to be used in the calculations was found by trial and

error in calculations where kp was varied over a wide range while keeping kapp equal to 1 and kf’/kapp in the range mentioned above. During the calculations where kp were varied,

kb was varied to be consistent with eq 2.4.

The Range of Rate Constants in the Calculated Data

The data in Tables 2-1 and 2-2 give the scope of the relative rate constants for

KSPAM (Table 2-1) and a preliminary indication of the deviations of the kinetic response

(Table 2-2) between data from KSPAM (Scheme 2-1) and the single-step mechanisms. 66

It should be noted that all rate constants conform to the case where kapp (eq 2.4) is equal to unity. As illustrated by Figure 2-2, as long as the relative values of the microscopic rate constants in eq 2.4 remain the same, the (1 – E.R.) – time profiles only differ by the time scale on the X axis.

TABLE 2-1. Rate Constant Matrix for the KSPAM

kp/kb = 10 2 1 0.5 0.25 0.125 0.0625 0.03125 0.015625

kf’ = 1.1 1.5 2 3 4 8 16 32 64

kp kb kb kb kb kb kb kb kb kb 512 51.2 256 512 1024 1536 3584 7680 15872 32256 256 25.6 128 256 512 768 1792 3840 7936 16128 128 12.8 64 128 256 384 896 1920 3968 8064 64 6.4 32 64 128 192 448 960 1984 4032 32 3.2 16 32 64 96 224 480 992 2016 16 1.6 8 16 32 48 112 240 496 1008 8 0.8 4 8 16 24 56 120 248 504 4 0.4 2 4 8 12 28 60 124 252 2 0.2 1 2 4 6 14 30 62 126 1 0.1 0.5 1 2 3 7 15 31 63 0.5 0.05 0.25 0.5 1 1.5 3.5 7.5 15.5 31.5 0.25 0.025 0.125 0.25 0.5 0.75 1.75 3.75 7.75 15.75 0.125 0.0125 0.0625 0.125 0.25 0.375 0.875 1.875 3.875 7.875 0.0625 0.00625 0.03125 0.0625 0.125 0.1875 0.4375 0.9375 1.9375 3.9375 0.03125 0.003125 0.015625 0.03125 0.0625 0.09375 0.21875 0.46875 0.96875 1.96875

The significance of t0.50/t0.05 in Table 2-2 for mechanism analysis is that the ratio

is a constant equal to 13.5 when monitoring both reactant decay and product evolution for

the single-step mechanism while the corresponding values for the KSPAM are ≥ 13.5

when reactant decay is monitored and are ≤ 13.5 when product evolution is monitored.20

The time ratio matrix for monitoring product evolution is shown in Table A.1 (Appendix

A). The designation equal to or less than 13.5 for t0.50/t0.05 for reactant decay emphasizes a

very important point. This is that it is not possible to rule out the pre-association

mechanism on the basis of kinetic studies. On the other hand, as will become apparent 67 latter in this chapter, the single-step mechanism can be ruled out from kinetic studies in which the pre-steady-state time period is accessed.

TABLE 2-2. Time Ratio (t0.50/t0.05) Matrix for the KSPAM When Reactant Decay Is Monitored

kp/kb = 10 2 1 0.5 0.25 0.125 0.0625 0.03125 0.015625

kf’ = 1.1 1.5 2 3 4 8 16 32 64

kp t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 512 13.56 13.67 13.76 13.84 13.88 13.94 13.98 13.99 14.00 256 13.60 13.84 14.01 14.18 14.27 14.41 14.47 14.51 14.52 128 13.69 14.19 14.55 14.93 15.13 15.43 15.59 15.67 15.71 64 13.87 14.94 15.78 16.72 17.23 18.04 18.48 18.70 18.82 32 14.13 16.27 18.41 21.53 23.64 27.57 29.77 30.97 31.61 16 14.37 17.67 21.58 28.96 35.97 62.44 112.69 210.34 400.58 8 14.50 18.45 23.39 33.23 43.03 82.12 160.11 315.44 624.79 4 14.43 18.20 23.10 33.16 43.32 84.10 165.73 328.98 652.09 2 14.19 16.84 20.12 26.96 34.28 65.62 129.26 256.48 509.93 1 13.93 15.36 16.79 18.94 20.57 24.78 29.36 34.22 39.27 0.5 13.74 14.46 15.05 15.76 16.17 16.89 17.31 17.53 17.64 0.25 13.64 13.98 14.25 14.54 14.69 14.93 15.06 15.12 15.15 0.125 13.58 13.75 13.87 14.00 14.07 14.17 14.22 14.25 14.25 0.0625 13.54 13.63 13.69 13.75 13.78 13.83 13.86 13.86 13.86 0.03125 13.53 13.57 13.60 13.63 13.65 13.67 13.68 13.68 13.68

The reason for singling out the values of kf’ in Table 2-1 and Table 2-2 is that in

7-15 all cases where experimental data are available for the KSPAM, the values of kf’/kapp fall in the range from 1.1 to 64, and when that is the case the kinetics of the complex mechanism can be resolved into the microscopic rate constants. We believe that this range of kf’/kapp will be that which will continue to be most prominent in future studies of this mechanism. Thus, our discussion will primarily be limited to calculated data in this range of kf’/kapp.

The most obvious trend in the data in Table 2-2 is that in all of the columns at the highest values of kp the values of t0.50/t0.05 approach 13.5 with increasing values of kp 68 and that at the lowest values of kp the ratio approach 13.5 with decreasing values of kp.

The maximum values of the ratio in all of the columns are found at nearly the mid-points of the range of kp values shown in Table 2-1 and 2-2. A second trend is that as the kf’/kapp ratios increase as we go from left to right in the tables, the values of t0.50/t0.05 increase from the values approaching 13.5 to higher values.

Treatment of Calculated Data for the KSPAM

We have chosen two independent data treatments, other than evaluation of t0.50/t0.05, to demonstrate how kinetic parameters do or do not differ significantly for the

two mechanisms. The first data treatment corresponds to the calculation of kinetic

parameters as a function of time based upon the instantaneous rate constant (kinst) – time

profile for the decay of reactant and the second involves the conventional plotting of -ln

(1 – E.R.) vs. time. In order to conserve space we have limited our kinetic plots to those for reactant decay but the corresponding concentration profiles vs. time are also plotted for the reactant, the intermediate and the product.

Since the IRC analysis14 is not generally known, the plots in Figure 2-3 can

serve as an introduction. The IRC plots are labeled R for reactant decay, P for product

evolution, kapp for the apparent rate constant and ks.s. for the steady-state rate constant

which is equal to the plateau value where R and P merge. The rate constants in the

calculations are given in the caption to Figure 2-3. The most characteristic features of the

kinst – time profiles in Figure 2-3 are that those based on reactant decay intercept the 0

time axis at the value of the microscopic rate constant for the first step in the reaction and

those based on product evolution intercept that axis at 0. The plots in Figure 2-3a and 69

2-3b illustrate that the longer it takes for the steady-state to be achieved the greater is the discrepancy between kapp and ks.s.. A reaction following the single-step mechanism with a

microscopic rate constant equal to kapp is expected to give an kinst – time profile which is a

straight line with zero slope. The plots in Figure 2-3 also serve to correct any false

impressions that may exist from the first mention of the IRC method20 where it is implied

that the ks.s. in the plateau region of the IRC plots can be equated to kapp defined in eq 2.4.

It is obvious from Figure 2-3 that the latter is at best an approximation.

b a R 0.9 R 0.9

0.6 0.6 -1 kapp -1 k kinst/s kinst/s app ks.s. ks.s.

0.3 0.3

P 0.0 P 0.0 0.0 0.5 1.0 1.5 2.0 0.00.51.01.52.0 time/s time/s

-1 Figure 2-3. Plots of calculated kinst – time profiles for kf’ equal to 1 s , kp and kb equal to -1 (a) 1, or to (b) 16 s . The value of kapp was equal to 0.50 in both (a) and (b)

Graphical Summary of the Kinetic Response to the KSPAM

-1 We chose the data from the extreme values of kp (128, 4 and 0.125 s ) at each of the kf’ values equal to 1.1, 2.0 and 4.0, respectively to graphically illustrate the kinetic

response as a function of kp. That for the other values of kp in Table 2-1 change smoothly

from one value of kp to the next and the complete set of data are shown in a separate

supplementary in order to save space. The kinetic plots for kf equal to 1.1, 2.0 and 4.0 are

illustrated in Figure 2-4, 2-5, and 2-6, respectively. 70

1.102 k = 1.0 s-1 0.8 -1 1.100 app kapp = 1.0 s 1.098 k ' = 1.1 s-1 -1 f kf' = 1.1 s

-1 0.6 -1 -1

/s 1.096 k = 0.125 s p kp = 0.125 s inst k 1.094 0.4 1.092 -ln(1 - E.R.) -ln(1 1.090 0.2 A = Calculated Data 1.088 B 0.0 B = Correlation Line 1.086 A 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 time/s time/s 0.8 1.10 -1 -1 k = 1.0 s kapp = 1.0 s 1.08 app 0.6 -1 k ' = 1.1 s-1 kf' = 1.1 s f -1 1.06 -1 /s -1 k = 4.0 s kp = 4.0 s 0.4 p inst

k 1.04 -ln(1 - E.R.) 1.02 0.2

1.00 A = Calculated Data B 0.0 B = Correlation Line 0.98 A 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 time/s time/s 0.8 1.10 -1 kapp = 1.0 s -1 kapp = 1.0 s -1 0.6 1.08 kf' = 1.1 s -1 kf' = 1.1 s -1 -1 /s kp = 128 s -1 1.06 kp = 128 s

inst 0.4 k

1.04 - E.R.) -ln(1 0.2 1.02 B A = C alculated D ata 0.0 1.00 A B = Correlation Line 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 time/s time/s

FIGURE 2-4. IRC – time profiles (left hand column) and conventional kinetic analysis -1 -1 (right hand column) for the KSPAM with kf’ = 1.1 s , kapp = 1.0 s and kp = 0.125, 4.0, and 128 s-1 from top to bottom, respectively 71

2.02 0.8 2.00 -1 k = 1.0 s-1 kapp = 1.0 s app 1.98 -1 0.6 k ' = 2.0 s-1 kf' = 2.0 s f -1 1.96 k = 0.125 s-1 k = 0.125 s-1 /s p p 0.4 inst 1.94 k

1.92 -ln(1 - E.R.) 0.2 1.90 1.88 B A = Calculated Data 0.0 B = Correlation Line 1.86 A 0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 time/s time/s

2.0 0.5 -1 k = 1.0 s-1 kapp = 1.0 s app 1.8 -1 0.4 k ' = 2.0 s-1 kf' = 2.0 s f -1 -1 -1 k = 4.0 s 1.6 kp = 4.0 s p

/s 0.3 inst

k 1.4

-ln(1 - E.R.) 0.2 1.2 0.1 1.0 B A = Calculated Data B = Correlation Line 0.0 A 0.8 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.5 time/s time/s

2.0 -1 0.4 -1 kapp = 1.0 s kapp = 1.0 s 1.8 k ' = 2.0 s-1 k ' = 2.0 s-1 f 0.3 f -1 -1 -1 /s k = 128 s k = 128 s 1.6 p p inst

k 0.2

1.4 - E.R.) -ln(1 0.1 1.2 B A = Calculated Data 0.0 B = Correlation Line 1.0 A 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 time/s time/s

FIGURE 2-5. IRC – time profiles (left hand column) and conventional kinetic analysis -1 -1 (right hand column) for the KSPAM with kf’ = 2.0 s , kapp = 1.0 s and kp = 0.125, 4.0, and 128 s-1 from top to bottom, respectively 72

0.8 4.0 -1 k = 1.0 s-1 kapp = 1.0 s app -1 0.6 k ' = 4.0 s-1 3.9 kf' = 4.0 s f -1 -1 -1 k = 0.125 s kp = 0.125 s p /s 0.4

inst 3.8 k -ln(1 -E.R.) 3.7 0.2

B A = Calculated Data 3.6 0.0 B = Correlation Line A 0.00 0.05 0.10 0.15 0.20 0.0 0.2 0.4 0.6 0.8 time/s time/s

0.4 4.0 -1 k = 1.0 s-1 k = 1.0 s 3.5 app app -1 0.3 -1 k ' = 4.0 s kf' = 4.0 s 3.0 f -1 -1 k = 4.0 s-1 /s kp = 4.0 s p 2.5 0.2 inst k 2.0 - E.R.) -ln(1 0.1 1.5 B A = Calculated Data 1.0 0.0 B = Correlation Line A 0.5 0.00 0.05 0.10 0.15 0.20 0.0 0.1 0.2 0.3 0.4 time/s time/s

4.0 0.20 k = 1.0 s-1 k = 1.0 s-1 app 3.5 app -1 -1 k ' = 4.0 s k ' = 4.0 s 0.15 f f -1 -1 3.0 -1 kp = 128 s /s kp = 128 s

inst 2.5 0.10 k

2.0 -ln(1 - E.R.) 0.05 1.5 B A = Calculated Data 0.00 B = Correlation Line 1.0 A 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20 time/s time/s

FIGURE 2-6. IRC – time profiles (left hand column) and conventional kinetic analysis -1 -1 (right hand column) for the KSPAM with kf’ = 4.0 s , kapp = 1.0 s and kp = 0.125, 4.0, and 128 s-1 from top to bottom, respectively

Discussion

The study of mechanisms of organic reactions is a fascinating topic which has been a central issue in physical organic chemistry since its birth in about 1940. Although the activity in this area is currently diminished from what it was at the height of the development of the science, it is still of immense importance. One reason for the diminished activity is that the fundamental reactions of organic chemistry have previously been studied intensely and the scientific community, in general, is satisfied that the basic fundamentals of the mechanisms of these reactions are understood. But as in all other areas of science which continue to develop, recent developments in digital technology have opened the door for new mechanism analysis techniques.

The development of instantaneous rate constant analysis14 has greatly enhanced

the physical organic chemist’s ability to differentiate between the simple single-step

mechanism (Scheme 2-3), in this case for the SN2 reaction of an alkyl halide, and the

KSPAM (Scheme 2-1).

SCEHME 2-3. The SN2 Reaction

We have chosen the SN2 reaction as one which has long been considered to take

place in a single step as the example of this mechanism. It may seem to be a mundane

task to distinguish between the two mechanisms and that this distinction should have

been achieved years ago. However when one considers the fact that the two mechanisms

are kinetically indistinguishable under the usual conditions of a kinetic study, the fact that 74 there is uncertainty in how the SN2 reaction takes place, is understandable.

It is on interest to consider the primary evidence that resulted in the single-step

mechanism for the SN2 reaction. The three main classes of evidence were: (a) optically

active alkyl halides and sulfonates were observed to undergo inversion during the

substitution process and to (b) racemize in the presence of excess leaving group and (c)

the reactions were observed to follow second order kinetics.21 Now, the question becomes:

“Is this evidence presented for the SN2 mechanism sufficient to show that the reactions

take place in a single step?” The answer to this question is clearly no. Since formation of

the “Reactant Complex” in the KSPAM in Scheme 2-1 does not involve the formation of a covalent bond, there is no reason to believe that its reversible formation and dissociation would cause racemization. Since the most likely trajectory of the nucleophile in the formation of the complex involves association with the positive end of the C–X dipole, continued reaction is expected to involve the back-side displacement of the leaving group and hence inversion. Furthermore, as will become apparent later in the discussion, the observation of linear ln (1 – E.R.) – time plots is not sufficient evidence to conclude that the reaction follows a single-step mechanism or that a kinetically significant intermediate is not formed.

The pre-association mechanism was postulated for the displacement of chloride ion in the identity reaction between methyl chloride and chloride ion in aprotic solvents but not in water about twenty years ago.22 The latter suggestion was based on a

theoretical study using Monte-Carlo calculations. In another study, no direct relationship

was found between the magnitude of the Brønsted βnuc and the extent of bond making or 75 breaking in the transition states for several SN2 reactions in DMSO and a two stage

mechanism involving ion-dipole complexes was proposed for these reactions.23 More recently, kinetic studies of the displacement of iodide ion from methyl iodide by p-nitrophenoxide ion in acetonitrile (AN) or aqueous acetonitrile were observed to be inconsistent with a single-step mechanism and it was concluded that the reaction takes place by the KSPAM (Scheme 2-4).11

SCHEME 2-4. KSPAM for SN2 Reaction of MeI with p-Nitrophenoxide

The point we wish to make here is that the added detail that accompanies the

finding that the SN2 mechanism in this case or if it turns out to be a general phenomenon

has a limited effect on our view of this mechanism. The most important aspect of this,

from a physical organic chemistry point of view, is that apparent rate constants cannot be

used to gain information about the structure of the transition state, a commonly stated

reason for carrying out kinetic studies. The latter is a consequence of the fact that the

single transition state model is not appropriate for the discussion of a reaction taking place by the KSPAM.

There has been a great deal of discussion of the SN2 mechanism in the gas

phase.24 Under these conditions the reaction can be described as the double potential well model illustrated in Figure 2-7a the energies of the separated reactants and product ion 76 molecule complexes. The close resemblance of the solution phase reaction coordinate diagram (Figure 2-7b) for the displacement of halide ion from either methyl iodide or m-nitrobenzyl bromide in AN/DMSO (75/25 vol %) to that for the SN2 mechanism in the

gas phase (Figure 2-7a)24 was recently pointed out.25 The primary difference between the

gas phase mechanism and that in AN/DMSO (75/25 vol %) appears to reside in the much

lower energy of the reactants and the products in solution as compared to the gas phase. It

25 was suggested that the main difference between the SN2 mechanism in the mixed

solvent and in protic solvents is most likely that the role of the reactant ion molecule is

masked in the latter solvents.

a b Y- + R-X T.S.2

Y-R + X -

T.S. Energy Energy T.S.1 Y- + R-X T.S.3 Y-R + X - (Y---R-X)- (Y---R-X)-

- (Y-R---X)- (Y-R---X)

Reactant Coordinate Reactant Coordinate

FIGURE 2-7. Reaction coordinate diagrams (a) for the SN2 reaction in the gas phase, and (b) for the reactions of methyl iodide or m-nitrobenzyl bromide and p-nitrophenoxide in AN/DMSO (75/25 vol %)

Before going into more detail on the results of the calculations, pointing out

some generalities are in order. The first is that our selection of the range of kp values appears to be adequate to insure that the calculations presented represent a cross-section of the combinations of rate constants that give rise to kinetic data which allow the experimental differentiation between the single-step mechanism and the KSPAM. This is 77 most easily observed from Table 2-2 where in each column the values of t0.50/t0.05 approach the single-step value of 13.5 as the limit. Another, perhaps less obvious trend in the data, is that as the kp/kb gets smaller as we approach the left side of Table 2-2, is that

the reaction begins to show the character of a single-step mechanism where R is

converted to I and formation of P becomes negligible during the time of practical kinetic measurements. This trend is already present at the horizontal midpoint of the table, as illustrated in Figure 2-8 which shows the concentration – time profiles for the case where

-1 -1 -1 kf’ = 4 s , kb = 0.50 s and kp = 0.125 s . The third generalization is an obvious one

which arises from the fact that kf’ cannot exceed kapp (eq 2.4). In the far left column of

Table 2-2, where kf’/kapp = 1.1 the values of t0.50/t0.05 are approaching 13.5 which is the

limiting value when kf’/kapp is equal to unity. The overall conclusion on the choice of

dimensionless microscopic rate constants derived from Table 2-1 for the KSPAM is that

all relevant combinations of the latter are included.

1.0

0.8 R 0.6 Conc 0.4 I 0.2 P 0.0 0.00 0.05 0.10 0.15 0.20 time/s

-1 -1 FIGURE 2-8. Concentration profiles for the KSPAM kf’ = 4 s , kb = 0.50 s and kp = 0.125 s-1 78

Another point of some importance is that essentially all of the figures for the conventional plots of -ln (1 – E.R.) vs. time, with the exception of those derived from rate constants near the horizontal mid-section of Table 2-1, show that there is negligible differences between the calculated data and the corresponding linear least squares correlation of the data. This emphasizes the fact that the conventional treatment of pseudo-first-order data generated for a process following the KSPAM does generally not differentiate between the single-step and the more complex mechanism.

The final generality deals with the range of the dimensionless rate constant combinations over which it is possible to distinguish between the single-step mechanism and the KSPAM. The t0.50/t0.05 data in Tables 2-2 provide the most convenient guide for

determining the possibility for experimentally distinguishing between the two

mechanisms. From these tables we conclude that the first column (kf’/kapp = 1.1)

represents data of borderline value for distinguishing between the mechanisms. The same

can be said for rows with kp/kapp equal to 128 and higher or 0.125 or lower. All other data

from calculations with kf’/kapp greater than 1.1 and/or those with kp/kapp in the range from

0.125 to 128 are suitable for distinguishing between the single-step mechanism and the

KSPAM. The further away from the extremes listed above, the greater the ease in

kinetically distinguishing between the mechanisms.

It should be kept in mind that since we are setting the limits in terms of

dimensionless rate constants, that the number of actual combinations of rate constants

that we are discussing is enormous. Of course there are other limitations, the most

important of which is the time necessary for the mixing of reactions during stopped-flow 79 spectrophotometric studies of rapid reactions.

Conclusions

Mechanisms involving the kinetically significant association complexes are defined as the kinetically significant pre-association mechanism (KSPAM). A dimensionless (1 – E.R.) – time profile was applied to limit the number of combinations of microscopic rate constants (kf, kb, kp) for the KSPAM that covers the range which

allows differentiation from the single-step mechanism. The kinetic responses were

calculated over the entire applicable range and verified that the instantaneous rate

constant procedure was much more capable of efficiently differentiating the mechanisms

than the conventional kinetic method of establishing first-order (or pseudo-first-order) kinetics which fails in most cases. The SN2 mechanism which has been suggested to

follow the multi-step mechanism was extensively discussed in the view of the KSPAM.

Refereces

(1) Hammett, L. P. Physical Organic Chemistry; McGraw Hill: New York, 1940; Tokyo, 2nd ed., 1970.

(2) Ridd, J. H. Adv. Phys. Org. Chem. 1978, 16, 1.

(3) Connors, K. A. Chemical Kinetics; New York: VCH Publisher, 1990; Chapter 3.2.

(4) (a) Brønsted, J. N.; Pedersen K. Z. Phys. Chem. 1924, 108, 185. (b) Brønsted, J. N., Chem. Rev. 1928, 5, 231.

(5) (a) Hammett, L. P. J. Am Chem, Soc. 1937, 59, 96. (b) Johnson, C. D. The Hammett equation; Cambridge University Press: Cambridge, 1973.

(6) (a) Jaffé, H. H. Chem. Rev. 1953, 53, 191. (b) Leffler, J. E.; Grunwald, E., In Rates and Equilibria of Organic Reactions; Wiley: New York, 1963; (c) Ehrenson, S. Prog. 80

Phys. Org. Chem. 1964, 2, 195. (d) Ritchie, C.; Sager, W. F. Prog. Phys. Org. Chem. 1964, 2, 323. (e) Wells, P. R. In Linear Free Energy Relationships; Academic Press: New York, 1968; (f) Shorter, J. Q. Rev. Chem. Soc. 1970, 24, 433. (g) Exner, O. In Advances in Linear Free Energy Relationships; Chapman, N. B.; Shorter, J., Ed.; Plenum: London, 1972; p 72. (h) Godfrey, M. Tetrahedron Lett. 1972, 753. (i) Johnson, K. F. The Hammett Equation; Cambridge University Press: New York, 1973. (j) Charton, M. Prog. Phys. Org. Chem. 1972, 10, 81. (k) Ehrenson, S.; Brownlee, R. T. C.; Taft, R. W. Prog. Phys. Org. Chem. 1973, 10, 1. (l) Hine, J. Structural Effects on Equilibria in Organic Chemistry; Wiley: New York, 1975. (m) Levitt, L. S.; Widing, H. F. Prog. Phys. Org. Chem. 1976, 12, 119. (n) Unger, S. H.; Hansch, C. Prog. Phys. Org. Chem. 1976, 12, 91. (o) Topsom, R. O. Prog. Phys. Org. Chem. 1976, 12, 1.

(7) (a) Parker, V. D.; Zhao, Y.; Lu, Y.; Zheng, G. J. Am. Chem. Soc. 1998, 120, 12720. (b) Lu, Y.; Zhao, Y.; Parker, V. D. J. Am. Chem. Soc. 2001, 123, 5900. (c) Zhao, Y.; Lu, Y. ; P a r k e r, V. D . J. Chem. Soc., Perkin Trans. 2 2001, 1481. (d) Parker, V. D.; Zhao, Y. ; L u , Y. Electrochemical Society, Proceedings Volume 2001-14, ISBN: 1-56677-320-2, pp 1-4. (e) Parker, V. D.; Lu, Y.; Zhao, Y. J. Org. Chem. 2005, 70, 1350.

(8) (a) Zhao, Y.; Lu, Y.; Parker, V. D. J. Am. Chem. Soc. 2001, 123, 1579. (b) Parker, V. D.; Zhao, Y. J. Phys. Org. Chem. 2001, 14, 604.

(9) Li, Z; Cheng, J.-P.; Parker, V. D. Org. Biomol. Chem. 2011, 9, 4563.

(10) Handoo, K. L.; Lu, Y.; Zhao, Y.; Parker, V. D. Org. Biomol. Chem. 2003, 1, 24.

(11) (a) Lu, Y.; Handoo, K. L.; Parker, V. D. Org. Biomol. Chem. 2003, 1, 36. (b) Parker, V. D.; Lu, Y. Org. Biomol. Chem. 2003, 1, 2621.

(12) Lu Y.; Zhao, Y.; Handoo, K. L.; Parker, V. D. Org. Biomol. Chem. 2003, 1, 173.

(13) Handoo, K. L.; Lu, Y.; Parker, V. D. J. Am. Chem. Soc. 2003, 125, 9381.

(14) Parker, V. D. J. Phys. Org. Chem. 2006, 14, 604. 81

(15) Hao, W.; Parker, V. D. J. Org. Chem. 2008, 73, 48.

(16) (a) Ba-Saif, S.; Luthra, A. K.; Williams, A. J. Am. Chem. Soc. 1987, 109, 6362. (b) Hengge, A. C.; Hess, R. A. J. Am. Chem. Soc. 1994, 116, 11256.

(17) Eigen, M.; Johnson, J. S. Annu. Rev. Phys. Chem. 1960, 11, 309.

(18) (a) Jencks, W. P. Acc. Chem. Res. 1980, 13, 161. (b) Jencks, W. P. Chem. Soc. Rev. 1981, 10, 345.

(19) Johnston, H. S. In Gas Phase Reaction Rate Theory; Ronald Press: Berkeley; Appendix, p. 439. A pair of brackets was omitted in third equation in (A-3) on p 439 (eq 2.1 in this thesis).

(20) (a) Parker, V. D. Pure Appl. Chem. 2005, 77, 1823. (b) Parker, V. D.; Hao, W.; Li, Z.; Scow, R. Int. J. Chem. Kinet. 2012, 44, 2.

(21) (a) Kenyon, J.; McNicol, R. A. J. Chem. Soc. 1923, 14. (b) Phillips, H. J. Chem. Soc. 1925, 2552. (c) Hughes, E. D.; Ingold, C. K.; Scott, A. D. J. Chem. Soc. 1937, 1201. (d) Cowdry, W. A.; Hughes, E. D.; Ingold, C. K.; Masterman, S.; Scott, A. D. J. Chem. Soc. 1937, 1252.

(22) (a) Chandrasekhar, J.; Jorgensen, W. L. J. Am. Chem. Soc. 1985, 107, 2974. (b) Jorgensen, W. L. Acc. Chem. Res. 1986, 22, 184.

(23) Bordwell, F. C.; Hughes, D. L. J. Am. Chem. Soc. 1986, 108, 7300.

(24) (a) Brauman, J. I. Science 2008, 319, 168. (b) Mikosch, J.; Trippel, S.; Eichhorn, C.; Otto, R.; Lourderaj, U.; Zhang, J. X.; Hase, W. L.; Weidemüller, M.; Wester, R. Science 2008, 319, 183.

(25) Weifang Hao, Ph.D. Dissertation, Utah State University, 2012.

CHAPTER 3

NEW METHODOLOGY FOR DIFFERENTIATING BETWEEN

SINGLE-STEP AND MULTI-STEP MECHANISMS*

Abstract

Four new analysis procedures for pseudo-first-order kinetics are introduced,

which consists of (1) half-life dependence of apparent rate constants (kapp), (2) sequential

linear pseudo-first-order correlation, (3) approximate instantaneous rate constant analysis, and (4) time-dependent apparent kinetic isotope effects. Each of the four procedures is capable of distinguishing between single-step and multi-step mechanisms, and the combination of the four procedures provides a powerful strategy for differentiating between the two mechanistic possibilities. This strategy has been successfully applied to

all of the reactions that we focus on.

Introduction

In 1997 Professor George S. Hammond1 published a short article entitled

Physical Organic Chemistry after 50 years: “It has changed, but is it still there?” In this

article Hammond summarized the remarkable developments in the sub-discipline since it

began with the work of Louis P. Hammett.2 No mention was made of the development of

pseudo-first-order kinetic methods which was the most important kinetic technique used

by the vast majority of physical organic chemists. Aside from the development of very

rapid kinetic techniques essentially no improvements were made in the methods for

* Some contents have been published in Int. J. Chem. Kinet. 2012, 44 (1), 2-12, coauthored by Vernon D. Parker, Weifang Hao, Zhao Li and Russell Scow, reproduced by permission of John Wiley and Sons. 83 which so many rate constants were measured for Linear Free Energy Relationships. This is evident from the classic book, Kinetics and Mechanism, by John W. Moore and Ralph

G. Pearson published in 1981.3 This deficiency continued for the remainder of the 20th century.

The digital revolution occurred during the time period of the development of physical organic chemistry. The latter had a great influence on the work of the physical chemists studying rapid kinetics but did not filter down to the physical organic chemists measuring rate constants of slower reactions. The objective of our work is to fill the gap by introducing work on the fundamental reactions of organic chemistry using new methods which take advantage of modern digital acquisition of absorbance – time data and extensive new data analysis of pseudo-first-order kinetics. During the current century, however several papers4 relevant to our work have appeared which deal with the

inadequacy of a simple fit of an exponential curve to establish a simple one-step

mechanism, this issue has not been widely recognized by the community of physical

organic chemists.

The purpose of this chapter is to show the capability of the new methodology in differentiation between the two mechanisms. This was done primarily with calculated data to eliminate the effects of experimental error upon our conclusions. The practical

application of these four new analysis procedures on the experimental data will be

introduced in the following chapters of this thesis.

Methodology and Data Manipulation

The methods discussed will be limited to four general procedures and the first is 84 a more detailed variable time period application of the conventional pseudo-first-order kinetic relationship in a way that in some cases clearly distinguishes between simple single-step and complex multi-step mechanisms. When a complex mechanism is indicated the next two procedures provide data which give more detail of the kinetic response and can verify that the reaction follows a complex mechanism. The last procedure, referring to the apparent KIE analysis, is developed upon the other three procedures and able to give obvious evidence of the complex mechanism for the reaction involving kinetic isotope effects.

Half-Life Dependence of Conventional Pseudo-First-Order Rate Constants

The procedure, which we usually call the Long-time-check, involves converting

absorbance – time profiles (Abs – t) to –ln (1 – E.R) – time profiles where E.R. is extent

of reaction. The latter are then subjected to linear least squares analysis on 5 different segments of the data over time ranges corresponding to 0 – 0.5 half-lives (HL), 0 – 1 HL,

0 – 2 HL, 0 – 3 HL and 0 – 4 HL.

Results of applying this analysis procedure on the calculated data for both

-1 -1 -1 reactant decay and product evolution in case of kapp = 1.0 s , kf’ = 1.1 s , kb = 0.5 s and

-1 kp = 5.0 s are summarized in Table 3-1. The data show that the values of the apparent

pseudo-first-order rate constant (kapp) and zero-time intercept over the five data segments

steadily vary with degree of conversion. Data values for reactant decay and product

evolution are changing in opposite directions.

While the changes in kapp observed are modest, the corresponding changes in the

zero-time intercepts are much larger and suggest that this parameter is much more 85 sensitive to the deviations from first-order kinetics than kapp is. Obviously, the response

expected for the single-step mechanism is a constant value of kapp and an intercept

independent of the number of HL taken into the linear least squares correlation.

Table 3-1. Changes in the Slopes and the Intercepts with the Extent of Reaction -1 During Conventional Pseudo-First-Order Analysis of the KSPAM with kapp = 1.0 s , -1 -1 -1 kf’ = 1.1 s , kb = 0.5 s , kp = 5.0 s Monitoring reactant decay Monitoring product evolution Number of HL -1 -1 -1 -1 kapp (s ) Intercept (s ) kapp (s ) Intercept (s ) 0.5 1.0459 0.00218 0.6454 -0.0383 1.0 1.0106 0.00743 0.8174 -0.0756 2.0 0.9907 0.01379 0.9113 -0.1127 3.0 0.9846 0.01725 0.9425 -0.1327 4.0 0.9821 0.01927 0.9562 -0.1446

Sequential Pseudo-First-Order Linear Correlation

This analysis procedure, that we usually call KCONT, involves recording 2000

point Abs – time profiles over about the first HL of the reaction. Linear least squares

analyses are then carried out over the following point segments; 1–11, 1–21 , 1–31, 1–41,

1–51, 1–101, 1–201, …, 1–1801, 1–1901, which gives 24 kapp values at the midpoints of

the segments (Table 3-2). In practice, the standard deviations (SD) of the kapp evaluated

for multiple (normally 10 – 20) stopped-flow shots are also recorded.

The expected result of the KCONT procedure for the single-step mechanism is a

rate constant, independent of time and of the particular time segment analyzed. For the

reactions following the complex mechanism, the apparent rate constants derived from

KCONT steadily change with reaction time in different directions dependent upon

whether reactant decay or product evolution is monitored. In Figure 3-1a, the upper

profile is for reactant decay and the lower one is for product evolution. 86

Table 3-2. Point Segment Set for KCONT Analysis Number Segment Midpoint Number Segment Midpoint 1 1-11 6 13 1-801 401 2 1-21 11 14 1-901 451 3 1-31 16 15 1-1001 501 4 1-41 21 16 1-1101 551 5 1-51 26 17 1-1201 601 6 1-101 51 18 1-1301 651 7 1-201 101 19 1-1401 701 8 1-301 151 20 1-1501 751 9 1-401 201 21 1-1601 801 10 1-501 251 22 1-1701 851 11 1-601 301 23 1-1801 901 12 1-701 351 24 1-1901 951

2.0 2.0 Reactant Decay a Reactant Decay b 1.5 1.5

k /s-1 k /s-1 IR C app 1.0 1.0 -1 -1 kapp = 1.0 s kapp = 1.0 s -1 -1 0.5 kf' = 2 s 0.5 kf' = 2 s Product E volution -1 Product E volution -1 kb = kp = 16 s kb = kp = 16 s 0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 time/s time/s

-1 -1 FIGURE 3-1. (a) kapp – time and (b) kIRC – time profiles for kapp = 1.0 s , kf’ = 2.0 s , kb -1 = kp = 16 s

A New Procedure for the Approximation of Instantaneous Rate Constant – Time Profiles.

An obvious extension of the method discussed above is to include additional

correlations. To do this the points in the data segment are 1–3, 1–4, 1–5, 1–6, …, 1–2000,

and a 1998 point array of kapp – time data is obtained (Figure 3-1b), where the kapp here

was expressed in terms of kIRC. The results were compared to kinst – time profiles obtained at the mid-point between all points as presented earlier.5 The comparison in Figure 3-2 87 shows that the kIRC values at short times are nearly identical to the corresponding kinst values. The largest deviations (about only 5%) may be found in values near the center or near the end of the correlation. It was concluded that for all practical purposes (such as for mechanism determination), the values obtained by the new procedure are equivalent to kinst values. The term kIRC is used in order to differentiate from the more precisely

defined kinst. The greatest value of kIRC over kinst is that since every value of the rate

constant in the former case results from a linear correlation over several points (3 to

2000), there is a very large difference in the experimental precision as compared to the

latter case.

2.0 a 2.0 b kinst 1.8 1.8 -1 kIR C kapp = 1.0 s

-1 t t k = 1.0 s app -1 an an 1.6 1.6

t k ' = 2.0 s t k ' = 2.0 s-1 f f -1 1.4 -1 1.4 kb = kp = 2.0 s kb = kp = 16 s e cons e cons t t k 1.2 1.2 inst ra ra kIR C 1.0 1.0 Reactant Decay Reactant Decay 0.8 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 time/s time/s 2.0 c 2.0 d -1 kapp = 1.0 s 1.9 -1 t kapp = 1.0 s t -1 1.9 kf' = 2.0 s an 1.8 -1 an t kf' = 2.0 s t -1 kb = kp = 0.25 s 1.7 -1 kb = kp = 0.5 s 1.8 k kinst e cons inst e cons t 1.6 t k ra k ra IR C IR C 1.7 1.5 Reactant Decay Reactant Decay 1.4 1.6 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 time/s time/s

-1 FIGURE 3-2. Comparison between kIRC – time and kinst – time profiles, kapp = 1.0 s , kf’ -1 -1 -1 -1 -1 = 2.0 s , kb = kp = (a) 16 s , (b) 2.0 s , (c) 0.5 s , (d) 0.25 s 88

As shown in Figure 3-1, the curves for kapp – time and kIRC – time profiles are

mostly identical, but only different in the point numbers. Therefore, in the practical work,

kIRC – time profiles are always plotted in advantage of its sufficiency in data points to

describe the detailed reaction kinetics; and the primary purpose of KCONT analysis is to

estimate the errors in kapp values, which are often tabulated with corresponding SD

values.

Apparent Deuterium Kinetic Isotope Effects

The non-conventional pseudo-first-order analysis procedures discussed above

also provide a practical way to study the apparent deuterium kinetic isotope effects. Two

parameters based on apparent KIE are defined depending either upon the extent of

reaction and or the reaction time. Both of which can play a significant role in the

determination of the mechanism for the reaction involving a C–H bond change. Since the

simple mechanism predicts that the KIE will always be independent of either extent of

reaction or reaction time.

Before introducing the two apparent KIE methods in detail, it is necessary to set

up a theoretical model for calculation and analysis. Consider a reaction involving

hydrogen atom, hydride or proton transfer, which follows a pre-association mechanism

and the H transfer only takes place in the product formation step, therefore, the H- and

D-reaction parameters only differ in the values of kapp and kp, and share the same microscopic rate constants of kf’ (or kf) and kb. In the model set in Table 3-3, the

H D traditional KIE (= kapp /kapp ) is equal to 10, while the value of KIEreal calculated in terms

H D of kp /kp is equal to 19. 89

TABLE 3-3 A Theoretical Model of Pre-Association Mechanism for Apparent KIE Analysis

-1 -1 -1 -1 -1 kapp (s ) kf’ (s ) kb (s ) kp (s ) t0.50 (s) ks.s. (s ) H-reaction 0.1 0.2 1.0 1.0 8 0.0950 D-reaction 0.01 0.2 1.0 1/19 80 0.00846

H D H D KIE = kapp /kapp = 10, KIEreal = kp /kp = 19

E.R. Extent of Reaction – Dependent Apparent Kinetic Isotope Effects. KIEapp is defined as the ratio of the time that the D-reaction and H-reaction need to reach the

E.R. same extent of reaction. KIEapp – E.R profiles in Figure 3-3 clearly show that the

E.R. values of KIEapp are steadily increasing with E.R., no matter whether reactant decay or product evolution is monitored

10 -1 -1 11 b kf' = 0.2 s , kb = 1.0 s a 8 k H = 1.0 s-1 p 10 D -1 kp = 1/19 s E.R. 6 E.R. 9 k ' = 0.2 s-1, k = 1.0 s-1 KIE = 10, KIEreal = 19 f b app app H -1 8 kp = 1.0 s KIE 4 KIE D -1 kp = 1/19 s 7 KIE = 10, KIEreal = 19 2 6 Reactant Decay Product Evolution 0 5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 E.R. E.R.

E.R. FIGURE 3-3. Calculated KIEapp – E.R. profiles for (a) reactant decay and (b) product evolution

The curve for reactant decay in Figure 3-3a rises from 1 at zero time and

continually increases to a value approaching to 10 during the first half-life. It is 90

E.R. noticeable that in the initial stage of the reaction (E.R. < 0.1), values of KIEapp are nearly constant in the neighborhood of 1. That is no doubt because that in the early stage, the accumulation of intermediate is predominant, and the product formation step is not yet significant enough to result in a significant change in KIE.

In Figure 3-3b, for monitoring the product evolution directly, the product curve does not involve a flat stage, but increases smoothly from a relatively high value of

E.R. KIEapp ( > 5.0) at zero time and beyond the classical KIE value when 25% conversion

has completed. As the steady states for both H- and D-reactions have reached, the value

E.R. of KIEapp will approach to a constant, which can be evaluated by the ratio of

H D steady-state rate constants of H- and D-reactions, ks.s. /ks.s. , equal to 11.2 for this case.

Reaction Time – Dependent Apparent Kinetic Isotope Effects. KIEapp is defined as the ratio of apparent rate constants (kapp) provided by the KCONT procedure

for the H- and D-reactions, which must be measured at the exactly the same time

intervals. KIEapp – time profiles in Figure 3-4 show that the profiles differ significantly

for product evolution and reactant decay. In Figure 3-4a, the profile for product evolution

decays exponentially and the zero time intercept is equal to the value of KIEreal. The curve for reactant decay steadily rises from 1 at zero time, since there is no kinetic isotope effect in the first step of the reaction. When the study time is extended to 100 s, in

Figure 3-4b, the two KIEapp – time profiles merge into a straight line with zero slope,

which indicates that steady state has been reached. The value of the final constant KIEapp

H D is also equal to ks.s. /ks.s. = 11.2. Additionally, it is obvious that the KIEapp – time profile

for product evolution reaches the plateau value much more early than that for reactant 91 decay.

It is concluded that the zero time intercepts of the KIEapp – time profiles for both

reactant decay and product evolution are of importance. During a reaction following a

pre-association mechanism, monitoring either product evolution or reactant decay will

result in the real kinetic isotope effect, while monitoring the reactant decay provides more

convincing evidence for the process of pre-association.

20 18 19 Product Evolution b 10 s a 16 100 s 15 14 Product Evolution 12 11.2 app k ' = 0.2 s-1, k = 1.0 s-1 app 10 10 f b -1 -1 KIE k ' = 0.2 s , k = 1.0 s H -1 KIE 8 f b kp = 1.0 s H -1 kp = 1.0 s k D = 1/19 s-1 6 p k D = 1/19 s-1 5 KIE = 10, KIE = 19 4 p re a l KIE = 10, KIE = 19 Reactant Decay 2 real 1 Reactant Decay 0 0 012345 0 1020304050 time/s time/s

FIGURE 3-4. KIEapp – time profiles calculated in (a) 10 s and (b) 100 s

Apparent Kinetic Concentration Effects. The origin of the apparent kinetic

isotope effect is the fact that the intermediate in the complex mechanism partitions

between return to reactants and irreversible product formation and the KIE is only

involved in the product forming step. A question arises as to whether or not the

methodology of apparent KIE can be used for a pair of reactions, which only differ in the

’ concentration of excess reactant, [B]0. In this case, kp is invariant while the value of kf varies directly with [B]o. For the simple one-step mechanism, the pseudo-first-order rate

constant, k1 is proportional to [B]0. For the pre-association mechanism, [B]0 is only able

to have a direct impact on the pre-association step (step one) and its concentration effect 92 on the kapp certainly will show a dependence on E.R. or time, which can be denoted as the apparent Kinetic Concentration Effects (KCE).

In the theoretical model (Table 3-4) designed for apparent KCE analysis, the

only different microscopic rate constant between the high- and low-reactions is kf’, which

H L is defined as kf[B]0. The ratios of pseudo-first-order rate constants (kapp /kapp ) is equal to

H L the ratio of kf’, and the ratio of steady-state rate constants (ks.s. /ks.s. ) is also calculated.

TABLE 3-4 A Theoretical Model of Pre-Association Mechanism for Apparent KCE Analysis -1 -1 -1 -1 -1 kapp (s ) kf’ (s ) kb (s ) kp (s ) t0.5 (s) ks.s. (s )

High [B]o 0.1 0.2 1.0 1.0 8 0.0950 Low [B]o 0.025 0.05 1.0 1.0 28 0.0247

H L H L kapp /kapp = 4.0, ks.s. /ks.s. = 3.84

4.02 5.5 H L b a kapp /kapp = 4.0 4.00 k H /k L = 3.84 3.98 1-step mechanism 5.0 s.s. s.s. Reactant Decay Reactant Decay 3.96 E.R. 4.5 app 3.94 k H /k L = 4.0 app app app 4.0 3.92 H L KCE k /k = 3.84 1-step mechanism s.s. s.s. KCE 3.5 3.90 Product Evolution 3.88 3.0 3.86 Product Evolution 2.5 3.84 0.0 0.1 0.2 0.3 0.4 0.5 012345 E.R. time/s

E.R. FIGURE 3-5. Calculated (a) KCEapp – E.R. and (b) KCEapp – time profiles

E.R. E.R. Following the concepts of KIEapp and KIEapp, both KCEapp – E.R. and

KCEapp – time profiles are recorded (Figure 3-5). In both cases, the value of KCE for

simple one-step is a constant equal to 4.0 and independent of E.R. or reaction time. For

the pre-association mechanisms, profiles for both reactant decay and product evolution in 93

H L each case are changing towards to ks.s. /ks.s. = 3.84, since the steady states achieved.

A comparison of these profiles to apparent KCEs in terms of the practical

application suggests that the KCEapp – time profiles (Figure 3-5b) are not very useful

H L since all of the KCEapp points vary in a narrow range of 3.84 – 4.0 (ks.s. /ks.s. –

H L E.R. kapp /kapp ), which is easily influenced by inherent experimental errors. The KCEapp –

E.R. profiles (Figure 3-5a) do not only have a wider range for data distribution, but also

differ significantly for reactant decay and product evolution.

As an extension of the study of the apparent kinetic isotope effect, the analysis

procedure of apparent kinetic concentration effects is not limited to the study of proton, hydride, or hydrogen atom transfer and is applicable all of the bimolecular reactions for

differentiating the pre-association mechanisms from single one-step mechanisms. As shown above, using only a two-concentration analysis does not give enough change in

apparent rate constants with 4-fold difference in concentration, the method can be

extended over a much wider change in concentration and provide substantial deviations between simple and complex mechanism behavior. The later is evident from the time ratios in Table 2-2 where kf’ increases from left to right and the corresponding time ratios

-1 show enormous variations when kp is varied in the range from 0.5 to 64 s .

Conclusions

Four different new pseudo-first-order kinetic procedures were applied in the theoretical data and verified to be capable of distinguishing between single-step and multi-step mechanisms. The procedures include (1) half-life dependence of kapp during convention pseudo-first-order analysis, (2) sequential linear pseudo-first-order correlation, 94

(3) approximate instantaneous rate constant analysis and (4) time-dependent apparent kinetic isotope effects. The theoretical analysis was carried out with the data calculated based on some particular combinations of rate constants. However, the number of actual combinations of rate constants is enormous, and the kinetic data obtained from actual reactions can be much more complicated than the calculated data. Using these new procedures, the determination as to whether a reaction follows a simple one-step or a more complex mechanism can be made using a minimum of both time and materials.

This, of course, is only the first step in the investigation of the mechanism of a reaction and should be followed by experiments under all applicable conditions, including changes in reactant concentrations, wavelengths at which absorbance – time data are obtained, temperature, and composition of the solvents to name the most common variables.

Reffereces

(1) Hammond, G. S. Pure & Appl. Chem. 1997, 69, 1919.

(2) Hammett, L. P. Physical Organic Chemistry; McGraw Hill: New York, 1940; Tokyo, 2nd ed., 1970.

(3) Moore, J. W.; Pearson, R. G. Kinetics and Mechanism, 3rd ed.; John Wiley and Sons: New York, 1981.

(4) (a) Nagy, T.; Turányi, T. Int. J. Chem. Kinet. 2011, 43, 359. (b) Kormányos, B.; Horváth, A. K.; Peintler, G.; Nagypál, I. J. Phys. Chem. A 2007, 111, 8104. (c) Bandstra, J. Z.; Tratnyek, P. G. J. Math. Chem. 2005, 37, 409. (d) Vidaurre, G.; Vasquez, V. R.; Whiting, W. B. Ind. Eng. Chem. Res. 2004, 43, 1395.

(5) Parker, V. D. J. Phys. Org. Chem. 2006, 14, 604. 95

CHAPTER 4

REACTIONS OF THE SIMPLE NITROALKANES WITH HYDROXIDE

ION IN WATER. EVIDENCE FOR A COMPLEX MECHANISM†

Abstract

Conventional kinetic analysis of the reactions of nitromethane (NM), nitroethane

(NE) and 2-nitropropane (2-NP) with hydroxide ion in water revealed that the reactions are complex and involve kinetically significant intermediates. Kinetic experiments at the isosbestic points where changes in reactant and product absorbance cancel indicate the evolution and decay of absorbance characteristic of the formation of reactive intermediates. The deviations from first-order kinetics were observed to increase with increasing extent of reaction and in the reactant order: NM < NE < 2-NP. The apparent

deuterium kinetic isotope effects for proton/deuteron transfer approach unity near zero time and increased with time toward plateau values as the reaction kinetics reach steady state. It is proposed that the initially formed pre-association complexes are transformed to more intimate reactant complexes which can give products by two possible pathways.

Introduction

The observation1 of the unusual inverse order of kinetic and thermodynamic

acidities of the simple nitroalkanes (nitromethane = NM, nitroethane = NE and

2-nitropropane = 2-NP) during their reactions with hydroxide ion in water more than a

half century ago was later referred to as the nitroalkane anomaly.2 Data for this novel

† This work has been published in Org. Biomol. Chem. 2011, 9 (12), 4563-4569, coauthored by Zhao Li, Jin-Pei Cheng and Vernon D. Parker, reproduced by permission of The Royal Society of Chemistry 96 relationship are reproduced in Table 4-1. This phenomenon has perplexed physical organic chemists ever since its discovery and a number of papers were published on the topic for these reactions in protic solvents,3 aprotic solvents,4 and mixed solvents.5

TABLE 4-1. Equilibrium and Rate Data Often Cited in Support of the “Nitroalkane Anomaly” Substrate NM NE 2-NP a a b pKa in Water 10.22 8.60 7.74 c Relative kapp 1.00 0.188 0.0114 aRef. 1e. bRef. 1b, 1c. cRef. 3a corrected for symmetry factor (NM = 3, NE = 2, 2-NP = 1)

The reactions of aryl nitroalkanes in the presence of benzoic acid buffers in

DMSO were observed to be free of complications from ion pairing and a one-step proton

transfer equilibrium was proposed.4 Recent studies6 led to the conclusion; “Calculations also show that the ‘nitroalkane anomaly,” well established in solution, does not exist in the gas phase.” It is important to note at the outset that explanations of the nitroalkane anomaly have generally involved a single transition state on the reaction coordinate, for example, the proton transfers have been assumed to take place in a single step, sometimes followed by rapid hydrogen bonding or ion pairing. An exception to the latter7 was the

proposal of slow reaction of a hydrogen bonded substrate molecule to an anionic

intermediate in which the charge is localized on the carbon attached to the nitro group by

the hydrogen bond. It was later pointed out8 that hydrogen bonding to oxygen of the

nitronate product by the conjugate acid of the base is more likely than the formation of an

intermediate. Reference to a 14C kinetic isotope effect study9 was cited as evidence

against the proposed reaction intermediate. We now report convincing experimental

evidence that the assumption that rate determining proton transfer is the first step in the 97 mechanism, is not correct.

The present work is a part of our general effort to determine the mechanisms of fundamental organic reactions. We have recently shown10 that the reaction of

2,4,6-trinitroanisole (TNA) with methoxide ion in methanol takes place by a reversible

consecutive mechanism (Scheme 4-1). The latter is contrary to the long accepted belief

that formation of the 2,4,6-trinitro-1,3-dimethoxycyclohexadienylide (I) and the

1,1-dimethoxy complex (II) take place by a competitive rather than a sequential

mechanism. The tentatively proposed intermediate (III) was not observed but the 1H

NMR spectrum had previously been recorded.11 A reversible consecutive mechanism was

previously proposed for the proton transfer reaction between 1-(4’-nitrophenyl)-

nitroethane (p-NPNE) with hydroxide ion in aqueous acetonitrile.12

SCHEME 4-1. Proposed Mechanism for the Reaction of TNA with MeO- in MeOH

OMe OMe O N O2N NO2 k1 2 NO2 +MeO H (1) k-1 OMe NO2 NO2 I OMe MeO OMe O2N O N NO NO2 kf 2 2 H +MeO OMe (2) OMe kb H H NO2 NO2 I III MeO OMe MeO OMe O2N NO2 k2 O2N NO2 OMe +MeO (3) H k-2 H NO NO2 2 III II

Results and Discussion

Absorbance – time profiles for the evolution of products at 240 nm over several

half-lives for the reactions of NM, NE and 2-NP with hydroxide ion in water at 298 K are 98 illustrated by the plots in the left column of Figure 4-1 (Spectra of anions of nitroalkanes in water have been reported.13 Reactant spectra and extinction coefficients of NM, NE

and 2-NP are shown in Figure B.4, Appendix B). It is evident that the reactions go to

completion and the absorbance values at the plateaus indicate that the reaction products are stable during the time periods of the experiments. 1H NMR spectra of reaction

mixtures after several half-lives show no significant signals indicative of side products.

The acid-base reactions produce the conjugate bases according to Scheme 4-2 where the

anionic products are represented as two resonance forms showing the distribution of the

negative charge.

- SCHEME 4-2. Reactions of Nitroalkanes with OH in H2O

The conventional first-order analyses of the reactions are revealing in terms

of whether or not the reactions conform to first-order kinetics as is expected from the

previous studies.3 The latter is illustrated by the ln(1 - E.R.) – time profiles, where E.R. is

the extent of reaction, along with the corresponding least squares correlation lines. The

degrees of deviation of the experimental data from the correlation lines were observed to

be inversely related to the kinetic reactivity of the nitroalkane, for example, deviations

are more pronounced in the order, 2-NP > NE > NM. The latter was also observed to

increase with increasing E.R. and the data for 2-NP began to deviate from that expected

for first-order kinetics during the first half-life of the reaction while deviations for the 99 other two substrates became significant at greater E.R. The relationships are illustrated by the plots in the right column of Figure 4-1 and in more detail in Appendix B.

1.6 1a 0 1a' [NM] = 0.20 mM 1.2 -1 [NaOH] = 20.0 mM in H2 O at 298K [NM] = 0.20 mM 5t 0.8 0.5 240nm [NaOH] = 20.0 mM -2 Abs /Abs A.U.

in H O at 298K E.R.) ln(1- 2 Slope= -0.431 0.4 240nm -3 R= 0.99621 t = 1.41s 0.0 0.5 -4 0 5 10 15 20 25 30 02468 time/s time/s

0.7 1b 0.0 1b' 0.6 -0.5 [NE] = 0.10 mM [NaOH] = 50.0 mM 0.5 -1.0 in H2 O at 298K 0.4 4t [NE] = 0.10 mM -1.5 0.5 240nm 0.3 [NaOH] = 50.0 mM Abs /Abs A.U. in H O at 298K E.R.) ln(1- -2.0 Slope= -0.201 0.2 2 240nm -2.5 R= 0.99178 0.1 -3.0 t0.5= 2.8s 0.0 0 10203040 -2 0 2 4 6 8 10 12 14 16 time/s time/s

1.0 1c 0.0 1c' [2-NP] = 0.20 mM 0.8 -0.5 [NaOH] = 50.0 mM

0.6 in H2 O at 298K [2-NP] = 0.20 mM -1.0 3t 0.5 240nm 0.4 [NaOH] = 50.0 mM Abs /A.U.

ln(1- E.R.) ln(1- -1.5 in H2 O at 298K Slope= -0.00809 0.2 R= 0.94721 240nm -2.0 0.0 t0.5= 48s -2.5 0 100 200 300 400 500 600 0 50 100 150 200 250 time/s time/s FIGURE 4-1. Absorbance – time profiles (a, b, c) and ln (1 – E.R.) – time profiles (a’, b’, - c’) for the reactions of nitroalkanes (a, a’ NM; b, b’ NE; c, c’ 2-NP) with OH in H2O at 298 K 100

In order to be able to describe the deviations of the nitroalkane proton transfer reactions with hydroxide ion in more detail, the least square correlations of ln(1 - E.R.) – time profiles were carried out incrementally14 over the 2000 point profiles by two

different procedures. In the first, the analyses were carried out on 101 point increments,

beginning with data points 1 to 101, followed by data points 101 to 201 and subsequent

increments with the final one being from data points 1701 to 1801. The data, summarized

in Table 4-2, clearly show that the apparent first-order rate constants are E.R. dependent,

decreasing continuously as the reactions proceed toward completion.

TABLE 4-2. Variations of the Apparent Pseudo-First-Order Rate Constants for the - Reactions of Nitroalkanes with OH in H2O over Several Half-Lives (5 Half-Lives for NM, 4 Half-Lives for NE, 3 Half-Lives for 2-NP) Point Rangea k/s-1 (NM)b k/s-1 (NE)b k/s-1 (2-NP)c 1-101 0.493 0.240 0.01506 101-201 0.494 0.242 0.01447 201-301 0.492 0.240 0.01377 301-401 0.486 0.234 0.01299 401-501 0.477 0.224 0.01215 501-601 0.465 0.211 0.01131 601-701 0.452 0.195 0.01049 701-801 0.440 0.179 0.00970 801-901 0.430 0.164 0.00896 901-1001 0.423 0.152 0.00824 1001-1101 0.416 0.141 0.00752 1101-1201 0.408 0.129 0.00677 1201-1301 0.394 0.112 0.00597 1301-1401 0.366 0.0885 0.00512 1401-1501 0.322 0.0585 0.00425 1501-1601 0.266 0.0289 0.00344 1601-1701 0.220 0.0117 0.00283 1701-1801 0.221 0.0215 0.00261 a described in the text. b c [NaOH] = 20 mM and 50 mM in H2O at 298 K.

101

TABLE 4-3. Apparent Rate Constants for the Reactions of Nitroalkanes with OH- in H2O over the First Half-Life at 298 K NMa NEb 2-NPc -1 -1 -1 Segment kapp/s ± kapp/s ± kapp/s ± 0.478 0.056 0.280 0.010 0.0248 0.0013 1 0.560 0.010 0.276 0.005 0.0223 0.0007 2 0.548 0.002 0.273 0.004 0.0214 0.0005 3 0.545 0.002 0.271 0.002 0.0210 0.0008 4 0.544 0.001 0.269 0.001 0.0206 0.0008 5 0.538 0.003 0.265 0.001 0.0200 0.0008 6 0.531 0.004 0.261 0.001 0.0193 0.0007 7 0.527 0.004 0.259 0.001 0.0187 0.0006 8 0.525 0.004 0.258 0.001 0.0183 0.0006 9 0.523 0.004 0.257 0.001 0.0179 0.0006 10 0.522 0.004 0.256 0.001 0.0176 0.0006 11 0.521 0.005 0.256 0.002 0.0173 0.0006 12 0.519 0.005 0.255 0.002 0.0171 0.0006 13 0.519 0.005 0.255 0.002 0.0170 0.0006 14 0.518 0.005 0.254 0.002 0.0168 0.0006 15 0.517 0.005 0.254 0.002 0.0167 0.0006 16 0.516 0.005 0.253 0.002 0.0166 0.0006 17 0.515 0.005 0.253 0.002 0.0165 0.0006 18 0.514 0.005 0.252 0.002 0.0164 0.0006 19 0.514 0.005 0.252 0.002 0.0163 0.0006 20 0.513 0.006 0.251 0.002 0.0162 0.0006 21 0.512 0.006 0.251 0.003 0.0162 0.0006 22 0.511 0.006 0.251 0.003 0.0161 0.0006 23 0.511 0.006 0.250 0.003 0.0161 0.0006 24 a [NM] = 0.10 mM, [NaOH] = 20.0 mM, average of 3 sets of 12-20 stopped-flow repetitions. b [NE] = 0.10 mM, [NaOH] = 50.0 mM, average of 4 sets of 10-20 stopped-flow repetitions. c [2-NP] = 0.10 mM, [NaOH] = 50.0 mM, average of 3 sets of 15-20 stopped-flow repetitions.

The data in Table 4-3 were obtained using a modification of the pseudo- first-order analysis procedure. The experimental procedure involved recording 2000 point absorbance – time (Abs – t) profiles over about the first half-life of the reactions and

carrying out a sequential first-order analysis on specific point segments of the Abs – t

profiles. The procedure also employed least squares linear correlation but in this case 24

different analyses were carried out over different point segments in the profile. The point 102 segments include points 1-11, 1-21, 1-31, 1-41, 1-51, 1-101, 1-201, 1-301, 1-401, 1-501,

1-601, 1-701, 1-801, 1-901, 1-1001, 1-1101, 1-1201, 1-1301, 1-1401, 1-1501, 1-1601,

1-1701, 1-1801 and 1-1901. If a reaction obeys first-order kinetics the values of the rate constants for all of the point segments are expected to be time independent and have the same value. This procedure was described earlier10 but is repeated here for clarity. A

factor that should be taken into account for the data in Table 4-3 in comparison to that in

Figure 4-1 is that the former corresponds to 2000 points over the first half-life and the

latter to 2000 points over more than 4 half-lives. This difference means that the data

segments for Table 4-3 begin at shorter times than those in Figure 4-1.

What is immediately apparent in Table 4-3 is that in all 3 series of reactions,

involving NM, NE and 2-NP as substrates, is that the kapp – time profiles begin at

relatively high values of kapp and decay with time toward steady state values. Although it

might be argued that the standard deviations of the short time data in Tables B.1 to B.3

(Appendix B) are relatively high, the mean values of three determinations (Table 4-3)

have a small degree of variance and are certainly significant.

E.R. The apparent deuterium kinetic isotope effects (KIEapp ) for all three nitroalkanes were observed to be E.R. dependent, with a low value at low conversion and to increase with increasing E.R.. This is illustrated in Figure 4-2 for the reaction of NE

(0.1 mM) with hydroxide ion (50 mM) and for NM and 2-NP in Figure B.1 and B.3

E.R. (Appendix B), respectively. The KIEapp – time profiles show a similar trend (Figure

B.9 (NM), B.10 (NE), and B.11 (2-NP)) but in this case the values are near unity at zero

time and approach a constant value at longer times where the reactions reach steady 103 states.

8.0

7.5

7.0 KIE ER app 6.5 [NE(-d2 )] = 0.1 mM 6.0 [NaOH] = 50.0 mM in H2 O at 298K 5.5 240nm 5.0 0.00.10.20.30.40.5 E. R.

FIGURE 4-2 Apparent KIE for the reactions of NE and NE-d2 as a function of degree of conversion under the conditions shown

The data discussed in the previous paragraphs clearly rule out a simple one-step

mechanism for the proton transfer reactions between the nitroalkanes and hydroxide ion.

Some form of the reversible consecutive mechanism (Mechanism 1 illustrated in Scheme

4-3) provides a starting point to search for a mechanism that is consistent with the

experimental data. The integrated rate law is available for this mechanism.15

SCHEME 4-3. The 2-Step Reversible Consecutive Mechanism Applied to the Proton - Transfer Reactions Between the Nitroalkanes and OH in H2O (Mechanism 1)

In the simplest form of Mechanism 1 (Scheme 4-3) the intermediate is a pre-association complex in which there are no new covalent bonds formed. Under those circumstances, a steady state would be expected to be reached early in the reaction.

However, contrary to the latter, the reactions of the simple nitroalkanes with hydroxide 104 ion in water reported here do not reach a steady state early in the reactions as shown by the data in Table 4-2. For this reason we believe that Mechanism 1 is unlikely for the proton transfer reactions between the nitroalkanes and hydroxide ion reported here.

A feature of the data in Tables 4-2 and 4-3 of great mechanistic significance is that the time-dependent kapp values for all three substrates decrease from the values at

short times toward steady-state values at longer times. The only circumstance that gives

rise to this general behavior is when the absorbances monitored, primarily due to the

anionic products, also have contributions due to intermediates. For purely product

absorbance (Figure 4-3a) the time-dependent rate constants (kinst) increase from zero to

the steady-state value for mechanism 1 (Figure 4-3b). The most significant point with

regard to the presence of an intermediate is that when the apparent absorbance includes

both that due to product and a significant contribution from an intermediate (Figure 4-3c)

the time-dependent rate constants decay from an initial value to a steady-state value

(Figure 4-3d). The very different form of the kinst – time profiles for analysis of pure

product absorbance (Figure 4-3b) and that in the presence of a significant concentration of intermediate (Figure 4-3d) provides a very definitive mechanism probe.

Due to the fact that we do not have reliable methods to estimate either the absorbance maximum wavelengths or the extinction coefficients of the intermediates, it is

pointless to attempt to fit experimental data to simulated data such as shown in Figure 4-3.

The simulation (Figure 4-3) assumed that the intermediate and product have equal

extinction coefficients in the simulated experiment. 105

a Profile (P) instk (P) b 0.9 0.0075

0.6 0.0050 k /s-1 -1 [P]/[R]o -1 inst kf' = kb = kp = 0.02 s kf' = kb = kp = 0.02 s 0.0025 0.3 t0.5 = 111 s t0.5 = 111 s

0.0 0.0000 0 100 200 300 400 0 100 200 300 400 time/s time/s

c 0.020 d Profile (P+I) instk (P+I) 0.9

0.016 0.6 -1 -1 kinst/s kf' = kb = kp = 0.02 s -1 [P+I]/[R]o k ' = k = k = 0.02 s 0.012 f b p 0.3 t0.5 = 53 s t0.5 = 53 s 0.008 0.0 0 100 200 300 400 0 100 200 300 400 500 time/s time/s

FIGURE 4-3. Simulated concentration – time (a, c) and kinst – time (b, d) profiles for the reversible consecutive mechanism with the rate constants shown, kf’ = kf[Excess Reactant]0

The presence of intermediates during the reactions was confirmed by carrying out the diode-array experiments (Figure 4-4) near the isosbestic points. There is no true isosbestic point for the absorbance – time curves illustrated in Figure 4-4 due to the interference of intermediate absorbance. How the latter can be determined in the presence of absorbance from intermediates is shown in Figure 4-6 in the experimental section. The rationale for these experiments was based upon the fact that reactant and product absorbance changes with time are cancelled at the isosbestic point. The absorbance – time data at the isosbestic points in Figure 4-5 were obtained during the reaction of (a) NE and 106

(b) NE-d2 with hydroxide ion in water at 298 K. Absorbance – time curves at isosbestic

points are shown in Figure B.5 to B.8 (Appendix B) for NE, NE-d2, 2-NP and 2-NP-d1, respectively.

1.2

1.0

0.8 Abs (A.U.) 0.6

0.4

0.2 264 266 268 270 272 (nm)

FIGURE 4-4. Diode-array UV absorption spectra of the reaction between NE-d2 (20.37 - mM) and OH (100.0 mM) in H2O at 298 K: start time, 0 s; cycle time, 10 s; total run time, 300 s

Simulations show that if the intermediate does not absorb at the isosbestic point,

a negative absorbance – time profile is observed due to decreases in absorbance of

reactant and product accompanying the intermediate formation. This is also the case if the

intermediate absorbs with an extinction coefficient less than that of the reactants and

product. The fact that positive absorbance – time profiles were observed (Figure 4-5, B.5

to B.8) suggests that the molecular extinction coefficients of the intermediates are greater

than that of products and reactants at the isosbestic wavelengths in this study.

It should be pointed out that the absorbance – time profiles of the intermediates

in Figure 4-5 (and Figure B.5 to B.8) were obtained at substrate concentrations much 107 greater than were used in the kinetic experiments. The fact that absorbance due to reactants and products cancel at the isosbestic points made the latter determinations possible.

0.356 a 269.6 nm 0.354

Abs / A.U. [NE] = 21.1 mM 0.352 [NaOH] = 50.0 mM

in H2 O at 298K 0.350

0.348 0 5 10 15 20 time/s b 0.52 267.5 nm

0.51 [NE-d2 ] = 20.37mM Abs / A.U. [NaOH] = 100.0 mM 0.50 in H2 O at 298K

0.49

0 50 100 150 200 250 300 time/s

FIGURE 4-5 Abs – time profiles at the isosbestic points for the reactions of (a) NE, (b) - NE-d2 with OH in H2O at 298 K

The absorbances due to the intermediates have a lesser effect on the absorbance

– time profiles under kinetic conditions. The most important effect of intermediate

absorbance under kinetic conditions is that illustrated in Figure 4-3a as compared to that

in Figure 4-3c. For the case where only product absorbs (Figure 4-3a), there is an evident

lag in the onset of product absorbance near zero time while were both product and 108 intermediate to absorb, the absorbance rises sharply from zero time. These facts give rise to a more dramatic effect in the corresponding kinst – time profiles. When only product

absorbs, kinst rises from 0 at zero time to a plateau value when steady state is achieved.

When the intermediate also absorbs at the wavelength where product absorbance is

monitored, kinst decreases from a relatively large value near zero time to the steady-state

plateau value. The latter assumes that the extinction coefficient of the intermediate is

sufficiently large to cause an increase in absorbance at the wavelength where product

evolution is monitored.

SCHEME 4-4. The 3-step Reversible Consecutive Mechanism Applied to the - Reactions Between the Nitroalkanes and OH in H2O (Mechanism 2)

Mechanisms that account for both our kinetic data and for the inverse

relationship between the kinetic and thermodynamic acidities of NM, NE and 2-NP are

necessary. Mechanism 2 (Scheme 4-4) involving either an intra-complex electron transfer

‡ coupled with hydrogen atom transfer (HACET Scheme 4-5) or a polar reaction (kprod) as

‡ It seems reasonable to suggest that electron tunneling will allow thermodynamically unfavorable inter-complex electron transfer to take place at rates greatly exceeding estimations based upon Eo differences. 109 shown in Scheme 4-4, accounts for the observations. In Mechanism 2 it is assumed that the association complex is in equilibrium (Kassoc) with reactants. Simulations of this

mechanism showed that to observe the “late” achievement of the steady state, it requires

kf’ (equal to kRCKassoc), k-RC and kHACET or kprod to be close in magnitude. Our data do not

allow us to differentiate between the two possibilities for product forming reactions

illustrated in Scheme 4-4.

SCHEME 4-5. The Intra-Complex Hydrogen Atom Coupled Electron Transfer from a “Reactant Complex”

The requirement of rate constants of similar magnitude is demonstrated by the

simulated kapp – time profile illustrated in Figure 4-3. With the three pertinent rate

constants equal at a value of 0.02 s-1, nearly three half-lives are required to reach steady

state (Figure 4-3d). The inverse relationship between the thermodynamic and kinetic

acidity can be explained by either option shown in Mechanism 2. First, the Eo values become more negative16 in the order NM > NE > 2-NP and the values of the equilibrium

constants for the formation of the reactant complexes are likely to be in the same order.

Taking these factors into account leads to the prediction that the kinetic order for proton

transfer to hydroxide ion is NM > NE > 2-NP which is the reverse of the thermodynamic acidity order of the substrates. The second option, direct proton transfer within the 110 reactant complex, is consistent with the observed result simply from the fact that the relative rates of reactions of substrates in a 3-step reaction cannot be predicted from the thermodynamic stabilities of reactants and products.

Some comment is necessary in order to explain how we view the association and reactant complexes to differ. The interactions between OH- and the nitroalkanes in the

former are expected to be relatively weak and the two entities are expected to retain their

solvation shells to a large degree. For this reason, the HACET is not expected to be

favorable at this stage. We view the formation of the reactant complex to involve

extrusion of solvent from the two entities and a change in geometry which allows the

concurrent transfer of an electron from hydroxide ion to the nitroalkane and a hydrogen

atom from the nitroalkane to hydroxide ion. The changes taking place in going to the

reactant complexes would also enhance the favorability of the direct proton transfer.

A question which arises from our work in relation to the previous work on these

reactions is: “Why was the complexity in mechanism not observed in the earlier studies?”

The work of Bell and Goodall3a was presented in greater detail than other kinetic work on

this reaction series. The most important details presented3a which explain why the

complexities that we have observed went unnoticed are: (a) the reactions were carried out

for only about one half-life and (b) the rates of reaction were followed by a pH-stat, a

procedure less reliable than the direct spectrophotometric monitoring of product formation used here. 111

Experimental

Materials

3a 2-NP-d1 was prepared by using the literature procedure. The other nitroalkanes

(NM, NE, 2-NP, NM-d3, NE-d2) were obtained commercially from Sigma-Aldrich and

were subjected to an additional purity check by 1H NMR spectrometry before use.

Distilled water was further purified by passing through a Barnsted Nanopure Water

System. Concentrated sodium hydroxide solution was commercially available from

Fisher Scientific, which had been determined by titration with standard oxalic acid

solutions.

Kinetic Experiments

Kinetic experiments were carried out using a Hi-Tech SF-61 stopped-flow spectrometer installed in a glove box and kept under a nitrogen atmosphere. The temperature was controlled at 298 K using a constant temperature flow system connected

directly to the reaction cell in the return pathway to a bath situated outside of the glove

box. All stopped-flow experiments included recording 10 – 20 absorbance – time profiles

at 240 nm. Each experiment was repeated at least three times. The 2000 point absorbance

– time curve data were collected either over 1+ or 5+ half-lives (HL).

Absorbance – time (Abs – t) profiles for product evolution were analyzed

individually by two different procedures. The first step in both procedures was to convert

the Abs – t profiles to (1 – E.R.) – time profiles. E.R. denotes extent of reaction, carried

out by dividing each absorbance value by the maximum absorbance value obtained in the

long-time (>10 HL) kinetic runs, when the reaction goes to completion, such as the 112 profiles shown in Figure 4-1. This procedure gave (1 – E.R.) – time profiles that decayed from (1 – E.R.) = 1 for either 1 or 5 HL depending on which analysis procedure was used.

For pseudo-first-order kinetic analysis, the (1 – E.R.) – time profiles were converted to ln(1 – E.R.) – time profiles. For further processing, the individual 5 HL (1 – E.R.) – time profiles were first averaged to give the average profiles.

The first kinetic procedure used was simply least squares linear correlation of the ln(1 – E.R.) – time profiles to give the apparent pseudo-first-order rate constants over either 1 or 5 HL. These values are recorded in the Results section. The second kinetic procedure, the modified pseudo-first-order analysis, has been described in detail in the former chapter. The second procedure involved recording the Abs – t profiles over slightly more than the first HL followed by the sequential 24 linear correlations described in the Results section.

Determination of Isosbestic Points

The diode-array kinetic experiments were carried out near the apparent

isosbestic points using an Agilent 8453 UV-vis spectrophotometer. The start time and

cycle time were set equal to 0 s and 1 s, respectively. The total run time was dependent

upon how long the reaction takes to reach completion. The resulting Abs – t profiles,

recorded at an interval of 1 s, were first converted to ΔAbs – time profiles by subtracting

the initial value from each absorbance value.

It was pointed out earlier that true isosbestic points were not observed due to the

contributions of absorbance of the intermediates. This is very obvious for the reactions of

NE-d2 (Figure 4-4) and 2-NP-d1 (Figure B.8) in which cases the lifetime of the 113 intermediates appears to be the longest observed. The latter is based upon the fact that the absorbance observed due to the intermediate is substantially greater than all other cases studied (see Figure B.5, B.7). The wavelength judged to be most close to the true isosbestic point was selected based upon the comparison of the ΔAbs – time profiles as shown in Figure 4-6. Although the absolute absorbance values are not known, due to inherent instrumental error, the ΔAbs values are expected to be reliable and have been verified by multiple determinations. The ΔAbs – time profile judged to be most significant is that with the long-time value approaching zero since the concentration of intermediate is expected to approach zero as the reaction goes to completion.

0.04 0.20 266.0 nm a b 0.15 0.03 267.3 nm 0.10 0.02 267.0 nm 0.05  Abs / A.U. 267.4 nm  Abs / A.U. 0.01 0.00 267.5 nm 268.0 nm 0.00 -0.05 267.6 nm -0.01 -0.10 269.0 nm 267.7 nm -0.15 -0.02 0 100 200 300 400 0 100 200 300 400 time/s time/s

- FIGURE 4-6. ΔAbs – time profiles for the reaction of NE-d2 (20.37 mM) with OH (50.0 mM) in H2O at 298 K near the isosbestic point, 267.5 nm (a: from 266.0 nm to 269.0 nm with the increment of 1.0 nm; b: from 267.3 nm to 267.7 nm with the increment of 0.1 nm). ΔAbs = Abst – Abs0

Conclusions

The proton transfer reactions of NM, NE and 2-NP with hydroxide ion in water take place by a complex mechanism. This conclusion is supported by a revised conventional first-order analysis as well as by a sequential first-order analysis designed to show changes with time in the apparent pseudo-first-order rate constant if they exist. For 114 all three reactions the kapp were observed to be relatively large at short times and to

decrease toward steady-state values later in the reaction. Absorbance – time profiles at

isosbestic points show the presence of intermediates which absorb at these wavelengths.

The absorbances due to intermediates are most persistent for NE-d2 (compare the time

scales in Figure B.5 and B.6) and 2-NP-d1 (compare the time scales in Figure B.7 and B.8)

in which the acidic protons are replaced by deuterons. The latter indicates that the

deuterium kinetic isotope effects are not associated with the formation of the

intermediates. This is also illustrated by the fact that the KIE are E.R. dependent

approaching unity near zero time and increasing toward a plateau value as steady state is

achieved. A reversible consecutive mechanism is proposed with two possible product

forming steps involving either a polar proton transfer or an intra-complex Hydrogen

Atom Coupled Electron Transfer from a “reactant complex.”

Refereces

(1) (a) Maron, S. H.; La Mer, V. K. J. Am. Chem. Soc. 1938, 60, 2588. (b) Turnbull, D.; Maron, S. H. J. Am. Chem. Soc. 1943, 65, 212. (c) Wheland, G. W.; Farr, J. J. Am. Chem. Soc. 1943, 65, 1433. (d) Pearson, R. G.; Dillon, R. L. J. Am. Chem. Soc. 1953, 75, 2439.

(2) Kresge, A. J. Can. J. Chem. 1975, 52, 1897.

(3) (a) Bell, R. P.; Goodall, D. M. Proc. Roy. Soc. A 1966, 294, 273. (b) Bordwell, F. G.; Boyle, W., Jr.; Hautala, J. A.; Yee, K. C. J. Am. Chem. Soc. 1969, 91, 4002. (c) Fukuyama, M; Flanagan, P. W. K.; Williams, F. T., Jr.; Franinier, L; Miller, S. A.; Shechter, H. J. Am. Chem. Soc. 1970, 92, 4689. (d) Kresge, A. J. J. Am. Chem. Soc. 1970, 92, 3210. (e) Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1971, 93, 512. (f) Kresge, A. J.; Chen, H.-L.; Chiang,Y.; Murrill, E.; Payne, M. A.; Sagatys, D. S. J. 115

Am. Chem. Soc. 1971, 93, 413. (g) Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1972, 94, 3907. (h) Marcus, R. A. J. Am. Chem. Soc. 1969, 91, 7224. (i) Agmon, N. J. Am. Chem. Soc. 1980, 102, 2164. (j) Albery,W. J.; Bernasconi, C. F.; Kresge, A. J. J. Phys. Org. Chem. 1988, 1, 29.

(4) Keeffe, J. R.; Morey, J.; Palmer, C. A.; Lee, L. C. J. Am. Chem. Soc. 1979, 101, 1295.

(5) (a) Gandler, J. R.; Bernasconi, C. F. J. Am. Chem. Soc. 1992, 114, 631. (b) Bernasconi, C. F.; Wiersema, D.; Stronach, M. W. J. Org. Chem. 1993, 58, 217. (c) Bernasconi C. F.; Ni, J.-X. J. Org. Chem. 1994, 59, 4910. (d) Bernasconi, C. F.; Panda, M; Stronach, M. W. J. Am. Chem. Soc. 1995, 117, 9206. (e) Bernasconi, C. F.; Montañez, R. F. J. Org. Chem. 1997, 62, 8162. (f) Bernasconi, C. F.; Kittredge, K. W. J. Org. Chem. 1998, 63, 1944. (g) Bernasconi, C. F.; Ali, M.; Gunter, J. C. J. Am. Chem. Soc. 2003, 125, 151. (h) Bernasconi, C. F.; Pérez-Lorenzo, M.; Brown, S. D. J. Org. Chem. 2007, 72, 4416.

(6) (a) Bernasconi, C. F.; Wenzel, P. J.; Keeffe, J. R.; Gronert, S. J. Am. Chem. Soc. 1997, 119, 4008. (b) Yamataka, H.; Mustanir; Mishima, M. J. Am. Chem. Soc. 1999, 121, 10223. (c) Bernasconi, C. F.; Wenze, P. J. J. Am. Chem. Soc. 2001, 123, 2430. (d) Bernasconi, C. F.; Wenzel, P. J. J. Org. Chem. 2003, 68, 6870. (e) Keeffe, J. R.; Gronert, S.; Colvin, M. E.; Tran, N. L. J. Am. Chem. Soc. 2003, 125, 11730. (f) Yamataka, H.; Ammal, S. C. ARKIVOC 2003, 59. (g) Sato, M.; Kitamura, Y.; Yoshimura, N.; Yamataka, H. J. Org. Chem. 2009, 74, 1268. (h) Ando, K; Shimazu, Y; Seki, N; Yamataka, H. J. Org. Chem. 2011, 76, 3937.

(7) Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1975, 97, 3447.

(8) Bernasconi, C. F.; Kliner, D. A.V.; Mullin, A. S.; Ni, J. X. J. Org. Chem. 1988, 53, 3342.

(9) Wilson, J. C.; Kallsson, I.; Saunders, W. H., Jr. J. Am. Chem. Soc. 1980, 102, 4780.

(10) Parker, V. D.; Li, Z.; Handoo, K. L.; Hao, W.; Cheng, J.-P. J. Org. Chem. 2011, 76, 1250. 116

(11) (a) Servis, K. L. J. Am. Chem. Soc. 1965, 87, 5495. (b) Servis, K. L. J. Am. Chem. Soc. 1967, 89, 1508.

(12) (a) Zhao, Y.; Lu, Y.; Parker, V. D. J. Am. Chem. Soc. 2001, 123, 1579. (b) Parker, V. D. Pure Appl. Chem. 2005, 77, 1823.

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(14) Parker, V. D. J. Phys. Org. Chem. 2006, 19, 714. Reviewers sometimes object to referring to ln(1 – E.R.) vs. time as the conventional first-order relationship. This is the general relationship which arises from the integration of the one-step mechanism

where E.R. refers to [product]/[reactant]o when [product] is monitored and to

(1-[reactant]/[reactant]o) when [reactant] is monitored.

(15) Johnston, H. S. Gas Phase Reaction Rate Theory; Ronald Press: Berkeley; Appendix, p. 439. A pair of brackets was omitted in third equation in (A-3) on p 439.

(16) (a) Evans, D. H.; Gilieinski, A. G. J. Phys. Chem. 1992, 96, 2528. (b) Petersen, R.; Evans, D. H. J. Electroanal. Chem. Interfacial Electrochem. 1987, 222, 129.

117

CHAPTER 5

KINETICS AND MECHANISMS OF THE PROTON TRNASFER REACTIONS

OF 1-NOTROPROPANE AND NITROCYCLOALKANES

WITH HYDROXIDE ION IN WATER

Abstract

Various conventional and nonconventional pseudo-first-order kinetic analyses of the reactions of 1-nitropropane (1-NP) and the nitrocycloalkanes (NC’s) with hydroxide ion in water revealed that the reactions are complex and involve kinetically significant intermediates. Spectral evidence for the formation of reactive intermediates was obtained by carrying out the kinetic experiments at the isosbestic points where changes in reactant and product absorbance cancel. The apparent deuterium kinetic isotope effects for proton/deuteron transfer are E.R. and time-dependent approaching unity near zero time and increasing with time toward plateau values as the reaction kinetics reach steady state.

The latter indicates that the deuterium kinetic isotope effects are not associated with the formation of the intermediates. All of the experimental kinetic results were found to significantly deviate from pseudo-first-order kinetics and can be rationalized by a three-step reversible consecutive mechanism as has been reported recently.1

Introduction

As the first examples2 of the nitroalkane anomaly,3 proton transfer reactions of

nitromethane (NM), nitroethane (NE) and 2-nitropropane (2-NP) have been extensively

studied during the past half century,3-6 while little attention was devoted to the other

aliphatic nitroalkanes, such as 1-nitropropane (1-NP) and to the nitrocycloalkanes. With 118 time the absence of interest in the latter became more apparent. Especially when another typical example of the nitroalkane anomaly, involving an extensive series of aryl nitroalkanes7,8 referring to an unusual Brønsted exponent greater than one, was reported.

Although the origin of nitroalkane anomaly is a conundrum thus far unanswered,

the fact that kinetic acidities of nitroalkanes are more sensitive to structural changes than

the corresponding thermodynamic acidities is generally accepted.7 The nitroalkane

anomaly with respect to the proton transfer reactions of NM, NE and 2-NP can be

discussed in terms of the effect of methyl substitution at the α-carbon. Likewise, either

the aliphatic series involving successive ethyl substitution at the α-carbon (CH3NO2,

CH3CH2CH2NO2, (CH3CH2)2CHNO2) or that involving methyl substitution at the

β-carbon (CH3CH2NO2, CH3CH2CH2NO2, (CH3)2CHCH2NO2, (CH3)3CCH2NO2) are of

interest for the sake of comparison. Obviously, the reactions of 1-NP, lying in both groups,

can be considered to be of especial importance in the exploration of the nitroalkane

anomaly.

TABLE 5-1. Equilibrium and Kinetic Acidities of Simple Aliphatic Nitroalkanes -1 -1 d pKa k2 (s M ) d H2O H2O/MeOH DMSO w/ NaOH w/ Pyridine NM 10.22a 11.11 17.20e 30 8.04 NE 8.60 a 9.63 16.72e 5.5 2.83 2-NP 7.74a,b 8.85 16.89f 0.26 1-NP 9.0c 9.99 17.01e 4.7 2.17 a b c d e f Ref. 4. Ref. 5. Ref. 13. Ref. 10, in H2O/MeOH (50/50 vol %). Ref. 9. Ref. 11

In the orders of equilibrium acidity in both protic and aprotic solvents (Table

5-1), 1-NP lies between NM and NE. In contrast, the rate of deprotonation for 1-NP is

somewhat lower than that of NE. The latter once more confirmed the general rule that the 119 rates of deprotonation of nitroalkanes are not governed by nitronate ion stabilities.9-12

The effect of ring size on the equilibria and kinetics of the proton transfer

reactions of cyclic nitroalkanes (NC’s) appears to be much more important than the other

structural effects that are also present in the reactions of acyclic nitroalkanes. The order

of equilibrium acidities of nitrocycloalkanes has been found to vary with ring size in the

order: NC8 > NC7 > NC5 > NC4 > NC6 >> NC3 (Table 5-2). However, the relative rates

of deprotonation were observed to vary with ring size in the order: NC4 > NC5 > NC7 >

NC8 > NC6 >> NC3. Except for NC3, nitrocycloalkanes were observed to be more reactive than their acyclic analogs during the proton transfer reactions. Moreover, it is of interest to note that the orders in parameters observed for nitrocycloalkanes in both equilibrium and kinetic acidities are evidently independent of solvents or base strength.

The trends in the latter are dominated by ring properties, which are often quantified using a combination of angle and torsional strain.

TABLE 5-2. Equilibrium and Kinetic Acidities of Nitrocycloalkanes -1 -1 - pKa k2 (s M ) w/ OH H O/MeOH H O/MeOH H O/MeOH H O/dioxane 2 2 DMSOa 2 2 (50/50 vol %)a (67/33 vol %)b (50/50 vol %)a (50/50 vol %)b,c NC3 > 18 26.90 0.0072 NC4 10.05 9.53 17.82 5.4 2.75 NC5 8.15 7.91 16.00 1.4 0.663 NC6 10.07 9.58 17.90 0.28 0.127 NC7 8.15 7.65 15.80 0.87 0.343 NC8 7.37 7.26 0.65 0.267 NC12 9.60 0.13 Me2CHNO2 8.85 16.89 0.26 0.134 Et2CHNO2 10.17 0.039 0.0282 Pr2CHNO2 9.85 0.0118 a Ref. 11. b Ref. 14. c 273 K

120

Although the early studies on nitrocycloalkanes can be trace back to the 1950s, few papers11,14 have been published which systematically discuss the correlation between

kinetic and equilibrium acidities of this reaction series with respect to structural effects.

Until recently15 this topic has not captured the eye of computational chemists.

The determination of the mechanisms of the proton transfer reactions of nitroalkanes is a long-term research topic that we have been devoting a great deal of effort to. The recent reinvestigation1 of the proton transfer reactions of three simple

aliphatic nitroalkanes, NM, NE and 2-NP, with hydroxide ion in water revealed that the

reactions follow a three-step reversible consecutive mechanism (Scheme 4-4) and involve

kinetically significant intermediates.

An extensive study has now been carried out on the kinetics of the proton

transfer reactions of 1-NP and five nitrocycloalkanes (NC4 – NC8) with hydroxide ion in

water, taking advantage of several recently developed analytic procedures for

pseudo-first-order kinetics. The objective of this investigation is to provide convincing

experimental evidence for the correct mechanism for the proton transfer reactions of

1-NP and the nitrocycloalkanes.

Results and Discussion

The anionic products formed in the reactions of 1-NP and nitrocycloalkanes with

hydroxide ion are stable in aqueous solution, and absorb intensively in the range, 225 –

275 nm (UV absorption spectra for corresponding reactions are shown in Figure C.1,

Appendix C). Kinetic measurements were carried out under pseudo-first-order conditions

by monitoring the absorbance evolution of the nitronate ions at 230 – 250 nm. 121

The Conventional View

The apparent second-order rate constants for proton transfer reactions of simple

aliphatic nitroalkanes with hydroxide ion in water (Table 5-3) are in the same order as that for their reactions in H2O/MeOH (50/50 vol %), namely, NM > NE > 1-NP > 2-NP, which is evidently independent of the acid strength. Comparison of the activation energies shows that the activation enthalpy change (ΔH≠) values for NM and NE are

nearly the same, but obviously higher than those of the slower reactions of 1-NP and

2-NP. A similar phenomenon has been found in computational analysis,§ in which the

calculated ΔH≠ values for NM, NE and 2-NP are equal to 12.24, 12.38, and 10.89

kcal/mol, respectively. In contrast, the value of the activation entropy change (ΔS≠) was observed to be more negative in the order: NM > NE > 1-NP > 2-NP, which suggests that the reactivity of these four simple nitroalkanes is mostly determined by ΔS≠.

- TABLE 5-3. pKa’s and Rates with OH of Simple Nitroalkanes in H2O at 298 K -1 -1 ≠ d ≠ d pKa k2 (s M ) ΔH (kcal/mol) ΔS (cal/mol·K) NM 10.22a 25.8 11.54 -13.33 NE 8.60 a 5.37 11.55 -16.38 1-NP 9.0c 4.42 10.72 -19.48 2-NP 7.74a,b 0.362 11.22 -22.88 a Ref. 4. b Ref. 5. c Ref. 13. d Calculated from data obtained at 288, 293, 298, 303 and 308 K.

Negative ΔS≠ indicates a more ordered transition state of the reaction or of the

rate determining step, which is generally attributed to solvation effects and (or) the

association of reactants. It is necessary to point out that the activation energies evaluated

from the conventional apparent second-order rate constants cannot provide much detailed

§ MP2/6-311++g(d,p)//B3LYP/6-31+g(d)/CPCM-UAKS(B3LYP/6-31+g(d)) 122 information of a complex mechanism. However, for the three-step reversible consecutive mechanism (Scheme 4-4) we assumed in a recent paper,1 that the changes in solvation

and geometry during the formation of the reactant complex are sufficient to cause a loss

in the apparent activation entropy (ΔS≠) for the overall reaction. The activation energies

for the deprotonations for nitrocycloalkanes (Table 5-4) may also offer a key to

rationalizing their kinetic reactivities. In comparison to the other nitrocycloalkanes, the

reaction of NC4 has the lowest energy barrier when expressed in enthalpy (ΔH≠),

probably due to the large angle strain energy. Additionally, the particular molecular

structure with respect to acidic hydrogen atom and favorable conformation for charge

delocalization to the nitro group may allow NC4 to react without too much loss in ΔS≠. In

the series of NC5 – NC8, the difference in reactivity has also been explained by the

conformation of acidic proton relative to the nitro group, as well as to the solvation of

transition state.14 All of these factors can exert considerable influence on the value of ΔS≠.

- TABLE 5-4. pKa’s and Rates with OH of Nitrocycloalkanes in H2O at 298 K a -1 -1 ≠ b ≠ b pKa k2 (s M ) ΔH (kcal/mol) ΔS (cal/mol·K) NC4 10.05 5.62 10.92 -18.48 NC5 8.15 1.46 11.26 -19.95 NC6 10.07 0.345 11.39 -22.41 NC7 8.15 0.992 11.52 -19.76 NC8 7.37 0.842 11.16 -21.43 a b Ref. 11, in H2O/MeOH (50/50 vol %). Calculated from data obtained at 288, 293, 298, 303 and 308 K.

Half-Life Dependent Conventional Pseudo-First-Order Rate Constants

The half-life (HL) dependence of pseudo-first-order rate constants, kapp, for the

- proton transfer reactions of 1-NP(-d2) and nitrocycloalkanes with OH in water obtained 123 by the application of conventional pseudo-first-order linear least squares procedure on 5 different segments of the data were determined over time ranges corresponding to 0 – 0.5

HL, 0 – 1 HL, 0 – 2 HL, 0 – 3 HL and 0 – 4 HL. The data in Table 5-5 and Table 5-6 show that the values of kapp steadily decreased with degree of conversion. While the

changes in kapp observed are modest, the corresponding changes in the zero-time

intercepts are much more sensitive to the deviations from first-order kinetics. The

deviation of both of these quantities from that expected for first-order kinetics is a clear

indication of the operation of a complex mechanism, since the response expected for the

simple one-step mechanism is a constant value of kapp and an intercept independent of the

number of HL taken into the linear least squares correlation.

Table 5-5. Changes in the Slopes and the Intercepts with the Extent of Reaction During Conventional Pseudo-First-Order Analysis of the Reactions of 0.1 mM 1-NP, - NC4 and NC5 with OH in H2O at 298 K (240 nm) 1-NPa NC4a NC5b No. HL -1 -1 -1 -1 -1 -1 kapp /s Int. /s kapp /s Int. /s kapp /s Int. /s 0.5 0.218 - 0.000230 0.270 - 0.00449 0.139 - 0.00526 1.0 0.215 0.00177 0.262 0.000210 0.136 - 0.00175 2.0 0.211 0.00859 0.250 0.0172 0.130 0.0148 3.0 0.206 0.0227 0.234 0.0567 0.120 0.0628 4.0 0.198 0.0523 0.202 0.179 0.0948 0.262 a [NaOH] = 50.0 mM. b[NaOH] = 100.0 mM.

Table 5-6. Changes in the Slopes and the Intercepts with the Extent of Reaction During Conventional Pseudo-First-Order Analysis of the Reactions of 0.1 mM NC6, - NC7 and NC8 with 100.0 mM OH in H2O at 298 K (240 nm) NC6 NC7 NC8 No. HL -1 -1 -1 -1 -1 -1 kapp /s Int. /s kapp /s Int. /s kapp /s Int. /s 0.5 0.0328 - 0.00251 0.0958 - 0.00432 0.0818 - 0.00317 1.0 0.0322 0.000820 0.0923 0.00187 0.0795 0.00158 2.0 0.0309 0.0150 0.0858 0.0280 0.0754 0.0203 3.0 0.0290 0.0538 0.0759 0.102 0.0694 0.0697 4.0 0.0247 0.188 0.0550 0.372 0.0568 0.239 124

Time-dependent Apparent (kapp) and Approximate Instantaneous (kIRC) Rate Constants

A kinetic simulation analysis showed that the time ratio, t0.50/t0.05 (times to reach

50 and 5% completion) is equal to 13.5 for simple one-step mechanism, and is ≤ 13.5 for

a two- or multi-step mechanism when product evolution is monitored. However, time

ratios for the reactions of 1-NP and nitrocycloalkanes, measured by monitoring product

evolution, were all larger than 13.5 (Table 5-7). The only circumstance that gives rise to

this abnormal behavior is when intermediates also have significant absorbance at the

wavelengths at the experimental wavelength. In this case, the overlap seems to cover the

whole range of wavelength examined, since large t0.50/t0.05 values are observed at all

wavelengths suitable for spectral measurement.

TABLE 5-7. Time Ratios (t0.50/t0.05) for the Reactions of 0.1 mM 1-NP and - Nitrocycloalkanes with OH in H2O at Various Wavelengths, When Product Evolution Is Monitored at 298 K 1-NPa NC4a NC5b NC6b NC7b NC8b 225 nm 13.99 230 nm 13.80 13.97 13.86 15.22 15.00 13.98 235 nm 13.67 240 nm 13.87 14.00 13.89 13.81 14.54 14.08 245 nm 13.55 250 nm 13.76 16.06 a [NaOH] = 50.0 mM. b[NaOH] = 100.0 mM.

The fact that intermediates absorb at 240 nm can be further verified by the 24

point sequential correlation of Abs – time data over 1 HL. In Table 5-8, kapp – time

profiles decrease from the maximum values of kapp (appear in the first three points) with

time toward steady-state values. The approximate instantaneous rate constant (kIRC) –

time plots in Figure 5-1 provide a convenient visual representation of this trend. Another 125 significant fact for mechanism elucidation revealed in Table 5-8 is that none of these six reactions reach steady state in the first HL. The complete result sets for the 24 point sequential correlation are shown in Table C.1 – C.6 (Appendix C), in which the SD’s are greatest for the initial kapp values but decrease steadily over the first six or seven segments

and then go to a constant value equal to 0.5 percent or less of the corresponding kapp.

Table 5-8. Apparent Rate constants Obtained by the 24-Point Sequential Analysis of - the Reactions of 0.1 mM 1-NP and Nitrocycloalkanes with OH in H2O at 298 K (240nm) k /s-1 No. app 1-NPa NC4a NC5b NC6b NC7b NC8b 1 0.1910 0.1374 0.00201 0.03884 0.0899 0.0900 2 0.2312 0.2862 0.1171 0.03658 0.1133 0.0898 3 0.2291 0.2824 0.1431 0.03557 0.1090 0.0865 4 0.2297 0.2998 0.1511 0.03506 0.1060 0.0850 5 0.2277 0.2962 0.1472 0.03488 0.1040 0.0837 6 0.2249 0.2847 0.1469 0.03465 0.0986 0.0812 7 0.2240 0.2810 0.1450 0.03447 0.0962 0.0812 8 0.2233 0.2796 0.1444 0.03442 0.0951 0.0805 9 0.2229 0.2784 0.1439 0.03434 0.0942 0.0802 10 0.2223 0.2775 0.1437 0.03429 0.0937 0.0799 11 0.2219 0.2766 0.1434 0.03424 0.0932 0.0796 12 0.2217 0.2758 0.1432 0.03420 0.0928 0.0793 13 0.2214 0.2749 0.1430 0.03415 0.0923 0.0790 14 0.2211 0.2743 0.1429 0.03410 0.0919 0.0787 15 0.2209 0.2736 0.1427 0.03406 0.0915 0.0784 16 0.2206 0.2730 0.1425 0.03402 0.0911 0.0781 17 0.2204 0.2723 0.1424 0.03398 0.0907 0.0779 18 0.2202 0.2717 0.1422 0.03394 0.0903 0.0776 19 0.2200 0.2712 0.1420 0.03391 0.0899 0.0773 20 0.2198 0.2706 0.1418 0.03387 0.0896 0.0771 21 0.2196 0.2701 0.1416 0.03384 0.0892 0.0768 22 0.2194 0.2695 0.1415 0.03380 0.0888 0.0766 23 0.2192 0.2689 0.1413 0.03377 0.0884 0.0763 24 0.2190 0.2684 0.1412 0.03374 0.0881 0.0760

a [NaOH] = 50.0 mM. b[NaOH] = 100.0 mM.

126

0.25 a 0.30 b 0.28 0.20 0.26 -1 [1-NP] = 0.10 mM -1 0.24 / s / [NaOH] = 50.0 mM / s [NC4] = 0.10 mM IRC 0.15 IRC 0.22 k k [NaOH] = 50.0 mM in H2 O at 240 nm, 298 K 0.20 in H2 O 0.10 0.18 at 240 nm, 298 K 0.16 0.05 0.14 0.0 0.5 1.0 1.5 2.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time/s time/s 0.16 c 0.04 d 0.14 0.12 0.03 -1 -1 0.10 [NC5] = 0.10 mM [NC6] = 0.10 mM / s [NaOH] = 100.0 mM s / [NaOH] = 100.0 mM IRC IRC 0.08 0.02 k k in H O in H O 0.06 2 2 at 240 nm, 298K 0.04 0.01 at 240 nm, 298 K 0.02 0.00 0.00 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 time/s time/s 0.12 0.10 e f 0.10 0.08 -1 -1 0.08 [NC7] = 0.10 mM 0.06 [NC8] = 0.10 mM / s [NaOH] = 100.0 mM / s [NaOH] = 100.0 mM IRC IRC k k 0.04 in H O 0.06 in H2 O 2 at 240 nm, 298 K at 240 nm, 298 K 0.02 0.04 0.00 0.02 01234 012345 time/s time/s

FIGURE 5-1. Approximate instantaneous rate constant (kIRC) – time profiles for the - reactions of 1-NP (a) and nitrocycloalkanes (b – f) with OH in H2O at 298 K

The initial conclusion arising from the kIRC – time profiles in Figure 5-1 is that the series of time-dependent approximate instantaneous rate constants effectively eliminates the need to consider the simple one-step mechanism, in which the expected result is a straight line with zero slope for any of these reactions. The kIRC – time profiles 127 for product formation during the reactions of the five nitrocycloalkanes and 2-NP increase sharply from relatively low values before reaching the maximum values in the initial 0.1 s, and then slowly decrease towards to constant values as steady state is achieved.

1 In the mechanism analyses in most recent paper, the decreasing kIRC – time profiles are attributed to the significant contribution of intermediates to the apparent absorbances monitored for product evolution. According to this interpretation, the accumulation of intermediates is responsible for the initial sharp increase in absorbance leading to the initial changes in kIRC, since product formation during the initial stages lags

behind the formation of intermediates.

Apparent Deuterium Kinetic Isotope Effects

Conventional deuterium KIE analysis results for the proton and deuterium

transfer reactions of NM, NE, 1-NP, 2-NP and NC6 in water are gathered in Table 5-9. As

reported earlier,2,16 large KIE are generally obtained during the study of the proton transfer reactions of nitroalkanes. According to Bell’s criteria17 for judging the extent of

H D D H proton tunneling from the corresponding Arrhenius parameters (k /k >10, Ea - Ea >

1.35 kcal/mol, AD/AH > 1), convincing evidence for proton tunneling can only be found

for the reaction of 2-NP.

If the reaction follows a complex mechanism and the proton transfer only takes

place in one step, the real KIE may be hidden since the other step(s) that does not involve

an isotope effect.18 We have previously resolved the proton transfer kinetics in order to evaluate the real KIE and the existence of tunneling effects based on the microscopic rate 128

H D 19 constants kp and kp for the steps involving proton and deuteron transfer. However, the

microscopic rate constants for the reactions shown in this chapter are not available due to

a lack of the extinction coefficients of intermediates at the wavelengths monitored during

the kinetic measurements. Of course, the method of apparent deuterium KIE is still

effective under this circumstance.

Table 5-9. KIE and Arrhenius Parameters for Proton- and Deuterium-Transfer - Reactions of Five Aliphatic Nitroalkanes with OH in H2O

NM(-d3) NE(-d2) 1-NP(-d2) 2-NP(-d1) NC6(-d1) KIE (298 K) 8.19 7.96 7.83 7.58 8.01 EaD- EaH (kcal/mol) 0.23 0.31 0.86 2.12 0.88 AD/AH 0.18 0.20 0.526 5.00 0.564

E.R. The apparent deuterium kinetic isotope effects (KIEapp and KIEapp) in Figure

5-2 for the reactions of 1-NP, NC5 and NC6 with hydroxide ion in water were observed

E.R. to be E.R. and time-dependent. The KIEapp – E.R. profiles begin at short times with

relatively low KIEapp values that increase with increasing time and the corresponding

KIEapp – time profiles show the same trend, but in this case the KIEapp values rise from

unity at zero time and approach a constant value at longer times when the steady state is

achieved. This is expected for a reaction with no KIE associated with the initial step,

which means that the C–H bond does not break in the formation step of the intermediate.

It is of interest to compare the apparent KIE profiles obtained over a range of

E.R. temperatures. Figure 5-3 includes four KIEapp – E.R. plots for the reaction of 1-NP

with hydroxide ion at 293, 298, 303 and 308 K, where the 293 K data are in the upper

plot and the 308 K data appear in the lower plot. The latter graphically illustrate the

temperature effect on the KIE values. Moreover, the plots seem to be similar, but not 129 parallel, probably due to the non-equivalent influence of temperature on the different steps. The higher the reaction temperature, the earlier steady state will be attained.

8.0 a 7.5 a' 7.5

ER 7.0 [1-NP(-d )] = 0.10 mM

app 2 7.0 app [1-NP(-d2 )] = 0.10 mM [NaOH] = 20.0 mM KIE

KIE 6.5 [NaOH] = 50.0 mM in H O at 298K 6.5 2 in H O at 298K 240 nm 2 6.0 240 nm 6.0 5.5 0.0 0.1 0.2 0.3 0.4 0.5 0246810 E. R. time/s 7.0 8 b b' 6.5 6

ER 6.0 [NC5(-d)] = 0.10 mM app app [NC5(-d)] = 0.10 mM 5.5 4 [NaOH] = 100.0 mM KIE KIE [NaOH] = 100.0 mM in H2 O 5.0 in H2 O at 240 nm, 298 K at 240 nm, 298 K 2 4.5

4.0 0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 2.0 2.5 E.R. time/s 8.0 8 c c' 7.5 7

ER 6 7.0 app app [NC6(-d)] = 0.10 mM 5 [NC6(-d)] = 0.10 mM KIE KIE 6.5 [NaOH] = 100.0 mM [NaOH] = 100.0 mM 4 in H2 O in H2 O 6.0 at 240 nm, 303 K 3 at 240 nm, 303 K

5.5 2 0.0 0.1 0.2 0.3 0.4 0.5 02468 E.R. time/s E.R. FIGURE 5-2. KIEapp – E.R. profiles (a, b, c) and KIEapp – time profiles (a’, b’, c’) for - the reactions of 1-NP (a, a’), NC5 (b, b’), and NC6 (c, c’) with OH in H2O under the conditions as shown 130

8.5 8.0 7.5

ER 7.0

app 6.5 [1-NP(-d2)] = 0.10 mM

KIE [NaOH] = 50.0 mM 6.0 20 o C in H2O 25 o C 5.5 240 nm 30 o C 5.0 35 o C 4.5 0.0 0.1 0.2 0.3 0.4 0.5 E.R.

E.R. - FIGURE 5-3. KIEapp – E.R. profiles for the reaction of 1-NP (0.1 mM) with OH (50.0 mM) in H2O at various temperatures

Absorbance at Isosbestic Points

For reactions following a complex mechanism, the isosbestic point can provide a potential way to trace the intermediate,20 since the absorbance changes of reactant and

product are effectively cancelled at that wavelength assuming the intermediate

concentration is low. We have observed reliable absorbance – time profiles for evolution

and decay of intermediates in the diode-array experiments carried out at apparent

isosbestic points for the proton transfer reactions of NM, NE and 2-NP.1 Similar curves

(Figure 5-4) were also found in the reactions of 1-NP and the nitrocycloalkanes, which

clearly indicate the presence of intermediates during these reactions. The analysis of the

absorbance – time curves at isosbestic points for the other aliphatic nitroalkanes, as well

as the general features of the application of isosbestic points in mechanistic analysis will

be introduced amply in the following chapter. 131

0.68 a b 260.7 nm 0.195 261.6 nm 0.66 0.190 [NC8] = 0.34 mM 0.64 [NC7] = 1.0 mM 0.185 [NaOH] = 20.0 mM [NaOH] = 20.0 mM Abs/A.U. in H O, 298K

Abs/A.U. 2 in H O, 303K 0.62 2 0.180

0.60 0.175

0 100 200 300 400 500 600 0 500 1000 1500 time/s time/s Figure 5-4. Abs – time profiles at the isosbestic points for the reactions of (a) NC7, (b) - NC8 with OH in H2O

Mechanism Elucidation

The primary credo that a physical organic chemist should inscribe to memory is

that we can only reject alternatives rather than prove a mechanism. The simple one-step

mechanism can be ruled out as the data discussed in the previous paragraphs show.

Considering the two-step reversible consecutive mechanism previously proposed for

several reactions in papers from this laboratory,19,21 the intermediate is assumed to arise

from the encounter complex and is viewed as a “kinetically significant” pre-association

complex and expected to form very rapidly, which would imply to achieving steady state

in the early stages of the reaction. In contrast, the reactions of 1-NP and nitrocycloalkanes

with hydroxide ion in water do not reach a steady state in the first half-life. Therefore,

this basic version of the mechanism for nitroalkane proton transfer must be extended in

order to fit the kinetic data. An appropriate change is to propose that a second

intermediate lies between the pre-association complex and products.

In our recent papers1 dealing with the reactions of NM, NE and 2-NP, a

three-step reversible consecutive mechanism (Scheme 4-4) was proposed, where the 132 initially formed pre-association complexes are transformed to more intimate reactant complexes which can give products by two possible pathways involving either a polar proton transfer or an intra-complex hydrogen atom coupled electron transfer reaction

(HACET). None of the kinetic results of the reactions of 1-NP and nitrocycloalkanes reported here is inconsistent with this three-step complex mechanism. In other words, it is appropriate to propose the mechanism in Scheme 4-4 for the proton transfer reactions of

1-NP and nitrocycloalkanes with hydroxide ion in water, which is reproduced in Scheme

5-1. It is necessary to emphasize that the spectral evidence of intermediate obtained in isosbestic point analysis should be attributed to the reactant complex, rather than the loose association complex (or encounter complex) which is not expected to be of kinetic significance.

SCHEME 5-1. The Three-Step Reversible Consecutive Mechanism Applied to the - Reactions Between the Aliphatic Nitroalkanes and OH in H2O

H kassoc NO Association 2 +OH Complex R1 k-assoc R2 k Association RC Reactant Complex k-RC Complex

kHACET O Reactant R1 or CN +HOH Complex O R2 kprod

Although our mechanism discussion in this chapter led to the proposal of the

three-step reversible consecutive mechanism for the proton transfer of the simple

nitroalkanes as previously shown to be consistent with all available data for the aliphatic

nitroalkanes, we were unable to distinguish between two possible product forming steps. 133

Further work is expected to clarify this issue and add detail to this mechanism.

Experimental Section

Materials

1-NP, NC5 and NC6 were obtained commercially from Sigma-Aldrich and were further purified by reduced pressure distillation and subjected to an additional purity check by 1H NMR spectrometry before use. NC4, NC7 and NC8 were prepared by using

22 a modification of the literature procedure (90% H2O2 was replace by 50% H2O2). The deuterated analogues, 1-NP-d2, NC5-d1 and NC6-d1, were prepared by following the

procedure suggested by Bell.2

Distilled water was further purified by passing through a Barnsted Nanopure

Water System. Fresh concentrated sodium hydroxide solution was commercially

available from Fisher Scientific, which had been determined by titration with standard

oxalic acid solutions.

Kinetic Experiments

Kinetic experiments (except isosbestic point study) were carried out using a

Hi-Tech SF-61 stopped-flow spectrometer installed in a glove box and kept under a

nitrogen atmosphere. The temperature was controlled by a constant temperature flow

system connected directly to the reaction cell in the return pathway to a bath situated

outside of the glove box.

All stopped-flow experiments included recording 10 – 20 absorbance – time

(Abs – t) profiles for product evolution at 225 – 250 nm. The 2000 point Abs – t curve 134 data were collected either over 1+ or 5+ HL, and then converted to (1 – E.R.) – time profiles that decayed from (1 – E.R.) = 1. The value of E.R. was calculated by dividing each absorbance value by the maximum absorbance value obtained in the long-time (>10

HL) kinetic runs, when the reaction goes to completion.

(1 – E.R.) – time profiles derived from experimental data collected over 5+ HL were used for the analysis procedure to figure out half-life dependence of kapp. The 24 point sequential correlation and apparent instantaneous rate constants analysis were applied on the (1 – E.R.) – time profiles over 1 HL.

Determination of Isosbestic Points

The diode-array kinetic experiments were carried out near the apparent

isosbestic points using an Agilent 8453 UV-vis spectrophotometer. The start time and

cycle time were set equal to 0 s and 1 s, respectively. The total run time was dependent

upon how long the reaction takes to reach completion. The resulting Abs – t profiles,

recorded at an interval of 1 s, were first converted to ΔAbs – time profiles by subtracting

the initial value from each absorbance value. The ΔAbs – time profile judged to be most

significant is that with the long-time value approaching zero since the concentration of

intermediate is expected to approach zero as the reaction goes to completion.

Refereces

(1) Li, Z; Cheng, J.-P.; Parker, V. D. Org. Biomol. Chem. 2011, 9, 4563.

(2) Bell, R. P.; Goodall, D. M. Proc. R. London, Ser. A 1966, 294, 273.

(3) Kresge, A. J. Can. J. Chem. 1974, 52, 1897. 135

(4) (a) Maron, S. H.; La Mer, V. K. J. Am. Chem. Soc. 1938, 60, 2588. (b) Wheland, G. W.; Farr, J. J. Am. Chem. Soc. 1943, 65, 1433. (c) Pearson, R. G.; Dillon, R. L. J. Am. Chem. Soc. 1953, 75, 2439. (d) Pearson, R. G.; Williams, F. V. J. Am. Chem. Soc. 1954, 76, 258.

(5) (a) Maron, S. H.; La Mer, V. K. J. Am. Chem. Soc. 1939, 61, 692. (b) Turnbull, D.; Maron, S. H. J. Am. Chem. Soc. 1943, 65, 212.

(6) (a) Kresge, A. J. J. Am. Chem. Soc. 1970, 92, 3210. (b) Kresge, A. J.; Drake, D. A.; Chiang, Y. Can. J. Chem. 1974, 52, 1889.(c) Lewis, E. S.; Funderburk, L. H. J. Am. Chem. Soc. 1967, 89, 2322. (d) Gregory, M. J.; Bruice, T. C. J. Am. Chem. Soc. 1967, 89, 2327. (e) Dixon, J. E.; Bruice, T. C. J. Am. Chem. Soc. 1970, 92, 905.

(7) (a) Bordwell, F. G.; Boyle, W., Jr.; Hautala, J. A.; Yee, K. C. J. Am. Chem. Soc. 1969, 91, 4002. (b) Bordwell, F. G.; Boyle, W., Jr.; Yee, K. C. J. Am. Chem. Soc. 1970, 92, 5926.

(8) Fukuyama, M; Flanagan, P. W. K.; Williams, F. T., Jr.; Franinier, L; Miller, S. A.; Shechter, H. J. Am. Chem. Soc. 1970, 92, 4689.

(9) Bordwell, F. G.; Bartmess, J. E. J. Org. Chem. 1978, 43, 3101.

(10) Bordwell, F. G.; Bartmess, J. E.; Hautala, J. A. J. Org. Chem. 1978, 43, 3107.

(11) Bordwell, F. G.; Bartmess, J. E.; Hautala, J. A. J. Org. Chem. 1978, 43, 3113.

(12) Bordwell, F. G.; Hautala, J. A. J. Org. Chem. 1978, 43, 3116.

(13) Bell, R. P.; Higginson, W. C. E. Pro. Royal Soc. 1949, 197, 141.

(14) Flanagan, P. W. K.; Amburn, H. W.; Stone, H. W.; Traynham, J. G.; Shechter, H. J. Am. Chem. Soc. 1969, 91, 2797.

Yamataka, H.; Ammal, S. C. ARKIVOC 2003, 59. (g) Sato, M.; Kitamura, Y.; Yoshimura, N.; Yamataka, H. J. Org. Chem. 2009, 74, 1268. (h) Ando, K; Shimazu, Y; Seki, N; Yamataka, H. J. Org. Chem. 2011, 76, 3937.

(16) (a) Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1971, 93, 512. (b) Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1975, 97, 3447.

(17) (a) Bell, R. P. Trans. Faraday Soc. 1959, 55, 1. (b) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: London, 1980.

(18) (a) Parker, V. D. Pure Appl. Chem. 2005, 77, 1823. (b) Parker, V. D.; Hao, W.; Li, Z.; Scow, R. Int. J. Chem. Kinet. 2012, 44, 2.

(19) (a) Zhao, Y.; Lu, Y.; Parker, V. D. J. Am. Chem. Soc. 2001, 123, 1579. (b) Parker, V. D.; Zhao, Y. J. Phys. Org. Chem. 2001, 14, 604.

(20) Bunnett, J. F. In Investigation of Rates and Mechanisms of Reactions, Part 1: General Considerations and Reactions at Conventional Rates, 3rd ed.; Lewis, E. S., Ed.; John Wiley: New York, 1974; Chapter 4.

(21) (a) Parker, V. D.; Zhao, Y.; Lu, Y.; Zheng, G. J. Am. Chem. Soc. 1998, 120, 12720. (b) Lu, Y.; Zhao, Y.; Parker, V. D. J. Am. Chem. Soc. 2001, 123, 5900. (c) Zhao, Y.; Lu, Y.; Parker, V. D. J. Chem. Soc., Perkin Trans. 2 2001, 1481. (d) Parker, V. D.; Zhao, Y.; Lu, Y. Electrochemical Society, Proceedings, Volume 2001-14; pp 1-4. (e) Parker, V. D.; Lu, Y.; Zhao, Y. J. Org. Chem. 2005, 70, 1350. (f) Handoo, K. L.; Lu, Y.; Zhao, Y.; Parker, V. D. Org. Biomol. Chem. 2003, 1, 24. (g) Lu, Y.; Handoo, K. L.; Parker, V. D. Org. Biomol. Chem. 2003, 1, 36. (h) Parker, V. D.; Lu, Y. Org. Biomol. Chem. 2003, 1, 2621. (i) Lu Y.; Zhao, Y.; Handoo, K. L.; Parker, V. D. Org. Biomol. Chem. 2003, 1, 173. (j) Handoo, K. L.; Lu, Y.; Parker, V. D. J. Am. Chem. Soc. 2003, 125, 9381. (k) Parker, V. D. J. Phys. Org. Chem. 2006, 14, 604. (l) Hao, W.; Parker, V. D. J. Org. Chem. 2008, 73, 48.

(22) Caldin, E. F.; Jarczewski, A.; Leffek, K. T. Trans. Faraday Soc. 1971, 67, 110.

137

CHAPTER 6

ISOSBESTIC POINTS STUDY OF THE PROTON TRANSFER REACTIONS

OF ALIPHATIC NITROALKANES WITH HYDROXIDE ION

IN AQUEOUS SOLUTIONS. A METHOD TO VERIFY

THE PRESENCEOF AN INTERMEDIATE

Abstract

The UV-vis spectrophotometric investigation of the proton transfer reactions of nine common aliphatic nitroalkanes with hydroxide ion in aqueous solutions revealed that there is no true isosbestic point found at the wavelengths where the extinction coefficients for reactants and products are equal. However, a series of evolution and decay absorbance

– time profiles, consistent to the absorbance characteristic of the formation of reactive intermediates, were observed at these apparent isosbestic wavelengths. The latter clearly indicate that the reactions are complex and involve kinetically significant intermediates.

Several procedures to verify the contribution of intermediates to the changes of absorbance were also carried out, and suggest that an isosbestic point study provides a means to trace the formation and decay of an intermediate. Moreover, the analysis revealed that the occurrence of a true isosbestic point is expected to be observed during the spectrophotometric study of a complex mechanism under the special circumstance where the reactant, intermediate and product all have the same extinction coefficient.

Introduction

Isosbestic points1 are commonly observed in the study of chemical reactions by

UV-vis,2-25 IR,26-28 fluorescence,29-30 and electronic31-34 spectroscopies, since absorbance 138 bands of products and reactants are generally broad and frequently overlap. Isosbestic point is defined1 as the wavelength, wave number, or frequency at which the total

absorbance of a sample does not change during a chemical reaction or a physical change

of the sample. A simple example of the occurrence of an isosbestic point is when two

substances, one of which can be converted into the other, have the same extinction

coefficient at a given wavelength.

Discussions of isosbestic points began as early as 1937.2 The first complete

isosbestic point theory was offered by Cohen and Fischer3 in 1962. Their conclusion is

that the appearance of an isosbestic point in a closed system requires that the changes in

the concentrations of the various components be linearly related. Although it was

criticized for lack of considerations of temperature and solvent composition,4 Cohen and

Fisher’s theory is generally accepted in practical kinetic studies with respect to the

developments in both theoretical5-7 and methodological8-10 aspects.

It is most often desirable to carry out kinetic measurements at wavelengths

where only product or reactant absorbs in order to avoid complications such as that due to

isosbestic points. However, analyses near isosbestic points can be carried out

qualitatively and quantitatively, and have been widely used as reference points for the

calibration of spectrophotometers35 and for chemical qualitative analysis.37

The existence of well-defined isosbestic points (true isosbestic points) has often

been considered to be proof of a single-step conversion11-18 or a parallel mechanism.19 On the other hand, the absence of a true isosbestic point, but rather a series of steadily shifting intersection points, has been attributed to complications in the reaction 139 mechanism.20-24 The isosbestic wavelength shift has been utilized to estimate the

conversion fraction of a precursor to the product.36 Recently, more and more chemical

physicists31-34 have paid attention to the occurrence of isosbestic points, and compared

these to the fingerprints of electronic correlations.34

Cohen and Fischer3 suggested that true isosbestic points would not occur in the

consecutive reactions, namely A → B → C, which is also the criterion often used to

differentiate the parallel and consecutive mechanisms.10 If the intermediate B

accumulates before converting to C, Bunnett38 presumed that evidence for the formation

of intermediate B could be obtained at the isosbestic point between A and C absorbance.

In our recent study39 of the proton transfer reactions of three simple nitroalkanes,

absorbance – time profiles due to the intermediates were observed at the isosbestic points.

Later, the same phenomenon at isosbestic point was also found during the course of this

work on other aliphatic nitroalkanes. The spectral evidence for intermediates and the

recent development in methodology will be discussed in detail in this chapter.

Theoretical Investigation

According to Cohen and Fischer’s theory, true isosbestic points are only

observed during spectral studies of reactions following the simple one-step mechanism

(or the parallel mechanism involving two or more parallel simple one-step

transformations), since the changes in the concentration of the product and reactant are

only linearly related under these conditions (Figure 6-1a). In contrast, the concentration

ratio of product to reactant is not constant for the reversible consecutive mechanism due

to the interference of intermediate absorbance, as shown as Figure 6-1b, especially during 140 the time before steady state has been achieved, the concentration ratio obviously varies with time. The latter would not result in a true isosbestic point, but a series of moving points at which spectral curves intersect. We have already indicated the one exception to this rule, when intermediate, product and reaction have the same extinction coefficient.

1.0 1-step mechanism 0.6 2-step reversible consecutive mechanism 0.8 k1 = 0.1 0.4 k = 0.1 0.6 app kf' = 0.2, kb = kp = 1 0.2 [Product] [Product] 0.4 steady state 0.2 0.0

0.0 non-steady state -0.2 1.0 0.8 0.6 0.4 0.2 0.0 1.00.80.60.4 [Reactant] [Reactant] (a) (b)

FIGURE 6-1. Correlation between the concentrations of product and reactant during the reactions following (a) simple one-step and (b) reversible consecutive mechanisms

For reactions following the two-step reversible consecutive mechanism shown in

Figure 6-1b, the observed absorbance can be treated as the sum of absorbances due to reactant, intermediate and product. According to the Lambert–Beer law, the observed absorbance is expressed as eq 6.1, where l and ε represent the path length of the optical cell and the molar extinction coefficient, respectively, and the stoichiometric ratio between reactant, intermediate and product is assumed to be 1:1:1.

Abs = [R]εRl + [P]εPl + [I]εIl (6.1)

At the isosbestic point of reactant and product, εR and εP have the same value, which is 141 defined as isosbestic extinction coefficient, εP/R, thus,

IP Abs = [R]εP/Rl + [P]εP/Rl + [I]εIl (6.2)

IP Abs = ([R] + [P] + [I])εP/Rl + [I]l(εI - εP/R) (6.3)

= [R]0εP/Rl + [I]l(εI – εP/R) (6.4)

IP = Abs0 + [I]l(εI – εP/R) (6.5)

define ΔAbs as the change in absorbance at a particular time, namely ΔAbst = Abst – Abs0.

As a result, ΔAbs at the isosbestic point (ΔAbsIP) is expressed as eq 6.6, which clearly

shows that the change of absorbance at the isosbestic point should be attributed to the

intermediate, since [I] is the only variable factor.

IP ΔAbs = [I]l(εI – εP/R) (6.6)

In eq 6.6, (εI – εP/R) is such an important factor that it can determine the form and

show the significance of the ΔAbs – time profile. If εI – εP/R > 0, all calculated values of

ΔAbs are positive, as shown in Figure 6-2, if εI – εP/R < 0, including the case of εI = 0, a negative ΔAbs – time profile will be observed.

0.006 [A]0 = 0.2 mM  -  = 104 k ' = 0.874 s-1 0.004 I P/R f k = 14.8 s-1 0.002 b -1 kp = 12.4 s 0.000 Abs / Abs A.U.  -0.002 4 -0.004  I -  P/R = -10

-0.006 0 5 10 15 time/s

FIGURE 6-2. Calculated ΔAbs – time profiles at the isosbestic point of reactant and product for the two-step reversible consecutive mechanism 142

If the values of εI and εP/R are the same (εI – εP/R = 0) or very nearly the same, the

kinetic experiment cannot provide a profile having the characteristic intermediate absorbance, but instead a nearly flat line swinging up or down in the neighborhood of zero within experimental error. Under these circumstances, an apparently well defined isosbestic point would be observed. Another case to observe a true isosbestic point will occur when the intermediate is short-lived on the time scale employed, and its absorbance

is negligible throughout the reaction.

In summary, the theoretical analysis above reveals that apparently true isosbestic

points may be observed in consecutive reactions. An isosbestic point study can provide an

efficient way to differentiate between the complex mechanism and the one-step

mechanism as long as intermediate absorbance is significant. In order to obtain spectral

evidence for an intermediate at the isosbestic point for reactant and product, two factors

are required, which are (1) a significant [I] builds up during the reaction, and (2) the

difference between εI and εP/R is not too small.

Methods and Results

The aliphatic nitroalkanes discussed here include nitromethane (NM),

nitroethane (NE), 1-nitropropane (1-NP), 2-nitropropane (2-NP), nitrocyclobutane (NC4),

nitrocyclopentane (NC5), nitrocyclohexane(NC6), nitrocycloheptane (NC7) and

nitrocyclooctane (NC8), as well as the deuterium analogs of some of these, such as

NE-d2, 1-NP-d2, 2-NP-d1, NC5-d1 and NC6-d1.

40 It has been reported that the aliphatic nitroalkanes exhibit very weak (εmax ~ 15

– 45) UV absorbance bands at 250 – 284 nm in aqueous solutions. In contrast, the 143 corresponding nitronate ions absorb intensely (εmax > 7000) at 220 – 275 nm. In the

proton transfer reactions of aliphatic nitroalkanes and sodium hydroxide (no absorbance >

220 nm) in aqueous solutions, the spectra for reactant and product intersect in the range

of 260 – 270 nm, which results in a series of apparent isosbestic points.

Diode-array UV-vis spectrophotometric experiments were carried out at wavelengths near the apparent isosbestic points. There are no true isosbestic points for

Abs – time curves illustrated in Figure 6-3, in which the intersections between the curve for first scan and subsequent curves change steadily towards lower wavelengths.

0.8 0.8 a b 0.7 [NE-d2] = 20.4 mM [2-NP-d ] = 19.5 mM 0.7 1 [NaOH] = 100.0mM [NaOH] = 100.0 mM in H O 0.6 1 2 in H2O 0.6 1 0.5 1 Abs (A.U.) Abs 1

Abs (A.U.) Abs 0.5 0.4 Run time = 300 s Run time = 900 s Cycle time = 10 s Cycle time = 30 s 0.3 0.4

266 267 268 269 270 267 268 269 270 271 272 (nm)  (nm)

FIGURE 6-3. Diode-array UV absorption spectra of the reactions of (a) NE-d2 (20.4 - mM), (b) 2-NP-d1 (19.5 mM) with OH (100.0 mM) in H2O at 298K

The wavelength judged to be most close to the true isosbestic point was selected

based upon the comparison of the ΔAbs – time profiles as shown in Figure 6-4. At the

true isosbestic points, the long-time values of ΔAbs should approach zero for the complex

mechanism since the absorbance of the intermediate is expected to approach zero as the

reaction goes toward completion. In Figure 6-4a, the isosbestic point was found between 144

267 and 268 nm. Figure 6-4b shows the Abs-time curves from 267.3 nm to 267.7 nm with a small increment of 0.1 nm. The true isosbestic point was finally determined at 267.5 nm

(Figure 6-5a). The Abs – time curves for the proton transfer reactions of some nitroalkanes with hydroxide ion in water at the isosbestic points are shown in Figure 6-5, which clearly illustrate the rise and fall of absorbance due to the formation and decay of intermediates during the reactions.

0.20 a 266.0 nm 0.15 0.10 267.0 nm 0.05

Abs / A.U. 0.00  268.0 nm -0.05

-0.10 269.0 nm -0.15 0 100 200 300 400 time/s

0.04 b 0.03 267.3 nm 0.02 267.4 nm 0.01 Abs /A.U.

 267.5 nm 0.00 267.6 nm -0.01 267.7 nm -0.02 0 100 200 300 400 time/s

- FIGURE 6-4. ΔAbs – time profiles for the reaction of NE-d2 (20.4 mM) with OH (50.0 mM) in H2O at 298K near the isosbestic point, 267.5 nm (a: from 266.0 nm to 269.0 nm with the increment of 1.0 nm; b: from 267.3 nm to 267.7 nm with the increment of 0.1 nm). ΔAbst = Abst – Abs0 145

b 0.52 267.5 nm a 0.454 268.4 nm

0.452 [2-NP] = 20.9 mM 0.51 [NaOH] = 100.0 mM [NE-d2 ] = 20.4mM 0.450 in H O at 298K [NaOH] = 100.0 mM 2 Abs / A.U. 0.50 in H O at 298K Abs / A.U. 2 0.448

0.49 0.446

0 50 100 150 200 250 300 0 50 100 150 200 250 300 time/s time/s

0.08 0.58 c d 269.4 nm 270.4 nm 0.57 0.06 [1-NP-d2 ] = 19.8 mM 0.56 [2-NP-d1 ] = 19.5 mM [NaOH] = 100.0 mM 0.04 [NaOH] = 100.0 mM in H O at 298K 0.55 2

in H O at 298K Abs / A.U. Abs / A.U. 2 0.54 0.02

0.53 0.00 0.52 0 200 400 600 800 1000 0 100 200 300 400 500 600 time/s time/s

0.68 e f 260.7 nm 0.195 261.6 nm 0.66 0.190 [NC8] = 0.34 mM 0.64 [NC7] = 1.0 mM [NaOH] = 20.0 mM 0.185

[NaOH] = 20.0 mM Abs/A.U. in H2 O, 298K Abs/A.U. in H O, 303K 0.62 2 0.180

0.60 0.175

0 100 200 300 400 500 600 700 0 500 1000 1500 2000 time/s time/s

FIGURE 6-5. Abs – time profiles at the isosbestic points for the reactions of (a) NE-d2, - (b) 2-NP, (c) 2-NP-d1, (d) 1-NP-d2, (e) NC7 and (f) NC8 with OH in H2O

146

The Abs – time profiles at the isosbestic points shown in Figure 6-5 were observed in the experiments using a diode-array UV-vis spectrophotometer, which requires the reactions to be sufficiently slow to provide a long time window ( > 10 s) for monitoring the absorbance evolution to a maximum or decay to a minimum.

Isosbestic point studies of more rapid reactions can be carried out using a stopped-flow spectrophotometer by following the same procedures. Figure 6-6 is an example illustrating a stopped-flow determination of the isosbestic point for the reaction between 2-NP-d1 (40.0 mM) and hydroxide ion (100.0 mM) in water. In Figure 6-6b, the

isosbestic point was found at 271.2 nm, but it was observed at 269.4 nm in Figure 6-5c

([2-NP-d1]0 = 20.0 mM). Differences observed in isosbestic wavelengths using different

spectrophotometers are due to the inherent errors in the latter. More stopped-flow derived

Abs – time profiles at the isosbestic points for the faster reactions are shown in Figure

6-7.

0.12 0.10 a 0.90 271.2 nm b [2-NP-d ] = 40.0 mM 0.08 1 0.88 [NaOH] = 100.0 mM 0.06 [2-NP-d1 ] = 40.0 mM in H O at 298K 0.04 2 0.86 [NaOH] = 100.0 mM 271.0 nm in H O at 298K Abs / A.U. 0.02 2 Abs/A.U. 0.84  271.1 nm 0.00 271.2 nm 0.82 -0.02 271.3 nm 271.4 nm -0.04 0.80 -0.06 0 400 800 1200 1600 2000 2400 0 500 1000 1500 2000 time/s time/s

FIGURE 6-6. (a) ΔAbs – time profiles near the isosbestic point 271.2 nm, and (b) Abs – - time profile at the isosbestic points for the reaction of 2-NP-d1 (40.0 mM) with OH (100.0 mM) in H2O at 298K, measured by SF-61 stopped-flow spectrophotometer 147

0.356 269.6nm a 0.700 269.8nm b 0.354 0.695 [NE] = 21.1mM [2-NP] = 40.6 mM [NaOH] = 100.0 mM 0.352 [NaOH] = 50.0mM 0.690 in H2 O at 298K in H2 O at 298K Abs / A.U. Abs /A.U. 0.350 0.685

0.348 0.680

0 5 10 15 20 0 50 100 150 200 250 300 time/s time/s

0.140 0.396 d 273.6 nm c 270.6 nm 0.394 [1-NP] = 19.1 mM 0.135 [NC4] = 2.7 mM 0.392 [NaOH] = 20.0 mM [NaOH] = 20.0 mM 0.390 in H2 O at 298K 0.130 in H2 O, at 298K

0.388 Abs/A.U. Abs / A.U. 0.386 0.125 0.384 0.382 0.120 0 50 100 150 200 0 20406080100 time/s time/s

0.670 1.02 e 0.668 275.7 nm f 270.0nm 0.666 [NC6] = 21.0 mM 1.00 0.664 [NaOH] = 100.0 mM in H O at 298K 0.662 2 0.98 [NC5] = 40.3 mM 0.660 Abs / A.U. Abs/ A.U. [NaOH] = 100.0 mM 0.658 0.96 in H2 O at 298K 0.656 0.94 0.654 0.652 0 102030405060 0 50 100 150 200 time/s time/s

Figure 6-7. Abs – time profiles at the isosbestic points for the reactions of (a) NE, (b) - 2-NP, (c) 1-NP, (d) NC4, (e) NC5 and (f) NC6 with OH in H2O, measured by SF-61 stopped-flow spectrophotometer 148

The observation that the absorbance changes in all profiles shown above are positive in all cases indicate that the extinction coefficients of the intermediates are greater than that of products and reactants at the isosbestic wavelengths under those conditions (in H2O at 298 or 303 K). On the other hand, according to the prediction based on eq 6.6, Abs – time profiles with negative absorbance changes may be observed at the

isosbestic wavelengths where εI is less than εP/R. The latter was readily affirmed by the

isosbestic points study (Figure 6-8) of the proton transfer reactions of NC5-d1 and

NC6-d1 in H2O-MeOH (50/50 vol %).

1.14 1.02 266.5 nm a 1.13 271.8 nm b 1.12 1.00 1.11 0.98 1.10 [NC6-d ] = 40.3 mM

[NC5-d ] = 40.3 mM Abs/A.U. 1 Abs/A.U. 1 1.09 0.96 [NaOH] = 100.0 mM [NaOH] = 100.0 mM 1.08 in H O:MeOH = 1:1 in H2 O:MeOH = 1:1 2 0.94 303K 1.07 303K 1.06 0 200 400 600 800 1000 0 500 1000 1500 2000 time/s time/s

FIGURE 6-8. Abs – time profiles at the isosbestic points for the reactions of (a) NC5-d1, - and (b) NC6-d1 with OH in H2O/MeOH (50/50 vol %) at 303K

In the isosbestic point study of the reaction between NM and hydroxide ion in

water, an intermediate-like Abs – time profile (Figure 6-9b) was observed at 282.8 nm

where the spectra of reactant and product intersect (Figure 6-9a). Although it involves a small rise part in the first 0.5 s, the maximum ΔAbs (0.004 A.U.) is so small that the absorbance change due to the intermediate cannot be differentiated from the instrumental noise. A reasonable explanation is that the intermediate may be too reactive to accumulate 149 in an appreciable amount to be detected. Of course, 0.004 A.U. may not be negligible if the profile in Figure 6-9b had been treated with a suitable data smoothing program.

However, it is necessary to point out that the Abs – time profiles shown above are all obtained from the experimental raw data without any smoothing procedure. This was done in order to provide unambiguous evidence for the formation of the intermediates during the proton transfer reactions of the nitroalkanes in aqueous solutions.

3.0 a 0.254 282.8nm b 2.5 [NM] = 19.9 mM 0.252 [NaOH] = 20.0 mM [NM] = 19.9 mM 2.0 in H2O at 298K [NaOH] = 50.0 mM 0.250 1.5 in H2 O at 298K Abs / A.U. / Abs Abs / A.U. 1.0 0.248 Abs0 Abs 0.5 0.246 0.0 200 225 250 275 300 325 350 375 0.0 0.5 1.0 1.5 2.0 2.5 3.0 / nm time/s

FIGURE 6-9. (a) UV absorption spectra and (b) Abs – time profile at 282.8 nm for the - reactions between NM (19.9 mM) and OH in H2O at 298K

Discussion

It should be pointed out that the Abs – time profiles shown above were obtained at substrate concentrations much greater than were used in the kinetic experiments ( ≥ 20

mM vs. ~ 0.1 mM), in order to observe significantly large absorbance changes of the intermediates at isosbestic points. Using these conditions we were able to strongly confirm the presence of the intermediates and to further verify the validity of the assignment of a complex mechanism for the proton transfer reactions of aliphatic nitroalkanes with hydroxide ion in aqueous solutions. 150

In accord with our positive results, we propose that an isosbestic point study is capable of providing a very definitive yet qualitative mechanism probe. The reason for the latter reservation is that at this time we have no reliable method to estimate the extinction coefficients of the intermediates, and thus we cannot consider an isosbestic study to be a quantitative kinetic analysis.

A question may be raised in relation to the small absorbance change (ΔAbs < 0.1) obtained in the Abs – time profiles at isosbestic points. That is, how can we be sure that the small changes in absorbance are really due to the formation of intermediates? In order to provide an answer to this question, two points must be verified by experiments and supported by simulation analysis. These points are (1) that the Abs – time profiles must represent the form expected for intermediates, and (2) that the absorbance changes at the isosbestic points are not the result of experimental errors.

Figure 6-10 illustrate the simulated concentration – time curves for intermediates based on two different kf’ values holding kb and kp constant in order to simulate the

experiments carried out at different concentrations of substrate B ([B]0), in which both

the maximum value of [I] and the time to reach that maximum are dependent on [B]0. In the experimental isosbestic point studies, very similar figures were obtained. For example,

Figure 6-11 illustrates the ΔAbs – time profiles at the isosbestic points obtained for the reactions of NE-d2 and 2-NP-d1 with hydroxide ion in water. The experiments were

carried out with hydroxide ion concentrations of 50 and 100 mM. From the analyses of

the experimental profiles, two important observations can be made. The first is that at the

lower concentration (profiles marked by (1)), the magnitude of the absorbance at the 151 maximum was of the order of 70 – 80 %, as great as that observed at the higher concentration. The second is that the absorbance maximum at the higher concentration appeared at significantly shorter times than that observed at the lower concentration.

These facts taken together, in addition to the overall similarity between experimental and simulated profiles, answer the question posed and lead to the acceptance of the validity of the experimental isosbestic analysis.

0.20 (3.30, 0.186) Calculated Profiles for

kf' = kf[B]0 0.15 -1 =(1) 0.1 s -1 [I] (4.15, 0.107) (2) 0.2 s 0.10 -1 kb = 0.5 s -1 0.05 kf = 0.25 s (1) (2) 0.00 0 20406080100 time/s

-1 FIGURE 6-10. Calculated [I] – time profiles based on two kf’ values (0.1 and 0.2 s ), kb -1 -1 = 0.5 s , kp = 0.25 s

0.035 267.5 nm a 0.10 b 0.030 271.2 nm [NE-d2 ] = 20.4 mM [2-NP-d ] = 40.0 mM 0.025 0.08 1 [NaOH] =(1) 50.0 mM [NaOH] = (1) 50.0 mM 0.020 (2) 100.0 mM 0.06 (2) 100.0 mM 0.015 in H2 O at 298K in H2 O at 298K Abs / A.U.

Abs/A.U. 0.04 

0.010  (1) (1) 0.005 0.02 (2) 0.000 (2) 0.00 -0.005 0 50 100 150 200 250 300 0 500 1000 1500 2000 time/s time/s

FIGURE 6-11. ΔAbs – time profiles at the isosbestic points for the reactions of (a) NE-d2 - and (b) 2-NP-d1 with OH of two concentrations in H2O at 298K 152

The temperature effect on isosbestic points was analyzed by Morrey5 fifty years ago. We also observed the temperature dependence of isosbestic points (Figure 6-12)

- during the reaction of 2-NP-d1 with OH in water carried out at 288, 298 and 308 K. A

red-shift of the isosbestic point accompanies the increase in the temperature. Moreover,

the profiles in Figure 6-12 also show that the higher the temperature is, the earlier the

absorbance maximum appears, which is also consistent with the experimental kinetic

behavior that intermediates always show. The three ΔAbs – time profiles in Figure 6-12

were obtained at different wavelengths rendering the comparison of the maximum values

to be inappropriate.

0.12 [2-NP-d ] = 39.8 mM 0.10 1 [NaOH] = 100.0 mM 0.08 in H2 O 0.06 (1) 270.0 nm at 288K (1) (2) 271.0 nm at 298K

Abs /Abs A.U. (3) 272.2 nm at 308K

 0.04 0.02 (2) 0.00 (3) -0.02 0 500 1000 1500 2000 time/s

FIGURE 3-22. ΔAbs – time profiles at the isosbestic points for the reaction of 2-NP-d1 - (39.8 mM) with OH (100.0 mM) in H2O at 288, 298 and 308 K

Although the current isosbestic point study out of necessity was limited to a qualitative investigation, it is important to note an additional critical factor. The possible influence of inherent instrumental errors on the spectral measurements must be taken seriously. The characteristics of the absorbance – time profiles observed at isosbestic 153 points must be verified by multiple determinations. We also recommend that the isosbestic characteristics be confirmed using two different spectrophotometers when possible. We are confident that the application of our experimental method and data analysis procedures will generally result in reliable results. With regard to stopped-flow investigations, it is always pertinent to verify that the time-scale selected is long enough to eliminate the possible effects due to incomplete mixing.

A reinvestigation of the acyl transfer reaction between p-nitrophenyl acetate

(PNPA) and hydroxide ion in water was undertaken41 to demonstrate our methodology on

a reaction which a number of competent kinetic studies had revealed to take place in a

single step. Our data at [OH-] equal to 0.1 M or less was observed to be consistent with

the simple mechanism, however at higher [OH-] evidence was obtained for a more

complex mechanism. On the other hand, in aqueous acetonitrile (AN) the reaction was

observed to take place by a reversible consecutive mechanism, involving a kinetically

significant intermediate (Scheme 6-1) under all conditions studied.41

SCHEME 6-1. The Reversible Consecutive Mechanism for Acyl Transfer Reaction - Between PNPA and OH in H2O

O kf - H3C C O NO2 +OH Reactant Complex kb PNPA

kp Reactant Complex CH3COOH + O NO2

The PNPA acyl transfer reaction affords the opportunity to carry out isosbestic

point studies under conditions where intermediate absorbance is not expected to be

observed. In water, two distinct isosbestic points were observed at 248.0 nm and 319.8 154 nm (Figure 6-13a), which should behave as true isosbestic points during the reaction where [OH-] is not more than 0.1 M.

3.0 3.0 [PNPA] = 0.2 mM a [PNPA] = 0.1 mM b 2.5 [NaOH] = 4.0 mM 2.5 [NaOH] = 10.0 mM in H2O in AN:H2O=4:1 2.0 2.0 Run time = 100s 1.5 1.5 Cycle time = 5s Abs (A.U.) 1.0 Abs (A.U.) 1.0

0.5 0.5 Run time = 30s 0.0 Cycle time = 3s 0.0 200 250 300 350 400 450 500 550 200 250 300 350 400 450 500 550  (nm)  (nm)

FIGURE 6-13. UV absorption spectra for the acyl transfer reaction between PNPA (0.2 - mM) and OH (4.0 mM) in (a) H2O and (b) AN-H2O (80/20 vol %) at 298K

The isosbestic point study of the acyl transfer reaction of PNPA was first carried

out in water with a hydroxide ion concentration of 0.004 M using the stopped-flow

spectrophotometer. Again, these experimental conditions are those where the observation of an intermediate is not expected. As shown in Figure 6-14, the isosbestic points at 248.0

nm and 319.8 nm remained unchanged throughout the reaction verifying them to be true isosbestic points. All Abs – time profiles near the isosbestic points distribute symmetrically about the isosbestic line and intersect at a common crossing point. This behavior is identical in form to that exhibited by the simulated profiles (Figure 6-15a) for the simple one-step mechanism.

The isosbestic point study of the acyl transfer from PNPA to hydroxide ion in water clearly reveals that the true isosbestic points can also be observed using our

experimental isosbestic point method, which supports the fact that the absorbance 155 changes at isosbestic points we have obtained in the reactions of aliphatic nitroalkanes cannot be attributed to inherent instrumental or experimental errors.

[PNPA] = 0.4 mM a [PNPA] = 0.8 mM b 2.1 1.30 [NaOH] = 50.0 mM in H O at 298K [NaOH] = 50.0 mM in H2 O at 298K 2 322.0 nm 245.0 nm 1.25 2.0 321.5 nm 246.0 nm 321.0 nm 247.0 nm 1.20 320.5 nm 1.9 320.0 nm 248.0 nm 1.15 319.8 nm Abs / A.U.

Abs / A.U. 319.5 nm 1.8 249.0 nm 1.10 319.0 nm 318.5 nm 250.0 nm 1.7 318.0 nm 251.0 nm 1.05

0 5 10 15 20 25 0 5 10 15 20 25 time/s time/s

FIGURE 6-14. Abs – time profiles near the isosbestic points (a) 248.0 nm and (b) 319.8 - nm for the reaction of PNPA with OH in H2O at 298K under the conditions as shown

b b 0.0675 0.0675 ECI = ECP c c d d e 0.0600 e 0.0600 f f Abs(I)/A.U. g Abs(I)/A.U. g h h 0.0525 0.0525 -1 i kf = 0.1 s i -1 -1 ksimple = 0.1 s j kb = 1.0 s j k = 0.5 s-1 0.0450 0.0450 p 0 5 10 15 20 25 30 0 20406080 time/s time/s (a) (b)

FIGURE 6-15. Calculated Abs – time profiles near the isosbestic point (274.5 nm) for (a) the single one-step mechanism and (b) the reversible consecutive mechanism when εI = εP. Curve b: 274.1 nm, c: 274.2 nm, d: 274.3 nm, e: 274.4 nm, f: 274.5 nm isosbestic point, g: 274.6 nm, h: 274.7 nm, i: 274.8, j: 274.9 nm. The εP and εR values at various wavelengths - are from the reaction between 2-NP and OH in H2O at 298K

On the other hand, the acyl transfer reaction between PNPA and hydroxide ion in

AN-H2O (80/20 vol %) was previously found to follow a reversible consecutive

mechanism (Scheme 6-1).41 If the extinction coefficient of the intermediate differs from 156 that of the product and reactant, significant Abs – time profiles indicating the formation and decay of intermediate absorbance may be obtained at the isosbestic points at 247.0 nm and 318.8 nm (Figure 6-13b). However, in aqueous acetonitrile a significant Abs – time profile due to the intermediate was not seen at either of the two isosbestic points

(Figure 6-16), both of which acted like the true isosbestic points that were observed in the reaction taking place by the simple one-step mechanism (Figure 6-14). The behaviors of the Abs – time profiles near the isosbestic points in Figure 6-16 are consistent to that exhibited by the simulation profiles for the reversible consecutive mechanism (Figure

6-15b) where the extinction coefficient values of intermediate and product are the same,

εI = εP.

1.95 [PNPA] = 0.4 mM a 0.90 [PNPA] = 0.8 mM b 1.90 [NaOH] = 10.0 mM [NaOH] = 10.0 mM in AN:H2 O = 4:1, at 298 K in AN:H2 O = 4:1, at 298 K 320.5 nm 1.85 245.0 nm 0.85 320.0 nm 1.80 319.5 nm 246.0 nm 0.80 319.0 nm 1.75 318.8 nm

Abs / A.U. 247.0 nm 1.70 Abs /A.U. 318.5 nm 248.0 nm 318.0 nm 1.65 0.75 317.5 nm 249.0 nm 1.60 317.0 nm 0.70 1.55 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 time/s time/s

FIGURE 6-16. Abs – time profiles near the isosbestic points (a) 247.0 nm and (b) 318.8 - nm for the reaction of PNPA with OH in AN-H2O (80/20 vol %) at 298K under the conditions as shown

Another possibility is that a short lived tetrahedral intermediate with an εI

considerably lower than εP/R due to the loss in conjugation and a shift in wavelength as

expected upon formation of this intermediate, is formed which eludes detection.

Therefore, the isosbestic point study of the PNPA acyl transfer reaction in 157 aqueous acetonitrile gives a typical example of the existence of true isosbestic points in a consecutive reaction. The latter had been deemed to be impossible by Cohen and Fisher3 since the changes in the concentration of the product and reactant are not linearly related.

However, it should be pointed out that enormous improvements in instrument quality and the ability to carry out multiple duplicate experiments have been made since their paper3 was published. Moreover, Childers20 et al have also observed a true isosbestic point at

434nm during the visible spectrophotometric investigation of hydrolysis of

tetraaquoethylenediaminechromium (III) cation, which was found to take place by a consecutive mechanism.

We find nothing wrong in Cohen and Fisher’s theoretical analysis, but the case that the reactant, intermediate and product absorb with the same extinction coefficient was omitted. However, it is noticeable that the application of the isosbestic points as a mechanistic criterion should be carried out more cautiously. For example, some incorrect points, such as the statement; “the occurrence of isosbestic points allows discarding the

consecutive mechanism,”10 should be rejected at once.

Conclusions

Our former conclusion39 that the proton transfer reactions of aliphatic nitroalkanes with hydroxide ion in aqueous solutions take place by a complex mechanism is strongly supported by the special spectrophotometric experiments carried out at the

isosbestic points where changes in reactant and product absorbances cancel. Both

simulation and experimental investigation indicate that the absorbance changes observed

at the isosbestic points can be attributed to the formation of intermediates. Isosbestic 158 point studies can provide a potential way to trace the intermediate and provide reliable evidence to rule out the simple one-step mechanisms. Moreover, well-defined isosbestic points were observed in the test reaction between PNPA and hydroxide ion in aqueous acetonitrile which had been proposed to take place by a reversible consecutive mechanism. The latter indicates that the conclusion that the observation of isosbestic points rules out the possibility of a consecutive reaction is not correct.

Experimental

NM, NE, NE-d2, 1-NP, 2-NP, NC5 and NC6 were obtained commercially from

Sigma-Aldrich and were further purified by reduced pressure distillation and subjected to

an additional purity check by 1H NMR spectrometry before use. NC4, NC7 and NC8

42 were prepared by using a modification of the literature procedure (90% H2O2 was

replace by 50% H2O2). The deuterated analogues, 1-NP-d2, 2-NP-d1, NC5-d1 and NC6-d1, were prepared by following the procedure suggested by Bell.43

The aqueous samples of nitroalkanes were prepared by adding 3 – 5 % acetonitrile to deal with the problem in solubility. Concentrated sodium hydroxide solution was commercially available from Fisher Scientific, which had been determined by titration with standard oxalic acid solutions.

Distilled water was further purified by passing through a Barnsted Nanopure

Water System. Acetonitrile (Aldrich, HPLC Grade) were distilled twice (collecting the middle fraction) after refluxing over P2O5 for 5 h, and then passed through an alumina

column. Methanol (Aldrich, HPLC Grade) was further purified by Lund-Bjerrum

method. 159

The determination of isosbestic points were finished by using an Agilent 8453

UV-vis and a Hi-Tech SF-61 stopped-flow spectrophotometers. The Abs – time profiles obtained from both instruments were first converted to ΔAbs – time profiles by subtracting the initial value from each absorbance value. The following procedures to judge the isosbestic points have been described in detail in the section of Methods and

Results

On the Agilent 8453 UV-vis spectrophotometer, the diode-array kinetic experiments were carried out near the apparent isosbestic points. The start time and cycle time were set equal to 0 s and 1 s, respectively. The total run time was dependent upon how long the reaction takes to reach completion.

The stopped-flow experiments were carried out at a series of wavelengths near the isosbestic points with an interval of 0.1 nm. Each Abs – time profile was the average of 5 – 10 stopped-flow shots. In each shot, the 2000-point Abs – time curve data were collected over more than 10 half-lives to allow the reaction to complete.

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163

CHAPTER 7

PROTON TRANSFER REACTIONS OF 1-ARYLNITROETHANES WITH

HYDOXIDE ION IN AQUEOUS SOLUTIONS. A RATIONAL

EXPLANATION OF THE NITROALKANE ANOMALY

Abstract

Three detailed applications of pseudo-first-order kinetics to the proton transfer reactions of 1-arylnitroethanes with hydroxide ion in aqueous solutions revealed that the reactions actually follow a reversible consecutive mechanism involving a kinetically significant intermediate. The formations of the intermediates do not involve C-H bond dissociation. The latter is shown by the fact that the apparent KIE are E.R. and time-dependent approaching unity near zero time and evolving toward plateau values as steady state is achieved. The Brønsted correlation was carried out by using the microscopic rate constants, kp, specific for the proton transfer step and the revised

Brønsted exponent αreal was observed to be in the normal range, which suggests that the

nitroalkane anomaly previously proposed for this reaction series does not exists. The

latter proposal was based on the false assumption that the reactions follow a simple

one-step mechanism. Thus the conundrum, having perplexed the physical organic

chemists for a half century, arose from an interpretation based upon the incorrect

mechanism.

Introduction

Kinetic studies of the proton transfer reactions of the simple nitroalkanes can be

traced back to the 1930s,1 while more extensive studies of these reactions in protic 164 solvents,2-10 aprotic solvents11,12 and mixed solvents13,14 were carried out during the past

80 years. With the development of the linear free energy relationships, the study of the

proton transfer reactions of nitroalkanes became to an active area for physical organic

chemical research, and led to what is now known as the “nitroalkane anomaly,”8 which

received this name because of the observation of anomalous Brønsted exponent α’s with

values of less than zero or greater than one, during the correlation analysis of the

reactions of aliphatic-10 and aryl-nitroalkanes,2,7 respectively. The anomalous α values,

outside the normal range of 0 – 1, not hinders the prediction of the extent of proton transfer at the transition state, but also questions the validity2 of applying the Brønsted

relationship in the mechanistic analysis of the proton transfer reactions of nitroalkanes.

It has been known for some time that the nitroalkane anomaly is restricted to the

proton transfer reactions in protic solvents, and has not been observed in aprotic solvents,

such as DMSO12 and acetonitrile.11 Moreover, the recent theoretical study15 found that the nitroalkane anomaly, well established in solution, is absent in the gas phase, providing evidence that strong specific intermolecular forces such as hydrogen bonding between solvent and nitronate anions are essential for the anomalous Brønsted behavior. This

conclusion is essentially consistent with the implications of “the principle of non-perfect

synchronization” proposed by Bernasconi,16 who proposed that the phenomenon can be rationalized within the concept of the single transition state model (such as a single-step mechanism) by allowing solvation and bond changes to have asynchronous character

(Scheme 7-1). The latter is still the basic assumption that the current explanations of the nitroalkanes anomaly generally depend on. In contrast, a kinetic isotope effect study 165 indicated that the reaction mechanism might not be so simple.4 A complex mechanism,4,5 including a tetrahedral hydrogen-bonded anionic intermediate, was cautiously proposed.

However the disparate mechanism, especially the structure of the intermediate proposed, as could be anticipated suffered severe criticism from the physical organic community and was consequentially rejected.13,17

SCHEME 7-1. Simple One-Step Mechanism for the Proton Transfer Reactions of Nitroalkanes

The intention of our reinvestigation on this classical reaction is to seek to reopen

the discussion and argument on the origin of the nitroalkane anomaly by means of new

experimental data obtained under a variety of conditions and new detailed

pseudo-first-order kinetic analyses. This study is a part of our general effort to determine

the mechanisms of fundamental organic reactions.18,19 We have previously presented

evidence that the proton transfer reaction between 1-(p-nitrophenyl)-nitroethane

(p-NPNE) and hydroxide ion in aqueous acetonitrile20 actually takes place by a reversible consecutive mechanism (Scheme 7-2). The recent reinvestigation on the proton transfer reactions of three simple aliphatic nitroalkanes; nitromethane, nitroethane and

2-nitropropane; with hydroxide ion in water21 revealed (contrary to long-held views) that

the reactions are complex and involve kinetically significant intermediates. This provided

the incentive for further studies in the anticipation that a rational explanatory key for the

origin of the negative Brønsted α’s may be found. 166

We now report convincing experimental evidence that the assumption of the simple one-step mechanism is not valid for the proton transfer reactions of aryl nitroalkanes with hydroxide ion in water and mixed aqueous solvents. The observation of anomalous Brønsted α > 1 based on apparent rate constants are also explained in the framework of the complex mechanism.

SCHEME 7-2. Reversible Consecutive Mechanism for the Proton Transfer Reaction Between p-NPNE and OH- in Aqueous Acetonitrile

Kinetic Data Manipulation and Results

The reactions between 1-arylnitroethanes (ArNE) and hydroxide ion in aqueous

solutions are illustrated by Scheme 7-3. The equilibrium constants for the reactions are all

greater than 105, which insure that the reactions go to completion and are free from

complications due to the reverse reaction. Moreover, the anionic products are stable and

readily monitored by spectrophotometry, which makes the reactions suitable for detailed

kinetic analyses. For the sake of comparison with previous results, the experimental

conditions were those employed previously during the kinetic reinvestigation of the

3,4 2 7 reactions in H2O, in H2O-MeOH (50/50 vol %), and in H2O-dioxane (50/50 vol %) at

298 K.

The kinetic data manipulation was achieved by means of the application of three different new pseudo-first-order procedures19 on the experimental data. The first 167 procedure involves successive conventional pseudo-first-order kinetic analyses on the experimental absorbance – time (Abs – t) profiles collected over different time periods; 0 to 0.5 half-lives (HL), 0 to 1.0 HL, 0 to 2.0 HL,… and so forth. This time dependence of the apparent rate constants provides a definitive mechanism probe for distinguishing between simple one-step and complex multi-step mechanisms. The other two procedures are generally used for manipulating the experimental data obtained in about the first half-life of the reaction and provide more detail of the kinetic response to verify the occurrence of a complex mechanism and to provide the errors in multiple determinations.

SCHEME 7-3. Proton Transfer Reactions Between ArNE and OH-

Time Dependence of Conventional Pseudo-First-Order Rate Constants

In this procedure, the absorbance – time profiles (Abs – t) obtained from the kinetic experiments were firstly converted to –ln(1 – E.R.) – time profiles where E.R. denotes extent of reaction. The latter are then subjected to linear least squares analysis on

5 different segments of the data over time ranges corresponding to 0 – 0.5 HL, 0 – 1 HL,

0 - 2 HL, 0 – 3 HL and 0 – 4 HL.

The data for the reactions of 1-(p-nitrophenyl)-nitroethane (p-NPNE) with

hydroxide ion in various aqueous solutions at 298 K are summarized in Table 7-1. In this 168 case, the data show that the values of the apparent pseudo-first-order rate constant (kapp) steadily decreased with degree of conversion, with a change of approximately 20 % over the range from 1 HL to 4 HL. In contrast to the modest changes in kapp observed, the

corresponding changes in the intercepts are much more remarkable, which indicates that this parameter is much more sensitive to the deviations from first-order kinetics.

Obviously, the values of kapp and the intercepts for the simple one-step mechanism are

expected to be independent of the number of HL taken into the linear least squares

correlations.

TABLE 7-1. Half-Life Dependence of Conventional Pseudo-First-Order Rate Constants and the Intercepts of Linear Correlations for the Reactions of p-NPNE with OH- in Various Solvents at 298 K in H O-MeOH in H O-dioxane in H O a 2 2 HL 2 (50/50 vol %) b (50/50 vol %) c -1 -1 -1 -1 -1 -1 kapp /s Int./s kapp /s Int./s kapp /s Int./s 0.5 0.690 -0.00666 0.340 -0.00332 0.478 0.00208 1.0 0.658 0.000800 0.330 0.00169 0.442 0.0144 2.0 0.632 0.0153 0.317 0.0161 0.415 0.0356 3.0 0.599 0.0466 0.303 0.0419 0.391 0.0693 4.0 0.539 0.133 0.286 0.0874 0.362 0.132 a p-NPNE (0.10 mM) + NaOH (10.0 mM) in H2O at 350 nm, 298 K b p-NPNE (0.10 mM) + NaOH (2.0 mM) in H2O-MeOH (50/50 vol %) at 395 nm, 298 K c p-NPNE (0.10 mM) + NaOH (2.0 mM) in H2O-dioxane (50/50 vol %) at 410 nm, 298 K

Similarly, this procedure can be abbreviated and illustrated by long-time (over

about 5 HL) –ln(1 – E.R.) – time profile along with the corresponding least squares

correlation lines in Figure 7-1, in which the obvious deviation reveals that the reaction

does not conform to first-order kinetics as is expected from the previous study,1-16 and suggest that the reactions follow a complex mechanism. A similar illustration of the method has been described earlier for the simple nitroalkanes.21 A comparison of the data 169 in Table 7-1 and the plots in Figure 7-1 indicates that both the degrees of the changes in kapp depending on HL and the deviations of –ln(1 – E.R.) – time profiles from the

corresponding correlation lines, lead to the same conclusion concerning the extent of the deviation of the data from that expected for first-order kinetics.

4 [p-NPNE] = 0.1 mM [NaOH] = 2.0 mM

3 in H2O:Dioxane = 1:1 at 298K, 410 nm 2 -ln(1 - E.R.) -ln(1

1 5t0.5 slope = 0.296 0 int. = 0.349

024681012 time/s

FIGURE 7-1. Long-time (over about 5 HL) –ln(1 – E.R.) – time profile and corresponding least squares correlation line for the reaction of p-NPNE with OH- in H2O-dioxane (50/50 vol %) at 298 K

In some cases, the obvious curvature of the –ln(1 – E.R.) – time profiles over 3 –

5 HL, as shown in Figure 7-2, is sufficient to describe the deviation of the reaction from

the simple one-step mechanism, however it is preferable to have a more quantitative

measure of the degree of deviation. A more complete set of long-time profiles for the

reactions of ArNE with hydroxide ion in various aqueous solutions can be found in

Figure D.1 – D.3 (Appendix D). 170

4 E.R. = 0.96 E.R. = 0.77 1.5 3 1.0 2 [m-CF3 -PNE] = 0.11 mM [m-NO -PNE] = 0.10 mM [NaOH] = 20.0 mM 2 -ln (1 - E.R.) (1 -ln

-ln (1 - E.R.) - (1 -ln 0.5 [NaOH] = 10.0 mM in H2 O 1 in H O 298K, 289nm 2 298K, 278nm 0 0.0

0 5 10 15 20 25 30 0 5 10 15 20 25 30 time/s time/s

4 3 Extent of Reaction = 0.93 Extent of Reaction = 0.96

3 2 2 [p-MeO-PNE] = 0.10 mM [PNE] = 0.10 mM [NaOH] = 40.0 mM E.R.) (1- -ln -ln (1- E.R.) (1- -ln 1 1 [NaOH] = 20.0 mM in MeOH:H2 O = 1:1 in MeOH:H O = 1:1 298K, 287nm 2 0 298K, 286nm 0 0 102030405060 0 102030405060 time/s time/s

4 Extent of Reaction = 0.935 Extent of Reaction = 0.96 3 3

2 2 [p-Me-PNE] = 0.10 mM [NaOH] = 50.0 mM [p-Cl-PNE] = 0.11 mM -ln (1 - E.R.) (1 -ln -ln (1 - E.R.) (1 -ln 1 1 in Dioxane:H2 O = 1:1 [NaOH] = 20.0 mM

298K, 300nm in Dioxane:H2 O = 1:1 0 298K, 300nm 0 010203040 0246810 time/s time/s

FIGURE 7-2. Long-time –ln(1 – E.R.) – time profiles for the reactions of ArNE with OH- in various solutions under the conditions shown 171

Sequential Pseudo-First-Order Linear Correlation

This analysis has been described in our recent papers,19,21,22 and involves 24

different analyses carried out over different point segments of the 2000 point Abs – t

profiles over about the first HL of the reaction. The point segments include points 1 – 11,

1- 21, 1 – 31, 1 – 41, 1 – 51, 1 – 101, 1 – 201, …, 1 – 1801, 1 – 1901. The procedure

provides 24 kapp values at the midpoints of the segments. If a reaction obeys first-order

kinetics the values of kapp for all of the 24 segments are expected to be independent of

time.

0.70 0.22 0.65 0.21 1 1 - - / s / 0.60 s / 0.20 [p-NPNE] = 0.1 mM app [p-NPNE] = 0.1 mM app k k [NaOH] = 2.0 mM [NaOH] = 10.0 mM 0.19 in H2O-MeOH (3:1) 0.55 in H O at 298K 2 at 298K,382 nm 350 nm 0.18 0.50 0.17 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.5 1.0 1.5 2.0 time/s time/s

0.36 0.38

0.34 0.37 1 1 - -

s 0.32 0.36 / [p-NPNE] = 0.1 mM s / [p-NPNE] = 0.1 mM app

0.30 app k [NaOH] = 2.0 mM k 0.35 [NaOH] = 2.0 mM 0.28 in H2O-MeOH (1:1) in H2O-MeOH (1:3) 0.34 at 298K,395 nm at 298K,393 nm 0.26 0.33 0.24 0.32 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.00.20.40.60.81.01.2 time/s time/s

FIGURE 7-3. Apparent rate constants (kapp) – time plots for the reaction between p-NPNE and OH- in various solvents at 298 K under the condition shown 172

What is immediately apparent in Figure 7-3 is that in all 4 series of reactions between p-NPNE and hydroxide ion in various aqueous solutions, is that the kapp – time profiles rapidly increase from relatively low values and subsequently decay slowly after maximum value of kapp is reached. The time-dependent kapp plots provide a convenient

visual representation to illustrate that the proton transfer reactions do not take place by a

single one-step mechanism. They also illustrate that the complex mechanism involves the

formation of kinetically significant intermediates.

TABLE 7-2. Apparent Rate Constants and Standard Deviations Obtained by the 24 Point Sequential Analysis of the Reaction of p-MePNE (0.1 mM) with OH- (50.0 mM) in H2O-Dioxane (50/50 vol %) at 298 K, 320 nm -1 -1 time /s kapp /s SD /s Segment 0.0084 1.110 0.340 1 0.0154 0.926 0.126 2 0.0224 0.758 0.078 3 0.0294 0.608 0.046 4 0.0364 0.522 0.038 5 0.0714 0.379 0.028 6 0.141 0.335 0.029 7 0.211 0.302 0.018 8 0.281 0.284 0.012 9 0.351 0.274 0.009 10 0.421 0.267 0.007 11 0.491 0.263 0.005 12 0.561 0.259 0.005 13 0.631 0.257 0.004 14 0.701 0.255 0.004 15 0.771 0.254 0.004 16 0.841 0.253 0.004 17 0.911 0.252 0.004 18 0.981 0.251 0.004 19 1.05 0.250 0.004 20 1.12 0.250 0.004 21 1.19 0.249 0.004 22 1.26 0.249 0.004 23 1.33 0.248 0.004 24

173

The 24 point sequential correlation of –ln(1 – E.R.) – time data over first half-life not only verifies the time-dependence of kapp but also provides standard

deviations (SD) of the latter for repetitive (normally 10 – 20) stopped-flow shots. The

analysis is illustrated in Table 7-2, exemplified by that for the reaction of

1-(p-methylphenyl)-nitroethane (p-MePNE) with hydroxide ion H2O-dioxane (50/50 vol %) at 298 K. The SD value for segment 1 is about ± 30% of the average kapp value and then decreases dramatically with increasing segments until it stabilizes to about ± 2 % of the corresponding mean value of kapp from segment 12 to 24. The large SD values for

the initial segments are due to the small number of data points used in the linear

correlations. Each stopped-flow experiment consisting of 10 – 20 shots is generally repeated at least three times and the mean values of kapp from the three determinations

always have a very small degree of variance which are certainly significant.21,22

Instantaneous Rate Constant Approximation

The procedure shares the same principle of operation with the 24-point sequential correlation, which is to carry out least squares linear correlation over different point segments. However, in this case, the 2000 point (1 – E.R.) – time profiles provide many more segments with much shorter time intervals. The logarithmic profiles correspond to points 1 – 3, 1 – 4, 1 – 5, …, 1 – 1999, 1 – 2000, and a 1998 point array of kapp – time data is finally obtained. The kapp at the two extreme of the profile are nearly

22 identical to the corresponding instantaneous rate constant – time (kinst – time) profiles

obtained at the mid-point between every adjacent two points.23 The deviations between kapp and kinst of the two types of profiles differ increasingly from either end of the time 174 scale so a maximum difference is obtained at the time of the midpoint of the (1 – E.R.) – time profile. The latter difference does not distract from the usefulness of the procedure and the term, kIRC – time profiles, is used to distinguish them from the more correctly defined kinst – time profiles.

0.144 0.150 0.142 0.140 0.145 1 1 - [PNE] = 0.11 mM - 0.138 / s [NaOH] = 20.0 mM / s 0.140 IRC 0.136 IRC in H2 O at 298K [m-FPNE] = 0.11 mM k k 0.135 0.134 300 nm [NaOH] = 10.0 mM in H O at 298K 0.132 0.130 2 286 nm 0.130 0.125 0.128 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 time/s time/s

0.26 0.27

0.24 0.26 -1 -1 0.22 0.25 / s / s IRC IRC [p-MePNE] = 0.10 mM [p-CF PNE] = 0.10 mM

k 0.24 k 0.20 3 [NaOH] = 40.0 mM [NaOH] = 5.0 mM 0.18 0.23 in H2 O:MeOH = 1:1 in H2 O:MeOH = 1:1 0.16 at 298K, 287 nm 0.22 at 298K, 310 nm

0.14 0.21 0.0 0.5 1.0 1.5 2.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time/s time/s 1.4 0.45 1.2 [m-MeOPNE] = 0.11 mM 0.40 -1 1.0 [NaOH] = 50.0 mM -1 [p-NPNE] = 0.10 mM / s in H O:Dioxane = 1:1 / s 0.35 [NaOH] = 2.0 mM

IRC 2 IRC k

0.8 k at 298K, 300 nm in H2 O:Dioxane = 1:1 0.30 at 298K, 440 nm 0.6 0.25 0.4 0.20 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 1.0 time/s time/s

- FIGURE 7-4. kIRC – time profiles for the reactions of ArNE with OH in various solvents 175

The advantage of using kIRC over kinst is that the experimental determination of

the latter is accompanied by much larger errors due to the very short time intervals

involved. Figure 7-4 shows the application of the procedure outlined above and a more

extensive compilation of kIRC – time profiles for the reaction of ArNE with hydroxide ion

in the three aqueous solutions are found in Figure D.4 – D.6 (Appendix D). It should be

noted that none of the kIRC – time plots presented in Figure 7-4 and Figure D.4 – D.6 are

straight lines with zero-slope, the expected result for the simple one-step mechanism.

Discussion

Variation in the Appearance of kIRC – time Profiles

The results of the three non-conventional pseudo-first-order kinetic procedures discussed in the previous paragraphs clearly rule out a simple one-step mechanism for the proton transfer reactions between ArNE and hydroxide ion, and indicate the formation of

a kinetically significant intermediate, which requires an additional explanation of the

variation in the appearance of the kIRC – time profiles in this case.

For purely product absorbance, the time-dependent rate constant (kapp) increases

with time from zero to the steady-state value for the reversible consecutive mechanism

(Figure 7-5a). This “normal” pattern is only found in a few cases (mostly for electron

withdrawing groups) in Figure 7-4 and Figure D.4 – D.6, while the changes in kIRC for the other profiles present either monotonic descending or non-monotonic trends. Simulated data show that the only circumstance giving rise to this complication is that the absorbances monitored, primarily due to the anionic products, also have contributions due to reaction intermediates. 176

SDKCONT - 5 s kapp = kapp(P) + x*kapp(I) 0.021 0.010 x = 2.0 [A] = 0.001 M, [B] = 1.0 M (a) (b) 0 0 0.018 -1 -1 [A] = 0.001 M, [B] = 1.0 M 0.008 kf = 0.01 M s 0 0 -1 0.015 -1 -1 1 1 x = 1.5 k = 0.01 M s - kb = kp = 1.0 s - f reactant -1

/ s 0.006 / s 0.012 kb = kp = 1.0 s

app app x = 0.75 k 0.004 product k 0.009 x = 1.0 0.006 0.002 x = 0.5 intermediate 0.003 x = 0.25 0.000 x = 0.1 0.000 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 time/s time/s

FIGURE 7-5. Simulated kapp – time profiles for (a) the reversible consecutive mechanism, and (b) a series of product profiles under the influence of the intermediate absorption over a wide range of degree

Furthermore, the nature of the kapp – time profiles in the latter case mostly

depends upon the relative intensity of the intermediate as compared to that of the product,

which is illustrated clearly in Figure 7-5b, where the parameter x denotes the molar extinction coefficient ratio of intermediate to corresponding product, εint/εp. With the

combination of the simulation microscopic rate constants shown, when x < 0.5, the

“normal” increasing trend for product absorbance can be retained to a certain extent. In

the other hand, if x > 0.5, a descending curve is obtained, which looks “normal” for

reactant decay even the wavelength range is specifically chosen for monitoring product

absorbance.

The non-monotonic simulated profiles arise from the cases when x is near to the

value at the transition point (equal to 0.5 in Figure 7-5b). Under these circumstances the

value of time-dependent kapp varies only slightly and is influenced greatly by the inherent experimental errors, which may cause the appearance of the kapp – time profiles to be

complicated. Since kinst are evaluated over extremely short time intervals, the 177 complications resulting near the transition point are much more severe in for kinst – time

profiles than for the corresponding kIRC – time profiles.

Therefore, the variation in the appearance of kIRC – time profiles could be

considered a consequence of the fact that the molar extinction coefficient ratio, εint/εp, varies with aryl substituent. The observation of the phenomenon is of great mechanistic importance since it enables us to verify the presence of a significant concentration of intermediate. However, because the molar extinction coefficient of the intermediate is generally unknown, its concentration cannot be estimated from the kIRC – time profiles.

Apparent Deuterium Kinetic Isotope Effects

The new detailed pseudo-first-order analyses also provide a practical way to

study the apparent deuterium kinetic isotope effects for the proton transfer reactions. Two

E.R. terms, KIEapp and KIEapp, are used to differentiate between apparent KIE based upon

E.R. and reaction time, respectively. Both of these analyses played a significant role in

the determination of the mechanism for proton transfer reactions between the simple

nitroalkanes and hydroxide ion in water.21

E.R. The term, KIEapp , is defined as the ratio of the time that the D-reaction and H

E.R. reaction require to reach the same extent of reaction. The KIEapp – E.R profiles in

E.R. Figure 7-6 show that the value of KIEapp is E.R. dependent, with a low value at low

conversion and to increase with increasing E.R.. The simple one-step mechanism in

E.R. which KIEapp is a constant and independent of the degree of conversion is readily

differentiated from the result expected for the complex mechanism. However, it must be

remembered that the fail to observe complex mechanism response does not establish a 178 single-step mechanism since the range of parameters which gives rise to variable kapp is rather small.

6.4 6.4 6.2 6.2 E.R. 6.0 E.R. 6.0 app 5.8 app 5.8 KIE 5.6 [p-NPNE(-d)] = 0.1 mM KIE 5.6 [m-NPNE(-d)] = 0.1 mM [NaOH] = 10.0 mM [NaOH] = 5.0 mM 5.4 5.4 in H O:MeOH = 1:1 in H2 O at 298K 2 5.2 370 nm 5.2 at 298K, 305 nm 5.0 5.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0. E.R. time/s

E.R. FIGURE 7-6. KIEapp – E.R. profiles for the reactions of p-NPNE (left) and m-NPNE (right) with OH- under the conditions shown

5.5 8

5.0 7 6 4.5 app app 5 [m-NPNE(-d)] = 0.1 mM KIE KIE 4.0 [p-NPNE(-d)] = 0.1 mM 4 [NaOH] = 2.0 mM [NaOH] = 2.0 mM 3.5 in H2 O:MeOH = 1:1 in H O:MeOH = 1:1 3 2 at 298K, 305 nm 3.0 at 298K, 385 nm 2 2.5 1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.5 1.0 1.5 time/s time/s

FIGURE 7-7. KIEapp – time profiles for the reactions of p-NPNE (left) and m-NPNE (right) with OH- under the conditions shown

The other term, KIEapp, is defined as the ratio of apparent rate constants (kapp) for

H- and D-reactions, which are measured at exactly the same time intervals. In Figure 7-7, the initial ascending KIEapp – time curves for the reactions of p-NPNE and m-NPNE

clearly rule out the simple one-step mechanism, in which the plot is expected to be a 179 straight line with zero-slope. The profiles also appear to indicate that the KIEapp value

rises from 1 at zero time to a constant value at longer times where the reactions reach a

steady state. The latter is expected for a reaction where no KIE is associated with the initial step, which means the C-H bond does not break during the formation of the intermediate.

Mechanism Elucidation

The discussion in the previous paragraphs concerning the proton transfer

reactions of ArNE with hydroxide ion in aqueous solutions points to two mechanistic

features of great significance. These are (1) the first step in the reaction leads to a kinetically significant intermediate; and (2) the proton is not transferred during the formation of the intermediate. Both these points are consistent with the complex mechanism suggested earlier for the reaction between p-NPNE and hydroxide ion in aqueous acetonitrile.20 In conclusion, the extension of the two-step reversible consecutive

mechanism (Scheme 7-3) can be rationally made to the entire series of reactions between

ArNE and hydroxide ion in aqueous solutions.

SCHEME 7-4. The Two-Step Reversible Consecutive Mechanism for the Proton Transfer Reactions Between ArNE and OH- in Aqueous Solutions

The intermediate is assumed as a pre-association complex which is expected to

form without formation of new covalent bonds in the reaction system. It is likely that the 180 extrusion of solvent molecule(s) from the two entities and a change in geometry which allows the proton transfer from the nitroalkane to hydroxide ion to occur are prominent features during this reaction.

It is expected that the influence of meta- and para-substituents on the strength of the C–H bond can also have an impact on the configuration of the pre-association complex. A reaction involving an electron withdrawing group in the substrate is inclined to result in a relatively loose complex, which does not have a strong absorbance band at the wavelength where product absorbs. This may be an explanation of the observation of less interference to the anionic product absorbance caused by the intermediate in the case of substrates with electron withdrawing substituents.

Reinvestigation of the Brønsted Correlations for the Proton Transfer Reactions

Anomalous Brønsted α with values greater than one (see Table 7-3) were observed in this study during the correlations of apparent second-order rate constants, kapp = kf /(1+kb/kp) and pKa values for ArNE, carried out in accordance to the classical

form of the Brønsted equation (eq 7.1). This phenomenon has been widely discussed in

previous work.2-16

TABLE 7-3. Brønsted α Values for the Reactions of ArNE with OH- in Aqueous Solutions at 298 K Brønsted α Solvent This work Literature a d H2O 1.12 (r = 0.994) 1.15 b e H2O-MeOH (50/50 vol %) 1.40 (r = 0.964) 1.37 c f H2O-dioxane (50/50 vol %) 1.08 (r = 0.990) 1.17 – 1.20 a Table D.1. b Table D.2. c Table D.3. d Ref. 3, 4. e Ref. 2, at 288K. f Ref. 7.

181

lg (kapp) = α (-pKa) + ca (7.1)

In the past, the proton transfer reactions of nitroalkanes were treated as taking

place by a single one-step mechanism, the utilization of the apparent rate constants in the

Brønsted correlation resulted in the various anomalous exponents. However, as pointed

out in the discussion in the former paragraphs, these reactions actually follow a two-step

reversible consecutive mechanism in which proton transfer takes place in the second step.

Therefore, kp is the only rate constant appropriate to use in the Brønsted correlation and the resulting exponent is expressed as αreal in eq 7.2.

lg (kp) = αreal (-pKa) + ca’ (7.2)

Unfortunately, due to the lack of the molar extinction coefficient of the

intermediate, we do not have a reliable method either to separate the absorbance of

intermediate from that due to product, or to estimate the correct values of kp and the other

two microscopic rate constants.

As shown by the simulated data in Figure 7-5, in order to observe a descending

kapp – time curve from the kinetic experiments designed to monitor only product, the

corresponding intermediate must absorb strongly at that wavelength with a relative molar

extinction coefficient ratio greater than 0.5 (εint/εp > 0.5). As the results shown in Table

7-4, making the assumption that εint = εp, a condition under which simulations resulted in

data clearly showing similar phenomena, is thus not completely arbitrary.

In Figure 7-8, the microscopic rate constants kp in Table 7-4 were employed for

the Brønsted correlation, in which the value of the corresponding αreal is equal to 0.76, at

the high end of the “normal” range for the Brønsted exponent, which indicates that in 182 regard to the complex mechanism shown in Scheme 7-3, the step for proton transfer does not give rise to an anomalous α. The latter clearly challenges the existence of so-called the nitroalkane anomaly, the proposal of which were based upon the simple one-step mechanism which we now know is not valid.

TABLE 7-4. Equilibrium and Rate Constants for the Reactions of ArNE with OH- in H2O at 298 K 38,39 -1 -1 -1 -1 a -1 a -1 a pKa kapp (M s ) kf (M s ) kb (s ) kp (s ) m-Me 7.49±0.01 5.51±0.07 5.75 0.0605 1.41 H 7.39±0.01 6.58±0.16 6.75 0.0697 2.30 m-F 7.05±0.01 15.1±0.3 15.5 0.0800 2.78 m-Cl 7.05±0.01 17.9±0.1 18.5 0.131 3.98 m-CF3 6.96±0.01 21.2±0.8 22.6 0.267 4.27 m-NO2 6.67±0.01 46.2±1.6 48.6 0.293 5.50 p-NO2 6.51±0.01 71.6±4.4 74.6 0.460 9.27 a The simulations for microscopic rate constants were carried out by the assumption of εint = εp

p-NO 1.0 2

0.8 m-CF 3 m-NO 2 0.6 m-Cl p k H

log 0.4 m-F  = 0.73 real 0.2 R = 0.916 m-CH 3 0.0 -7.6 -7.4 -7.2 -7.0 -6.8 -6.6 -6.4 -pK a

FIGURE 7-8. Brønsted correlation of kp with pKa and αreal for the reactions of ArNE with - OH in H2O

It is should be noted that the value of the correlation coefficient, 0.916, obtained

from the correlation with kp is relatively low in comparison with the corresponding values 183 in Table 7-3, perhaps in consequence of the assumption of εint = εp, which is not supposed

to affect the slope of the correlation line too much. However, it could make a strong impact on the value of the correlation coefficient. Coincidently, the conventional

Brønsted correlations for the reactions of arylnitromethanes in aprotic solvents also

produced low correlation coefficients (in Figure 7-9)**, as well as α values in the normal

range of 0.7 – 0.8.

6 ArCH NO + PhCOO- 2 2 p,p'-(NO ) - 2 2 ArCH2NO2 + PhCOO 2.0 p,p'-(NO ) 5 in DMSO 2 2 in Acetonitrile  = 0.76 m-NO  = 0.78 r = 0.909 2 4 p-NO 1.5 r = 0.916 f 2

k p-CN 1 k log 3 log 1.0 p-Br p-NO2 2 H m-NO 2 0.5 p-CH3 1 -13 -12 -11 -10 -9 -8 -22.0 -21.5 -21.0 -20.5 -20.0 -19.5 -pKa -pKa (a) (b)

FIGURE 7-9. Conventional Brønsted correlations of apparent rate constants with pKa for the proton transfer reactions of arylnitromethanes with benzoate anion in (a) DMSO and (b) acetonitrile

Mechanistic Interpretation of the Nitroalkane Anomaly

During the 80 years since its birth, the Brønsted relationship has been shown,

hundreds of times in actual application, to be a practical and efficient key in mechanistic

determinations of organic reactions. John E. Leffler24 in his paper concerning the

application of the Brønsted relationship made the following statement: “A proper value of

** Figure 7-9a and 7-9b were constructed from the experimental data in Ref. 12 and 11, respectively. 184

α is one more criterion for an acceptable mechanism”; and “If the observed value of α is

outside this (normal) range, the mechanism should be discarded.”

Like many other linear free energy relationships, the Brønsted relationship is

only appropriate for the description of the single-step reaction or for one step of a

multi-step reaction. Our recent kinetic studies have shown that the proton transfer

reactions of aliphatic-21 and aryl-nitroalkanes actually follow a complex mechanism.

Therefore, as a result of using apparent rate constants assuming a single-step mechanism

in the correlations without a proper mechanism determination, the nitroalkane anomaly

was proposed to account for the anomalous α values.

Additionally, the fact that the complex mechanism rather than a simple one-step

mechanism is followed in the nitroalkane proton transfer reaction may also provide the

answer to the question, “Why is the phenomenon of the nitroalkane anomaly only

observed in the proton transfer reactions of nitroalkanes in protic solvents, but not in

aprotic solvents?”

Due to the weak interactions between the reactant and solvent molecules in

aprotic solvents, the formation of reactant complex may be too fast to make a significant

impact on the overall process, which may lead to substituent effects on the apparent rate

constant, kapp, that do not differ greatly from that on the microscopic rate constant, kp. As a result of the latter, the value of the apparent Brønsted exponent, α, obtained from the

11,12 correlation of kapp with the corresponding pKa value in aprotic solvents, do not only

fall into the normal range of 0 – 1, but may also be close to the real value of αreal.

In protic solvents, the strong H-bonding interaction between the reactant and 185 solvent molecules creates a barrier to disruption of the solvent shells near the reactive sites during the formation of the reactant complex. The energy barrier for the first step includes no C-H bond breaking and the latter becomes more significant continually while proceeding along the reaction coordinate since kp continually becomes a more dominant

feature of the apparent rate constant kapp. In this case, the Brønsted α based on the kapp correlation may have either a normal or an anomalous value and will not be appropriate for the discussion of the mechanism of the proton transfer. In other words, the relative rates of the reactions for a series of substrates following a multi-step reaction cannot be simply predicted from the thermodynamic stabilities of reactants and products as required for the application of the Brønsted relationship.

As viewed having the knowledge that the proton transfer reactions take place by a complex mechanism, the nitroalkane anomaly will not exist as long as the Brønsted relationship is applied correctly. However, this does not mean that the earlier studies on this topic, mostly carried out with the assumption of simple one-step mechanism, were in vain. Reviewing the course of searching for the origin of the nitroalkane anomaly during the past half century, it becomes more and more apparent just how important reaction mechanisms are to the field of organic chemistry and to science in general.

Experimental

Materials

Thirteen 1-arylnitroethanes were prepared by using a modification of the

25 literature procedure (50% H2O2 was substituted for 90% H2O2). The deuterated

analogues of p-NPNE and m-NPNE were prepared by hydrogen/deuterium exchange as 186 reported earlier.26 Concentrated sodium hydroxide solution was commercially available

from Fisher Scientific, which had been determined by titration with standard oxalic acid

solutions. Distilled water was further purified by passing through a Barnsted Nanopure

Water System. Dioxane (Aldrich, HPLC Grade) and acetonitrile (Aldrich, HPLC Grade)

were distilled twice (collecting the middle fraction) after refluxing over P2O5 for 5 h, and

then passed through an alumina column. Methanol (Aldrich, HPLC Grade) was further

purified by Lund-Bjerrum method.

Kinetic Experiments

Kinetic experiments were carried out by using a Hi-Tech SF-61 stopped-flow

spectrophotometer installed in a glove box and kept under a nitrogen atmosphere. The

temperature was controlled at 298 K using a constant temperature flow system connected

directly to the reaction cell in the return pathway to a bath situated outside of the glove

box. All stopped-flow experiments included recording 10 – 20 Abs – t profiles at λmax for product absorbance. Each experiment was repeated at least three times. The 2000 point absorbance – time curve data were collected either over 1+ or 5+ HL.

Abs – t profiles for product evolution were analyzed individually by three different data manipulation procedures as described in main text, all of which include two general steps. The initial step was to convert the Abs – t profiles to (1 – E.R.) – time profiles, which decayed from (1 – E.R.) = 1 for either 1 or 5 HL depending on which data manipulation procedures was used. In the second step, the modified pseudo-first-order analysis was carried out on -ln(1 – E.R.) – time profiles to give the apparent pseudo-first-order rate constants over various point segments, which has been described 187 in detail in the section of Kinetic Data Manipulation and Results.

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52, 1889. (e) Murdoch, J. R. J. Am. Chem. Soc. 1980, 102, 71. (f) Agmon, N. J. Am. Chem. Soc. 1980, 102, 2164. (g) Bernasconi, C. F. Pure & Appl. Chem. 1982, 54, 2335. (h) Albery, W. J.; Bernasconi, C. F.; Kresge, A. J. J. Phys. Org. Chem. 1988, 1, 29. (i) Gandler, J. R.; Saunders, O. L.; Barbosa, R. J. Org. Chem. 1997, 62, 4677.

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190

CHAPTER 8

THE REVERSIBLE CONSECUTIVE MECHANISM FOR THE REACTION

OF TRINITROANISOLE WITH METHOXIDE ION††

Abstract

Although the competitive mechanism for Meisenheimer complex formation

during the reaction of 2,4,6-trinitroanisole with methoxide ion in methanol is generally

accepted, no kinetic evidence has been presented to rule out a reversible consecutive mechanism. Simulation of the competitive mechanism revealed that a fractional order in

[MeO-] is predicted by the latter. Conventional pseudo-first-order analysis of the kinetics

resulted in cleanly first-order in [MeO-] which rules out the competitive mechanism. The

kinetic data are consistent with the reversible consecutive mechanism and which is proposed for this important reaction. An intermediate is required for this mechanism and we propose that a dianion complex (III) is formed reversibly from the initial

1,3-σ-omplex (I). The trimethoxy complex (III), the 1H NMR spectrum of which was observed earlier by Servis (Servis, K. L. J. Am. Chem. Soc. 1965, 87, 5495; 1967, 89,

1508), then eliminates methoxide ion reversibly to form the 1,1-σ- complex product (II).

Introduction

The reactions of electron deficient aromatic compounds with nucleophiles give rise to an important class of fundamental organic reactions, “Nucleophilic Aromatic

Substitution”. Reactions of trinitroarenes exemplified by 1,3,5-trinitrobenzene (TNB) and

†† This work has been published in J. Org. Chem. 2011, 76 (5), 1250-1256, coauthored by Vernon D. Parker, Zhao Li, Kishan L. Handoo, Weifang Hao and Jin-Pei Cheng, Reprinted with permission from J. Org. Chem. 2011, 76 (5), 1250-1256. © 2011 American Chemical Society. 191

2,4,6-trinitroanisole (TNA), with both anionic and neutral nucleophiles have been studied extensively.1-25

The reactions of TNA with alkoxide ions has received special attention in that

both kinetically and thermodynamically controlled Meisenheimer complexes have been

observed. The work of Servis6 in this respect has been of great importance in that he was

able to follow the rapid formation of 1,3-dimethoxy-2,4,6-trinitro- cyclohexadienylide (I) and the slower formation of the 1,1-dimethoxy complex (II) by H1 NMR spectroscopy.

This work led to the assumption of the competitive mechanism illustrated in Scheme 8-1 and to thorough investigations of the energetics of these reactions by the

Bernasconi12,19-21 and the Fendler13,14,16,18 groups. Bernasconi’s and Fendler’s kinetic and

equilibrium data for the reactions of TNA with methoxide ion are summarized in Table

8-1.

SCHEME 8-1. Assumed Mechanism for the Formation of 1,3 (I)- and 1,1 (II)- Dimethoxy Complexes in MeOH Containing MeO-

192

TABLE 8-1. Rate and Equilibrium Constants for the Formation of 1,3-Dimethoxy and 1,1-Dimethoxy Complexes During the Reaction of TNA with OH- in MeOH at 298 K, According to the Competitive Mechanism Shown in Scheme 8-1a -1 -1 -1 -1 -1 -1 -1 -1 k1/M s k-1/s K1/M k2/M s k-2/s K2/M 950 350 2.71 17.3 0.00104 17,000 a Ref. 16, 20

In contrast to the extensive work carried out on determining the apparent rate

and equilibrium constants summarized in Table 8-1, no work to determine the

mechanisms of the reactions was reported. It appears that the mechanisms shown in

Scheme 8-1 were taken for granted by all workers in this area.

Results

The first question which must be addressed is whether or not complex I is on the

reaction coordinate leading to complex II. If the latter is indeed the case, it is obvious that

a single-step conversion of I to II is unlikely. This may account for the fact that the details

of the mechanism have not been reported. However, it should be pointed out that

determining whether the overall mechanism consists of two competing pathways

(Scheme 8-1) or is a reversible consecutive mechanism in which complex I lies on the

reaction coordinate for the formation of II is straight forward. The latter is the first task

taken on in our reinvestigation of the mechanism of Meisenheimer complex formation

during the reaction of TNA with methoxide ion in methanol.

Simulation of the Kinetics of the Competing Mechanism (Scheme 8-1)

The kinetic data in Table 8-1 show that the reversible formation of complex I is rapid

in comparison to the formation of complex II for the reaction of TNA with methoxide ion 193 in methanol at 298 K. This fact allows the assumption that complex I is in equilibrium with reactants under the reaction conditions to be tested. Taking the latter into consideration leads to eq 8.1 which gives the equilibrium concentration of TNA as a function of its initial concentration, the equilibrium constant (K1) and the methoxide ion

concentration. Substitution of eq 8.1 into the rate law for formation of II gives eq 8.2

which describes the rate of the essentially irreversible formation of II before the latter

becomes significant. Eq 8.2 suggests a fractional reaction order in [MeO-] and that

carrying out the kinetic study over a range of methoxide ion concentration is the best way to probe for the applicability of Scheme 8-1.

- [TNA]equil = [TNA]0/(K1[MeO ] + 1) (8.1)

- d[II]/dt = k2[MeO ][TNA]equil

- - = k2[MeO ][TNA]0/(K1[MeO ] + 1) (8.2)

- - d[II]/dt = k2[MeO ][TNA]start/(K1[MeO ] + 1) (8.3)

Simulations were carried out by simple finite difference integration with the time

for four half-lives divided into equal time increments and [TNA]0 was set equal to

0.0001 M. In the simulation, eq 8.2 was used for the first time step but required

modification to eq 8.3 in subsequent steps. In each subsequent time step, [TNA]start was first evaluated by subtracting the accumulated concentration of II formed in previous steps from [TNA]0. Numerical integration methods, in contrast to integrated rate

equations, are associated with finite errors due to the sequential calculation of quantities.

This error is minimized by using very small time steps. It is important to note that the

derivations of eq 8.1, 8.2 and 8.3 involve two assumptions; (a) Complex I was assumed 194 to be in equilibrium with reactants at all times during the reaction and (b) the changes in

[MeO-] during reaction are negligible.

An effective way to test a finite difference simulation is to vary the length of the

time steps. The values of parameters calculated are expected to change toward the true

value as the length of the time steps is decreased. The simulations of the mechanism in

Scheme 8-1 as a function of time step length are summarized in Table 8-2. The

experimentally derived second-order rate constants are labeled k2’ in order to differentiate

- them from those derived by simulation (k2). The concentration of [MeO ] in the

simulations was varied from 15.0 to 120.0 mM, an 8- fold range, K1 was taken to be

-1 -1 -1 - equal to 2.71 M and k2 was assumed to equal 17.3 M s . The ratios of the initial MeO

- to TNA concentrations ([MeO ]0/[TNA]0) equal to 1200, 600 and 150, respectively, for

- simulations at [MeO ]0 equal to 120, 60 and 15 mM, satisfy the pseudo-first-order

condition.

TABLE 8-2. Simulation of the Kinetics of the Reaction of TNA with MeO- in MeOH According to Scheme 8-1 Applying Input Data from Table 8-1 [MeO-] = 120 mM [MeO-] = 60 mM [MeO-] = 15 mM # 0 0 0 Simulation time = 2 s Simulation time = 4 s Simulation time = 16 s Points -1 a -1 -1 b -1 a -1 -1 b -1 a -1 -1 b kapp/s k2/M s kapp/s k2/M s kapp/s k2/M s 1000 1.5690 13.075 0.8944 14.907 0.2499 16.660 2000 1.5677 13.064 0.8936 14.893 0.2496 16.640 4000 1.5672 13.060 0.8932 14.887 0.2495 16.633 7000 1.5669 13.058 0.8930 14.883 0.2494 16.627 10000 1.5667 13.056 0.8929 14.882 0.2494 16.627 a Apparent pseudo-first-order rate constant. b Apparent second-order rate constant.

The apparent pseudo-first-order rate constants (kapp) in Table 8-2 vary

- considerably from the expected 2-fold change for a 2-fold decrease in [MeO ]0 verifying 195 the fractional reaction order. These results provide an excellent guide for the experimental investigation. The data in Table 8-3 verify the time independence of kapp as well. The

slight variations in the rate constants as the length of the time steps are decreased show

that none of rate constants are in serious error and those obtained in the 10000 point

simulations are most reliable.

The linearity test provided by the data in Table 8-3 show that simulated kinetic

data for the competitive mechanism described in Scheme 8-1, under the conditions given,

show no deviations from first-order behavior over the first four half-lives of the reaction.

TABLE 8-3. Test for Linearity of ln (1 – E.R.) from the 10000 Point Simulation with - [MeO ]0 Equal to 120 mM -1 -1 -1 Points in correlation kapp/s k2/M s 1-10 1.5668 13.057 1-100 1.5668 13.057 1-1000 1.5668 13.057 1-2000 1.5668 13.057 1-10000 1.5667 13.056

Experimental Investigation of the Applicability of Scheme 8-1 to the Reactions of TNA with Methoxide Ion in Methanol at 298 K

Contrary to the expectation according to Scheme 8-1, the second-order rate

- constants (k2’) in Table 8-4 were observed to be independent of [MeO ]0. The values of k2’ vary from 11.48 to 11.83 M-1s-1 with an average percent deviation of ± 0.7%.

- Furthermore, the variations show no relationship to [MeO ]0. We attribute these

- variations to experimental error. The latter should be compared to the [MeO ]0 dependent

variations in the simulated data in Table 8-2. The simulated value of k2 was observed to

-1 -1 - -1 -1 - be equal to 13.06 M s ([MeO ]0 = 120 mM), to 16.63 M s ([MeO ]0 = 15 mM). 196

TABLE 8-4. Experimental Rate Constants for the Reaction of TNA (0.0001 M) with MeO- in MeOH at 293 K - -1 a ’ -1 -1 b [MeO ]0/mM Number t0.50 kapp/s k2 /M s 120 4 1.405 11.71 60 4 0.689 11.48 15 4 0.1772 11.81 120 3 1.403 11.69 60 3 0.698 11.63 15 3 0.1751 11.67 120 2 1.397 11.64 60 2 0.694 11.57 15 2 0.1738 11.59 120 1 1.383 11.53 60 1 0.689 11.48 30 1 0.355 11.83 15 1 0.1738 11.59 Average ± Ave. % Dev 11.63 ± 0.7% aExperimental pseudo- first-order rate constant. bApparent second-order rate constant.

The data in Table 8-4 are supported by the first-order plots as a function of

- reaction period illustrated in Figure 8-1 to 8-3 for cases where [MeO ]0 was 15 mM

(Figure 8-1), 60 mM (Figure 8-2) and 120 mM (Figure 8-3). Raw data were used in the

linear correlations without any further treatment. For the 4 half-lives data there is scatter

in the data at long times but no indication of non-linearity.

The data in Table 8-4 and Figure 8-1 to 8-3 are clearly inconsistent with the

competitive reaction mechanism in Scheme 8-1, which requires the second-order rate

- constants to increase with decreasing values of [MeO ]0, and suggest that complex I is an

intermediate during the formation of complex II. 197

Pseudo first-order plot Pseudo first-order plot 0.6 1.2 2.0 half-lives 1.0 half-lives -1 k1 = 0.1738 s k = 0.1738 s-1 0.4 1 0.8 -ln (1-ER) -ln (1-ER) 0.2 0.4 [TNA] = 0.10 mM [TNA] = 0.10 mM [NaOMe] = 15 mM 0.0 [NaOMe] = 15 mM 0.0

01234 02468 time/s time/s

1.5 3 Pseudo first-order plot Pseudo first-order plot 3.0 half-lives 1.0 2 4.0 half-lives k = 0.1751 s-1 1 k = 0.1772 s-1 -ln (1-ER) -ln (1-ER) 1 0.5 1 [TNA] = 0.10 mM [TNA] = 0.10 mM [NaOMe] = 15 mM [NaOMe] = 15 mM 0.0 0 02468 0481216 time/s time/s - FIGURE 8-1. Pseudo-first-order plots for the reaction of TNA with [MeO ]0 equal to 15 mM

The data in Table 8-5 were obtained using a modification of the

pseudo-first-order analysis procedure. The experimental procedure involved recording

2000 point absorbance – time (Abs – t) profiles over about the first half-life of the reactions and doing a sequential first-order analysis on specific point segments of the Abs

– t profiles. The procedure also employed least squares linear correlation but in this case

24 different analyses were carried out over different point segments in the profile. The point segments include points 1-11, 1-21, 1-31, 1-41, 1-51, 1-101, 1-201, 1-301, 1-401,

1-501, 1-601, 1-701, 1-801, 1-901, 1-1001, 1-1101, 1-1201, 1-1301, 1-1401, 1-1501,

1-1601, 1-1701, 1-1801 and 1-1901. If a reaction obeys first-order kinetics the values of 198 the rate constants for all of the point segments are expected to be time independent and have the same value. A factor that should be taken into account of the data in Table 8-5 when compared to that in Table 8-4 and Figure 8-1 to 8-3 is that the former corresponds to 2000 points over the first half-life of the reactions and the latter to 2000 points over more than 4 half-lives. This difference means that the data segments for Table 8-5 begin at shorter times than those in Table 8-4 and Figure 8-1 to 8-3.

0.8 1.5 Pseudo first-order plot Pseudo first-order plot 0.6 1.0 half-lives 2.0 half-lives 1.0 -1 -1 k = 0.689 s k1 = 0.694 s 0.4 1 -ln (1-ER) -ln (1-ER) 0.5 0.2 [TNA] = 0.10 mM [TNA] = 0.10 mM [NaOMe] = 60 mM [NaOMe] = 60 mM 0.0 0.0

0.00.20.40.60.81.0 0.0 0.5 1.0 1.5 2.0 time/s time/s

2.0 Pseudo first-order plot 3 Pseudo first-order plot 3.0 half-lives 1.5 4.0 half-lives -1 -1 k1 = 0.698 s -ln (1-ER) 2 k1 = 0.689 s 1.0 -ln (1-ER)

[TNA] = 0.10 mM 1 0.5 [TNA] = 0.10 mM [NaOMe] = 60 mM [NaOMe] = 60 mM 0.0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 01234 time/s time/s

- FIGURE 8-2. Pseudo-first-order plots for the reaction of TNA with [MeO ]0 equal to 60 mM

What is immediately apparent in Table 8-5 is that in all 4 series of reactions,

- with [MeO ]0 ranging from 15 to 120 mM, the kapp – time profiles begin at relatively high 199 values of kapp and decay with time to steady-state values. Although it might be argued

that the standard deviations of the short time points in Figures E.1 to E.4 (Appendix E)

are relatively high, the mean values of three determinations have a small degree of

variance and are certainly significant.

0.8 1.6 Pseudo first-order plot Pseudo first-order plot 0.6 1.2 2.0 half-lives k = 1.397 s-1 1.0 half-lives -ln (1-ER) 1 -1 0.4 k1 = 1.383 s 0.8 -ln (1-ER)

0.2 [TNA] = 0.10 mM 0.4 [TNA] = 0.10 mM [NaOMe] = 120 mM [NaOMe] = 120 mM 0.0 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.2 0.4 0.6 0.8 1.0 time/s time/s

3.00 1.8 Pseudo first-order plot Pseudo first-order plot 3.0 half-lives 2.25 4.0 half-lives k = 1.405 s-1 1.2 -1 -ln (1-ER) 1 k1 = 1.403 s -ln (1-ER) 1.50

0.6 [TNA] = 0.10 mM [TNA] = 0.10 mM 0.75 [NaOMe] = 120 mM 0.0 [NaOMe] = 120 mM 0.00 0.00.40.81.21.6 0.0 0.5 1.0 1.5 2.0 time/s time/s

- FIGURE 8-3. Pseudo-first-order plots for the reaction of TNA with [MeO ]0 equal to 120 mM

It is of interest to determine how the magnitude of K1 must be adjusted in order

- for calculated k2 values to be independent of [MeO ]0 according to the mechanism in

Scheme 8-1. The data in Table 8-6 show the convergence of k2 obtained from data from

- [MeO ]0 equal 120 mM with that from data from the 15 mM simulation (the value of k2 in 200

-1 -1 the simulation was 17.30 M s ). It would appear that the value of K1 would have to be of

- the order of 0.10 for the k2 values obtained at [MeO ]0 equal to 120 and 15 mM to be

within experimental error of each other. The latter is clearly out of the range of the

16,20 experimental values of K1.

TABLE 8-5. Apparent Rate Constants as a Function of Degree of Conversion and - a [MeO ]0 15 mM 30 mM 60 mM 120 mM c -1 b -1 b -1 b -1 b Segment kapp/s ± kapp/s ± kapp/s ± kapp/s ± 0.294 0.011 0.855 0.032 2.941 0.199 10.420 0.200 1 0.191 0.004 0.542 0.016 1.792 0.097 7.320 0.055 2 0.178 0.001 0.452 0.012 1.330 0.048 5.510 0.052 3 0.173 0.001 0.417 0.010 0.101 0.040 4.340 0.051 4 0.170 0.002 0.395 0.009 0.977 0.033 3.600 0.044 5 0.169 0.001 0.363 0.008 0.776 0.022 3.150 0.056 6 0.172 0.001 0.357 0.009 0.713 0.019 1.630 0.060 7 0.173 0.002 0.357 0.008 0.701 0.019 1.517 0.062 8 0.175 0.001 0.357 0.009 0.696 0.019 1.473 0.065 9 0.174 0.001 0.358 0.009 0.694 0.019 1.451 0.067 10 0.174 0.002 0.359 0.009 0.694 0.019 1.439 0.069 11 0.174 0.002 0.360 0.010 0.693 0.020 1.432 0.071 12 0.174 0.002 0.360 0.010 0.693 0.020 1.427 0.072 13 0.175 0.002 0.360 0.010 0.692 0.020 1.424 0.074 14 0.175 0.002 0.361 0.010 0.692 0.021 1.421 0.076 15 0.175 0.002 0.361 0.010 0.692 0.022 1.420 0.078 16 0.175 0.002 0.362 0.011 0.694 0.022 1.419 0.080 17 0.175 0.002 0.362 0.011 0.694 0.022 1.418 0.082 18 0.175 0.002 0.363 0.012 0.694 0.022 1.418 0.084 19 0.175 0.002 0.363 0.012 0.695 0.022 1.417 0.086 20 0.174 0.002 0.364 0.012 0.695 0.022 1.417 0.080 21 0.174 0.002 0.364 0.012 0.696 0.023 1.418 0.090 22 0.174 0.002 0.365 0.013 0.696 0.023 1.417 0.092 23 0.174 0.002 0.365 0.013 0.697 0.024 1.418 0.094 24 a Average of 3 sets of 15-20 stopped-flow repetitions. Data listed in Tables E.1 to E.4. b Average deviation of a set. c Data segment of analysis, see text for explanation.

201

TABLE 8-6. The Effect of K1 Magnitude on the Value of the Apparent Second-Order Rate Constants (k2’) Obtained from Simulated Data for the Mechanism in Scheme 8-1 -1 -1 -1 -1 -1 -1 -1 K1/M kapp(120 mM)/s k2(120 mM)/M s kapp(15 mM)/s k2(15 mM)/M s 2.71 1.567 13.08 0.2499 16.60 2.00 1.674 13.95 0.2520 16.80 1.00 1.854 15.45 0.2557 17.05 0.50 1.959 16.33 0.2576 17.17 0.25 2.016 16.80 0.2586 17.24 0.10 2.052 17.10 0.2592 17.28 0.050 2.064 17.20 0.2594 17.29 0.025 2.070 17.25 0.2594 17.29 0.0125 2.073 17.28 0.2595 17.30

TABLE 8-7. Simulated Values of the Ratios of Rates of Formation and Decay of Complex II - - a [MeO ]0 Extent of Reaction (E.R.) k2[MeO ][TNA]equil / k-2[TNA]0(E.R.) 120 0.1 13557 120 0.5 1506 120 0.9 167.6 60 0.1 7726 60 0.5 858.5 60 0.9 95.4 30 0.1 4153 30 0.5 461.5 30 0.9 51.2 15 0.1 2158 15 0.5 239.8 15 0.9 26.6 a - [TNA]equil = (1 – E.R.)[TNA]0/(K1[MeO ] + 1), E.R. = Extent of Reaction.

It is possible that the neglect of the reverse rate constant k-2 gives rise to error in

- the simulations. Instantaneous rates at various values of E.R. and [MeO ]0 were

- calculated using the expression, k2[MeO ][TNA]equil/k-2[TNA]0(E.R.) in which the units

cancel. Calculations of the relative instantaneous rates at 10, 50 and 90% conversion are

shown in Table 8-7. The data above show that the assumption that product formation is

-1 essentially irreversible, as expected due to the large value of K2 (equal to 17,000 M ), is 202 valid and that the reaction goes to completion rather than to an equilibrium state.

Discussion

A very likely mechanism for the transformation of TNA to complex II is the reversible formation of a “reactant complex” by conversion of the σ-complex (I) as shown in Scheme 8-2. We are reluctant to designate this species as the π-complex since it could form directly from the reactants and then partition between the two σ-complexes, I and II. That being the case, the overall result would be the same as expected for Scheme

1. A reversible consecutive mechanism which takes into account all of the experimental kinetic data is illustrated in Scheme 8-2. The rapidly decaying values of kapp at short times are characteristic for reactions in which an intermediate absorbs at the wavelength where the evolution of product is monitored and the decreasing kapp at short times are due

to the decay of the intermediate.

SCHEME 8-2. Reversible Consecutive Mechanism for the Formation of Complex II During the Reaction of TNA with MeO- in MeOH

203

A plausible structure of the “Reactant Complex” is the dianion complex III.

Servis6 found that in the presence of 1.0 equivalent of methoxide ion, the rapid formation

of complex I was followed by the slower transformation of complex I to complex II.

However, in the presence of 1.8 equivalents of methoxide ion, the predominant species

present showed 1H NMR resonances at 6.13 and 8.80 ppm in the ratio of 1:1. He assigned these resonances to the dianion complex III. A possible reaction sequence for the formation of III is illustrated in Scheme 8-3. It must be point out that the conditions of

NMR studies6 differ considerably from those in the kinetic study and the most pertinent

differences are the methoxide concentrations (<0.8 M in the NMR study and < 0.12 M in

our study) and the solvent (DMSO in the NMR study and methanol in our study).

SCHEME 8-3. Possible Reaction of Complex I with MeO- to Form the Dianion Complex III (“Reactant Complex” = III) Which Eliminates MeO- to Produce Complex II

It may appear possible that the “exalted” kapp values at short times (Table 8-5,

E.1 – E.4) are plausibly explained by assuming that the reaction forming Complex I has

not quite reached equilibrium at short times and that the observed kinetic process is

contaminated by that rapid reaction. The latter appeared to be a reasonable assumption and we tested that possibility by simulating the time necessary for the reaction leading to

Complex I to come to equilibrium under conditions where the slower formation of 204

Complex II was neglected. The simulation results are illustrated in Figure 8-4 for the reaction of TNA (0.1 mM) with MeO- (15 and 120 mM). The times necessary to reach the plateau regions of the two plots are indicative of the time necessary for reaction (1)

(Scheme 8-2) to reach the equilibrium state. The plateau regions for both curves (Figure

8-4) are reached during the same time interval (10 – 15 ms). From the latter, we conclude that equilibrium is established prior to the shortest kinetic time point (15 ms) for the

- th slowest reaction ([MeO ]0 = 15 mM) and prior to the 6 time point (15 ms) for the other

- extreme ([MeO ]0 = 120 mM). The time to reach equilibrium in reaction (1) is dependent

- - on (k1[MeO ] + k-1) and the values of this term are 464 ([MeO ]0 = 120 mM) and 364

- ([MeO ]0 = 15 mM). From the latter we conclude that the time to reach equilibrium is not

an important factor in the “exalted” rate constants at short times.

0.024 [TNA]o = 120 mM

0.016 [Complex I]

0.008

[TNA] = 15 mM 0.000 o 0.000 0.008 0.016 0.024 time/s FIGURE 8-4. Simulated concentration – time plots for the reaction of TNA (0.1 mM) - with [MeO ]0 equal to 15 and 120 mM

The plots in Figure 8-4 also illustrate another point which is in opposition to the

latter explanation. If the kinetic process observed is contaminated by absorbance due to

the formation of Complex I, this positive absorbance would give rise to an increase in kapp 205 rather than the decreasing values observed at short times. Absorbance values at short times actually decrease with time and can readily be explained by the decay of an intermediate as proposed above.

The question as to why the 1,3-complex is formed more rapidly than the more stable 1,1-complex was addressed by Bernasconi.19 A comparison of the known rate

retarding effect26 due to ground state stabilization during the hydrolysis of p-methoxydiazonium ion was cited in support of the relative rates on unsubstituted vs

methoxy substituted ring positions. In the latter case, the unsubstituted benzenediazonium

ion was observed to react about 6000 time faster than p-methoxydiazonium ion.

The reactions of 1-X-2,4,6-trinitrobenzenes (where X is alkyloxy or aryloxy

groups) with nucleophiles have been classified as K3T1, K3T3, K1T1 or K1T3 by the

Buncel group27 where for example K3T1 represents kinetic control (K3) by attack at the

3-position and T1 by thermodynamic control by attack at the 1-position. The

classification was supported by a number of papers from that group.28 The Buncel

group27,28 continued to assume that these reactions are described by the competing

mechanism described in Scheme 8-1.

The first reaction in Scheme 8-2 may consist of two steps involving a species

other than the π-complex but at this stage of our investigation we are not ready to suggest

that much detail in our mechanism. Our conclusions at this time are that the formation of

the 1,1-complex does not take place according to the accepted mechanism in Scheme 8-1

and that the 1,3-complex lies on the reaction coordinate for the formation of the

thermodynamically more stable II. The dianion σ-complex (Scheme 8-3) is a reasonable 206 suggestion of the structure of the intermediate. The detailed mechanism of the formation of the σ-complexes of TNA and TNB with methoxide ion and other nucleophiles is under investigation.

Experimental

TNA was obtained commercially and was recrystallized from methanol before use. No impurities could be detected by H1 NMR spectrometry. Methanol was of the highest grade available and used without further purification. Sodium methoxide solutions were prepared by allowing freshly cut sodium slices to react in methanol under a nitrogen atmosphere.

Kinetic experiments were carried out using a Hi-Tech SX2 stopped-flow spectrometer installed in a glove box and kept under a nitrogen atmosphere. The temperature was controlled at 293 K using a constant temperature flow system connected directly to the reaction cell through a bath situated outside of the glove box. All stopped-flow experiments included recording 15 – 20 Abs – t profiles at 485 nm. Each experiment was repeated three times. The 2000 point Abs – t curve data were collected either over 1+ or 4+ half-lives (HL).

Abs – t profiles for product evolution were analyzed individually by two

different procedures. The first step in both procedures was to convert the Abs – t profiles

to (1 – E.R.) – time profiles where E.R. denotes extent of reaction. This was carried out by dividing each absorbance value by the infinity value obtained from the product extinction coefficient and the reactant concentration and subtracting the value from 1.0.

This procedure gave (1 – E.R.) – time profiles that decayed from (1 – E.R.) = 1 for either 207

1 or 4 HL depending on which analysis procedure was used. For pseudo-first-order kinetic analysis the (1 – E.R.) – time profiles were converted to ln (1 – E.R.) – time profiles. For further processing, the individual 4 HL (1 – E.R.) – time profiles were first averaged to give the average profiles.

The first kinetic procedure used was simply least squares linear correlation of the

-ln(1 – E.R.) – time profiles to give the apparent pseudo-first-order rate constants over either 1, 2, 3 or 4 HL. These values are recorded in the Results section. The second procedure involved recording the Abs – t profiles over slightly more than the first HL followed by the sequential 24 linear correlations described in the Results section. Figures

E.1 – E.4 (Appendix E) were included to show the difficulty of differentiating between the simple one-step mechanism and more complex mechanisms. The deviations from apparent first-order kinetics might be considered as negligible based upon these ln (1 –

E.R.) – time profiles.

Refereces

(1) Bunnett, J. F.; Morath, R. J. J. Am. Chem. Soc. 1955, 77, 5051.

(2) Ainscough, J. B.; Caldin, E. F. J. Chem. Soc. 1956, 2528.

(3) Gold, V.; Rochester, C. H. J. Chem. Soc. 1964, 1987.

(4) Bolles, T. F.; Drago, R. S. J. Am. Chem. Soc. 1965, 87, 5015.

(5) Crampton, M. R.; Gold, V. J. Chem. Soc., B 1966, 893.

(6) Servis, K. L. J. Am. Chem. Soc. 1965, 87, 5495; 1967, 89, 1508.

(7) Foster, R; Fyfe, C. A. Tetrahedron 1965, 21, 3363.

(8) Norris, A. R. Can. J. Chem. 1967, 45, 2703. 208

(9) Byrne, W. E.; Fendler, E. J.; Fendler, J. H.; Griffin, C. E. J. Org. Chem. 1967, 32, 2506.

(10) Buncel, E.; Norris, A. R.; Proudlock, W. Can. J. Chem. 1968, 46, 2759.

(11) Buncel, E.; Norris, A. R.; Russell, K. E. Q. Rev. Chem. Soc. 1968, 22, 123.

(12) Bernasconi, C. F. J. Am. Chem. Soc. 1968, 90, 4982.

(13) Fendler, E. J.; Griffin, C. E.; Fendler, J. H. Tetrahedron Lett. 1969, 5631.

(14) Fendler, E. J.; Fendler, J. H.; Byrne, W; Griffin, C. E. J. Org. Chem. 1968, 33, 4141.

(15) Buncel, E.; Norris, A. R.; Russell, K. E.; Proudlock, W. Can. J. Chem. 1969, 47, 4129.

(16) Fendler, J. H.; Fendler, E. J.; Griffin, C. E. J. Org. Chem. 1969, 34, 689.

(17) Crampton, M. R. Adv. Phys. Org. Chem. 1969, 7, 211.

(18) Fendler, E. J.; Fendler, J. H.; Griffin, C. E.; Larsen, J. W. J. Org. Chem. 1970, 35, 287.

(19) Bernasconi, C. F. J. Am. Chem. Soc. 1970, 92, 4682.

(20) Bernasconi, C. F. J. Am. Chem. Soc. 1971, 93, 6975.

(21) Bernasconi, C. F.; Bergstrom, R. G. J. Org. Chem. 1971, 36, 1325.

(22) Crampton, M. R.; Khan, H. A. J. Chem. Soc., Perkin Trans. 2 1972, 733.

(23) Gan, L. H.; Norris, A. R. Can. J. Chem. 1974, 52, 8.

(24) Sasaki, M. Rev. Phys. Chem. Japan 1973, 41, 44.

(25) Fyfe, C. A.; Damji, S. W. H.; Koll, A. J. Am. Chem. Soc. 1979, 101, 956.

(26) Corssley, M. L.; Kienle, R. H.; Benbrook, C. H. J. Am. Chem. Soc. 1940, 62, 14.

(27) Buncel, E.; Dust, J. M.; Manderville, R.A.; Tarkka, R. M. Can. J. Chem. 2003, 81, 443.

(28) (a) Buncel, E.; Murarka, S. K.; Norris. A. R. Can. J. Chem. 1984, 62, 534.(b) 209

Buncel, E.; Dust, J. M.; Jonczyk, A.; Manderville, R.A.; Onyido, I. J. Am. Chem. Soc. 1992, 114, 5610. (c) Manderville, R. A. Buncel, E. J. Am. Chem. Soc. 1993, 115, 8985. (d) Buncel, E.; Tarkka, R.M.; Dust, J. M. Can. J. Chem. 1994, 72, 1709. (e) Buncel, E.; Dust, J. M.; Terrier, F. Chem. Rev. 1995, 95, 2261.

210

CHAPTER 9

CONCLUSIONS

The work outlined in this dissertation that focuses on the rigorous investigation of the kinetics and mechanisms of some fundamental organic reactions of nitro compounds has been successfully carried out by means of an efficient combination of modern digital technology of kinetic data acquisition and new data analysis procedures especially suitable for the differentiation of reaction mechanisms.

Theoretical analyses revealed that the conventional method of establishing first-order (or pseudo-first-order) kinetics, the correlation of -ln (1 – E.R.) – time profiles, does in no applicable case differentiate between the single one-step and the kinetically significant pre-association mechanisms. Four new analysis procedures for pseudo-first-order kinetics have been introduced, which consist of (1) half-life dependence of apparent rate constant during convention pseudo-first-order analysis, (2) sequential linear pseudo-first-order correlation, (3) approximate instantaneous rate constant analysis, and (4) time-dependent apparent kinetic isotope effects. Each of the four procedures is capable of distinguishing between single-step and multi-step mechanisms, and the combination of the four procedures provides a powerful strategy for differentiating between the two mechanistic possibilities, that has been extensively confirmed during the application in our kinetic study of a wide variety of fundamental organic reactions.

Kinetic investigation of the proton transfer reactions of aliphatic nitroalkanes with hydroxide ion in water revealed that the reactions are complex and involve 211 kinetically significant intermediates. This conclusion is supported by a revised conventional first-order analysis as well as by a sequential first-order analysis designed to show changes with time in the apparent pseudo-first-order rate constant (kapp) if they exist.

For all reactions the kapp were observed to be relatively large at short times and to

decrease toward steady-state values later in the reaction. Absorbance – time profiles at

isosbestic points show the presence of intermediates which absorb at these wavelengths.

The apparent deuterium kinetic isotope effects for proton/deuteron transfer are E.R. and

time-dependent approaching unity near zero time and increasing with time toward plateau

values as the reaction kinetics reach steady state. The latter indicates that the deuterium

kinetic isotope effects are not associated with the formation of the intermediates. In order

to rationalize the kinetic results as well as the inverse relationship between the kinetic and

thermodynamic acidities of NM, NE and 2-NP, a three-step reversible consecutive

mechanism has been proposed, in which the initially formed pre-association complexes

are transformed to more intimate reactant complexes which can give products by two

possible pathways involving either a polar proton transfer or an intra-complex hydrogen

atom coupled electron transfer (HACET) from a reactant complex. However, we have not

been unable to distinguish between two possible product forming steps. The further work

is expected to clarify this issue and add detail to this mechanism.

The UV-vis spectrophotometric investigation of the proton transfer reactions of

nine common aliphatic nitroalkanes with hydroxide ion in aqueous solutions revealed that

there is no true isosbestic point found at the wavelengths where the extinction coefficients

for reactants and products are equal, A series of evolution and decay absorbance – time 212 profiles, consistent with the absorbance characteristic of the formation of reactive intermediates, were observed at these apparent isosbestic wavelengths. Several theoretical and experimental investigations have been carried out to verify the contribution of intermediates to the changes of absorbance. The recent development in methodology has been discussed in detail, and suggested that an isosbestic point study provides a potential way to trace the formation and decay of an intermediate.

Three detailed applications of pseudo-first-order kinetics to the proton transfer reactions of 1-arylnitroethanes with hydroxide ion in aqueous solutions revealed that the reactions are complex and a reversible consecutive mechanism involving a kinetically significant intermediate was proposed. The formation of the intermediates does not involve C–H bond dissociation. The latter has been strongly confirmed by the fact that the apparent KIE’s are E.R. and time-dependent approaching unity near zero time and evolving toward a plateau value as steady state is achieved. The Brønsted correlation was carried out by using the microscopic rate constants, kp, specific for the proton transfer

step and the Brønsted exponent αreal was observed to be in the normal range, which suggests that the nitroalkane anomaly previously proposed for this reaction series does

not exists as long as the Brønsted relationship is applied correctly. This conundrum,

having perplexed physical organic chemists for a half century, was just a consequence of

the incorrect assumption that the reactions follow a simple one-step mechanism.

The aromatic nucleophilic reaction of 2,4,6-trinitroanisole (TNA) with methoxide ion in methanol have been found to follow a reversible consecutive

mechanism. The latter is contrary to the long accepted belief that the formation of the 213

2,4,6-trinitro-1,3-dimethoxy-cyclohexadienylide (I) and the 1,1-dimethoxy complex (II) take place by a competitive rather than a sequential mechanism. Simulation of the competitive mechanism revealed that a fractional order in [MeO-] is predicted by the latter. Conventional pseudo-first-order analysis of the kinetics resulted in cleanly first-order in [MeO-] which rules out the competitive mechanism. The kinetic data are

consistent with the reversible consecutive mechanism and which is proposed for this

important reaction. An intermediate is required for this mechanism and we propose that a

trimethoxy dianion complex (III) is formed reversibly from the initial 1,3-σ-complex (I),

and then eliminates methoxide ion to form the 1,1-σ-complex product (II). The

tentatively proposed intermediate (III) was not observed but the 1H NMR spectrum had

previously been observed by Servis.

In summary, our answer to the question posed at the very beginning, “Is the

single transition-state model appropriate for (1) the proton transfer reactions of

nitroalkanes and (2) the aromatic nucleophilic reactions of trinitroarenes?” is no. The

results shown in this dissertation have challenged the long established beliefs that have

dominated the thinking of physical organic chemists for more than half a century. One of

the most essential objectives of this work is to call for more attentions paid to the

importance of reaction mechanism to the field of organic chemistry. In my opinion, as the

development of experimental technology continues, the mechanistic analyses will

become more and more careful and rigorous, and that further probing of this area in the

future may possibly bring about a profound change in the thinking of physical organic

chemists, as well as the way they approach the study of organic reaction mechanisms. 214

APPENDICES

215

Appendix A. Supplementary Table for Theoretical Differentiation Between Mechanisms

216

TABLE A.1. Time Ratio (t0.50/t0.05) Matrix for the KSPAM When Product Evolution Is Monitored

kapp = 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

kp/kb = 10 2 1 0.5 0.25 0.125 0.0625 0.03125 0.015625

kf’ = 1.1 1.5 2 3 4 8 16 32 64

kp t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 t0.50/t0.05 512 13.09 13.20 13.28 13.36 13.40 13.45 13.48 13.50 13.51 256 12.70 12.91 13.06 13.20 13.28 13.40 13.45 13.48 13.50 128 11.99 12.36 12.63 12.91 13.06 13.28 13.40 13.46 13.48 64 10.82 11.42 11.88 12.38 12.64 13.07 13.29 13.40 13.46 32 9.25 10.02 10.68 11.47 11.92 12.67 13.08 13.29 13.40 16 7.64 8.42 9.16 10.16 10.80 12.00 12.72 13.10 13.30 8 6.31 7.00 7.69 8.72 9.45 11.04 12.15 12.80 13.15 4 5.43 5.97 6.56 7.50 8.22 9.97 11.43 12.39 12.93 2 4.48 5.40 5.89 6.73 7.40 9.15 10.80 12.00 12.71 1 3.12 3.72 3.94 4.99 5.43 6.63 7.83 8.76 9.32 0.5 2.36 2.43 3.01 3.24 3.44 4.89 5.66 6.23 6.57 0.25 1.52 1.55 1.57 2.21 2.30 2.56 2.81 4.05 4.19 0.125 1.00 1.24 1.38 1.54 1.73 1.85 1.94 1.99 2.02 0.0625 1.00 1.00 1.00 1.00 1.00 1.00 1.19 1.20 1.20 0.03125 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

217

Appendix B. Supplementary Information for Reactions of the Simple Nitroalkanes with

Hydroxide Ion in Water

218

TABLE B.1. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments on the Reaction of NM (0.10 mM) with NaOH (20.0 mM) in H2O at 298 K Set 1a Set 2b Set 3c time/s -1 -1 -1 Segment kapp/s SD kapp/s SD kapp/s SD 0.009 0.550 0.083 0.394 0.119 0.489 0.128 1 0.013 0.545 0.035 0.559 0.070 0.576 0.036 2 0.017 0.548 0.026 0.546 0.032 0.550 0.030 3 0.020 0.542 0.016 0.548 0.012 0.545 0.021 4 0.024 0.542 0.013 0.546 0.009 0.544 0.013 5 0.043 0.537 0.008 0.543 0.007 0.534 0.007 6 0.080 0.532 0.004 0.536 0.003 0.525 0.003 7 0.118 0.528 0.003 0.533 0.002 0.521 0.002 8 0.155 0.525 0.003 0.531 0.002 0.518 0.002 9 0.193 0.523 0.003 0.530 0.001 0.517 0.002 10 0.230 0.522 0.003 0.529 0.001 0.515 0.002 11 0.268 0.520 0.003 0.527 0.001 0.514 0.002 12 0.305 0.519 0.003 0.527 0.001 0.513 0.002 13 0.343 0.518 0.003 0.526 0.001 0.512 0.002 14 0.380 0.517 0.003 0.525 0.001 0.511 0.002 15 0.418 0.516 0.003 0.525 0.001 0.510 0.002 16 0.455 0.515 0.004 0.524 0.001 0.509 0.002 17 0.493 0.514 0.004 0.523 0.001 0.508 0.002 18 0.530 0.513 0.004 0.522 0.001 0.507 0.002 19 0.568 0.512 0.004 0.522 0.001 0.507 0.002 20 0.605 0.511 0.004 0.521 0.001 0.506 0.002 21 0.643 0.511 0.004 0.521 0.001 0.505 0.003 22 0.680 0.510 0.004 0.520 0.001 0.504 0.003 23 0.718 0.509 0.004 0.519 0.001 0.504 0.003 24

aSet 1: 20 stopped-flow repetitions. bSet 2: 12 stopped-flow repetitions. cSet 3: 20 stopped-flow repetitions.

219

TABLE B.2. Apparent Rate Constants and Standard Deviations for 4 Sets of Experiments on the Reaction of NE (0.10 mM) with NaOH (50.0 mM) in H2O at 298 K Set 1a Set 2b Set 3c Set 4d time/s -1 -1 -1 -1 Segment kapp/s SD kapp/s SD kapp/s SD kapp/s SD 0.014 0.290 0.097 0.275 0.067 0.289 0.081 0.266 0.110 1 0.021 0.286 0.044 0.274 0.039 0.274 0.046 0.271 0.037 2 0.029 0.280 0.019 0.271 0.028 0.274 0.018 0.267 0.024 3 0.036 0.276 0.014 0.271 0.022 0.269 0.011 0.269 0.017 4 0.044 0.270 0.014 0.269 0.016 0.269 0.008 0.267 0.013 5 0.081 0.265 0.006 0.264 0.005 0.266 0.004 0.264 0.006 6 0.156 0.260 0.002 0.259 0.001 0.262 0.002 0.261 0.002 7 0.231 0.258 0.001 0.257 0.001 0.260 0.001 0.260 0.001 8 0.306 0.256 0.001 0.256 0.001 0.259 0.001 0.259 0.001 9 0.381 0.255 0.001 0.255 0.001 0.259 0.001 0.258 0.001 10 0.456 0.255 0.001 0.255 0.001 0.258 0.001 0.257 0.001 11 0.531 0.254 0.001 0.254 0.001 0.257 0.001 0.257 0.001 12 0.606 0.254 0.001 0.253 0.001 0.257 0.001 0.256 0.001 13 0.681 0.253 0.001 0.253 0.001 0.257 0.001 0.256 0.001 14 0.756 0.253 0.001 0.252 0.001 0.256 0.001 0.255 0.001 15 0.831 0.252 0.001 0.251 0.001 0.256 0.001 0.255 0.001 16 0.906 0.252 0.001 0.251 0.001 0.255 0.001 0.255 0.001 17 0.981 0.251 0.001 0.250 0.001 0.255 0.001 0.254 0.001 18 1.056 0.251 0.001 0.249 0.001 0.255 0.001 0.254 0.001 19 1.131 0.251 0.001 0.248 0.001 0.254 0.001 0.254 0.001 20 1.206 0.250 0.001 0.248 0.001 0.254 0.001 0.254 0.001 21 1.281 0.250 0.001 0.247 0.001 0.254 0.001 0.253 0.001 22 1.356 0.249 0.001 0.246 0.001 0.253 0.001 0.253 0.001 23 1.431 0.249 0.001 0.246 0.001 0.253 0.001 0.253 0.001 24

aSet 1: 20 stopped-flow repetitions. bSet 2: 10 stopped-flow repetitions. cSet 3: 20 stopped-flow repetitions. dSet 4: 20 stopped-flow repetitions.

220

TABLE B.3. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments on the Reaction of 2-NP (0.10 mM) with NaOH (50.0 mM) in H2O at 298 K Set 1a Set 2b Set 3c time/s -1 -1 -1 Segment kapp/s SD kapp/s SD kapp/s SD 0.135 0.0248 0.0045 0.0229 0.0081 0.0267 0.0071 1 0.248 0.0221 0.0013 0.0215 0.0023 0.0233 0.0032 2 0.360 0.0216 0.0012 0.0206 0.0014 0.0219 0.0011 3 0.473 0.0214 0.0008 0.0197 0.0012 0.0218 0.0010 4 0.585 0.0212 0.0006 0.0195 0.0009 0.0212 0.0007 5 1.148 0.0207 0.0002 0.0188 0.0004 0.0204 0.0003 6 2.273 0.0199 0.0002 0.0182 0.0001 0.0197 0.0002 7 3.398 0.0193 0.0002 0.0178 0.0001 0.0192 0.0002 8 4.523 0.0187 0.0002 0.0173 0.0001 0.0188 0.0002 9 5.648 0.0183 0.0002 0.0170 0.0001 0.0184 0.0002 10 6.773 0.0180 0.0002 0.0167 0.0001 0.0181 0.0002 11 7.898 0.0177 0.0002 0.0165 0.0001 0.0179 0.0002 12 9.023 0.0175 0.0002 0.0163 0.0001 0.0177 0.0002 13 10.148 0.0173 0.0002 0.0161 0.0001 0.0175 0.0002 14 11.273 0.0172 0.0002 0.0159 0.0001 0.0174 0.0002 15 12.398 0.0170 0.0002 0.0158 0.0001 0.0172 0.0002 16 13.523 0.0169 0.0002 0.0157 0.0001 0.0171 0.0002 17 14.648 0.0168 0.0002 0.0156 0.0001 0.0171 0.0002 18 15.773 0.0167 0.0002 0.0155 0.0001 0.0170 0.0002 19 16.898 0.0166 0.0002 0.0154 0.0001 0.0169 0.0002 20 18.023 0.0165 0.0002 0.0153 0.0001 0.0169 0.0002 21 19.148 0.0165 0.0002 0.0153 0.0001 0.0168 0.0002 22 20.273 0.0164 0.0002 0.0152 0.0001 0.0167 0.0002 23 21.398 0.0163 0.0002 0.0151 0.0001 0.0167 0.0002 24

aSet 1: 15 stopped-flow repetitions. bSet 2: 15 stopped-flow repetitions. cSet 3: 20 stopped-flow repetitions.

221

8.5 8.0 7.5

ER 7.0 [NM(-d3 )] = 0.1mM app 6.5 [NaOH] = 20.0mM KIE in H O at 298K 6.0 2 240 nm 5.5 5.0 0.0 0.1 0.2 0.3 0.4 0.5 E. R.

FIGURE B.1. Apparent KIE for the reactions of NM and NM-d3 in H2O at 298 K as a function of degree of conversion

8.5 8.0 7.5

ER 7.0 app 6.5 [NE(-d2 )] = 0.1 mM KIE [NaOH] = 50.0 mM 6.0 in H2 O at 298K 5.5 240nm 5.0 0.0 0.1 0.2 0.3 0.4 0.5 E. R.

FIGURE B.2. Apparent KIE for the reactions of NE and NE-d2 in H2O at 298 K as a function of degree of conversion 222

8.5 8.0 7.5

ER 7.0 app 6.5 KIE 6.0 [2-NP(-d)] = 0.1mM [NaOH] = 100.0mM 5.5 in H2 O at 298K 5.0 0.0 0.1 0.2 0.3 0.4 0.5 time/s

FIGURE B.3. Apparent KIE for the reactions of 2-NP and 2-NP-d1 in H2O at 298 K as a function of degree of conversion

223

3.5 a 3.0 a'

3.0 [NM] = 0.205 mM 2.5 [NM] = 19.12 mM 2.5 [NaOH] = 10.0 mM [NaOH] = 20.0 mM 2.0 in H2O at 298K in H2O at 298K 2.0 1.5 1.5

Abs / Abs A.U. 1.0 1.0 Abs / A.U. Abs Abs0 Abs 0.5 0.5 Abs0 0.0 0.0 200 220 240 260 280 300 200 225 250 275 300 325 350 375

nm nm 4.0 3.5 b 3.5 b' 3.0 [NE] = 0.1954 mM 3.0 [NE] = 21.127 mM [NaOH] = 10.0 mM 2.5 2.5 [NaOH] = 50.0mM in H O at 298K 2 in H2O at 298K 2.0 2.0 1.5 1.5 Abs0 Abs Abs / A.U. 1.0 Abs Abs / A.U. 1.0

0.5 Abs0 0.5 0.0 0.0 200 220 240 260 280 300 200 225 250 275 300 325 350 375

nm nm 4.0 4.0 c c' 3.5 3.5 3.0 [2-NP] = 0.202 mM 3.0 [2-NP] = 20.9mM [NaOH] = 50.0 mM [NaOH] = 100.0mM 2.5 2.5 in H2O at 298K in H2O at 298K 2.0 2.0 1.5 1.5 Abs Abs / A.U. Abs / A.U. 0 Abs 1.0 Abs0 Abs 1.0 0.5 0.5 0.0 0.0 200 220 240 260 280 300 200 225 250 275 300 325 350 375 nm nm Product Absorption Reactant Absorption -1 -1 -1 -1 λmax (nm) εmax (M cm ) λmax (nm) εmax (M cm ) NM 234 7310 269 15.9 NE 229 8347 272 17.7 2-NP 224 9779 275 19.5 FIGURE B.4. UV absorption spectra for the reactions of NM (a, a’), NE (b, b’), 2-NP (c, - c’) with OH in H2O under the conditions as shown 224

0.356 269.6 nm 0.354

Abs / A.U. [NE] = 21.1 mM 0.352 [NaOH] = 50.0 mM

in H2 O at 298K 0.350

0.348 0 5 10 15 20 time/s

FIGURE B.5. Absorbance – time profile at the isosbestic point near 269.6 nm for the - reaction of NE (21.1 mM) with OH (50.0 mM) in H2O at 298 K

0.52 267.5 nm

0.51 [NE-d ] = 20.37mM Abs / A.U. 2 [NaOH] = 100.0 mM 0.50 in H2 O at 298K

0.49

0 50 100 150 200 250 300 time/s

FIGURE B.6. Absorbance – time profile at the isosbestic point near 267.5 nm for the - reaction of NE-d2 (20.37 mM) with OH (100.0 mM) in H2O at 298 K 225

0.454 268.4 nm [2-NP] = 20.9 mM 0.452 [NaOH] = 100.0 mM Abs / A.U. in H O at 298K 0.450 2

0.448

0.446

0 50 100 150 200 250 300 350 time/s

FIGURE B.7. Absorbance – time profile at the isosbestic point near 268.4 nm for the - reaction of 2-NP (20.9 mM) with OH (100.0 mM) in H2O at 298 K

0.58 269.4 nm 0.57

0.56 [2-NP-d1 ] = 19.5 mM Abs / A.U. [NaOH] = 100.0 mM 0.55 in H2 O at 298K 0.54

0.53

0.52 0 200 400 600 800 1000 time/s

FIGURE B.8. Absorbance – time profile at the isosbestic point near 269.4 nm for the - reaction of 2-NP-d1 (19.5 mM) with OH (100.0 mM) in H2O at 298 K 226

7 KIEapp 6 [NM(-d3 )] = 0.1mM 5 [NaOH] = 10.0mM in H2 O at 298K 4 240nm

3 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time/s

FIGURE B.9. Apparent KIE for the reactions of NM and NM-d3 in H2O at 298 K as a function of reaction time

5 KIEapp 4 [NE(-d2 )] = 0.1mM [NaOH] = 50.0mM 3 in H2 O at 298K 2 240nm

1 0.00.20.40.60.81.01.21.41.6 time/s

FIGURE B.10. Apparent KIE for the reactions of NE and NE-d2 in H2O at 298 K as a function of reaction time 227

KIEapp [2-NP(-d)] = 0.1 mM 4 [NaOH] = 50.0 mM

in H2 O at 298K 3 230nm

012345 time/s

FIGURE B.11. Apparent KIE for the reactions of 2-NP and 2-NP-d1 in H2O at 298 K as a function of reaction time

228

Appendix C. Supplementary Information for Reactions of 1-NP and nitrocycloalkanes

with Hydroxide Ion in Water

229

3.5 3.0 a b 3.0 2.5 0.10 mM 1-NP + 20.0 mM NaOH 0.10 mM NC4 + 20.0 mM NaOH in H O at 298 K 2.5 in H O at 298 K 2.0 2 2  = 233 nm  = 230 nm max 2.0 max 1.5 1.5 Abs (A.U.) Abs Abs (A.U.) Abs 1.0 1.0 Abs  Abs 0.5 0.5  Abs Abs 0 0 0.0 0.0 200 220 240 260 280 300 200 220 240 260 280 300 (nm)  (nm)

3.5 3.5 c d 3.0 3.0 0.10 mM NC5 + 20.0 mM NaOH 0.10 mM NC6 + 50.0 mM NaOH 2.5 in H O at 298 K 2.5 in H O at 298 K 2 2  = 227 nm  = 232 nm 2.0 max 2.0 max

1.5 1.5 Abs (A.U.) Abs (A.U.) Abs 1.0 1.0 Abs  Abs  0.5 0.5 Abs Abs 0 0 0.0 0.0 200 220 240 260 280 300 200 220 240 260 280 300  (nm)  (nm)

3.5 e 3.5 f 3.0 0.10 mM NC7 + 20.0 mM NaOH 3.0 0.10 mM NC8 + 20.0 mM NaOH 2.5 in H O at 298 K in H O at 298 K 2 2.5 2  = 231 nm  = 232 nm 2.0 max max 2.0

1.5 1.5 Abs (A.U.) Abs (A.U.) Abs 1.0 Abs 1.0  Abs 0.5 Abs  0 0.5 Abs 0 0.0 0.0 200 220 240 260 280 300 200 220 240 260 280 300 (nm) (nm)

FIGURE C.1. UV absorption spectra for the reactions of (a) 1-NP, (b) NC4, (c) NC5, (d) - NC6, (e) NC7, and (f) NC8 with OH in H2O under the conditions as shown

230

Table C.1. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of 1-NP (0.1 mM) with OH- (50.0 mM) a in H2O at 298 K (240 nm) -1 -1 Time/s kapp/s SD/s Segment 0.012 0.1910 0.0598 1 0.022 0.2312 0.0192 2 0.032 0.2291 0.0053 3 0.042 0.2297 0.0063 4 0.052 0.2277 0.0042 5 0.102 0.2249 0.0019 6 0.202 0.2240 0.0008 7 0.302 0.2233 0.0007 8 0.402 0.2229 0.0005 9 0.502 0.2223 0.0004 10 0.602 0.2219 0.0003 11 0.702 0.2217 0.0003 12 0.802 0.2214 0.0003 13 0.902 0.2211 0.0004 14 1.002 0.2209 0.0003 15 1.102 0.2206 0.0003 16 1.202 0.2204 0.0004 17 1.302 0.2202 0.0004 18 1.402 0.2200 0.0004 19 1.502 0.2198 0.0004 20 1.602 0.2196 0.0004 21 1.702 0.2194 0.0004 22 1.802 0.2192 0.0004 23 1.902 0.2190 0.0004 24 a 14 stopped-flow repetitions

231

Table C.2. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC4 (0.1 mM) with OH- (50.0 mM) a in H2O at 298 K (240 nm) -1 -1 Time/s kapp/s SD/s Segment 0.0090 0.1374 0.0988 1 0.0165 0.2862 0.0327 2 0.0240 0.2824 0.0264 3 0.0315 0.2998 0.0324 4 0.0390 0.2962 0.0220 5 0.0765 0.2847 0.0064 6 0.1515 0.2810 0.0026 7 0.2265 0.2796 0.0014 8 0.3015 0.2784 0.0010 9 0.3765 0.2775 0.0008 10 0.4515 0.2766 0.0008 11 0.5265 0.2758 0.0008 12 0.6015 0.2749 0.0007 13 0.6765 0.2743 0.0007 14 0.7515 0.2736 0.0007 15 0.8265 0.2730 0.0007 16 0.9015 0.2723 0.0007 17 0.9765 0.2717 0.0007 18 1.0515 0.2712 0.0007 19 1.1265 0.2706 0.0007 20 1.2015 0.2701 0.0007 21 1.2765 0.2695 0.0007 22 1.3515 0.2689 0.0008 23 1.4265 0.2684 0.0008 24 a 15 stopped-flow repetitions

232

Table C.3. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC5 (0.1 mM) with OH- (100.0 mM) a in H2O at 298 K (240 nm) -1 -1 Time/s kapp/s SD/s Segment 0.0150 0.00201 0.0637 1 0.0275 0.1171 0.0177 2 0.0400 0.1431 0.0158 3 0.0525 0.1511 0.0130 4 0.0650 0.1472 0.0120 5 0.1275 0.1469 0.0036 6 0.2525 0.1450 0.0012 7 0.3775 0.1444 0.0007 8 0.5025 0.1439 0.0004 9 0.6275 0.1437 0.0004 10 0.7525 0.1434 0.0004 11 0.8775 0.1432 0.0004 12 1.0025 0.1430 0.0003 13 1.1275 0.1429 0.0003 14 1.2525 0.1427 0.0003 15 1.3775 0.1425 0.0003 16 1.5025 0.1424 0.0003 17 1.6275 0.1422 0.0003 18 1.7525 0.1420 0.0003 19 1.8775 0.1418 0.0003 20 2.0025 0.1416 0.0003 21 2.1275 0.1415 0.0004 22 2.2525 0.1413 0.0004 23 2.3775 0.1412 0.0004 24 a 16 stopped-flow repetitions

233

Table C.4. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC6 (0.1 mM) with OH- (100.0 mM) a in H2O at 298 K (240 nm) -1 -1 Time/s kapp/s SD/s Segment 0.0750 0.03884 0.00477 1 0.1375 0.03658 0.00210 2 0.2000 0.03557 0.00083 3 0.2625 0.03506 0.00071 4 0.3250 0.03488 0.00045 5 0.6375 0.03465 0.00022 6 1.2625 0.03447 0.00014 7 1.8875 0.03442 0.00008 8 2.5125 0.03434 0.00006 9 3.1375 0.03429 0.00004 10 3.7625 0.03424 0.00005 11 4.3875 0.03420 0.00005 12 5.0125 0.03415 0.00004 13 5.6375 0.03410 0.00004 14 6.2625 0.03406 0.00004 15 6.8875 0.03402 0.00005 16 7.5125 0.03398 0.00005 17 8.1375 0.03394 0.00005 18 8.7625 0.03391 0.00005 19 9.3875 0.03387 0.00005 20 10.0125 0.03384 0.00006 21 10.6375 0.03380 0.00006 22 11.2625 0.03377 0.00006 23 11.8875 0.03374 0.00006 24 a 14 stopped-flow repetitions

234

Table C.5. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC7 (0.1 mM) with OH- (100.0 mM) a in H2O at 298 K (240 nm) -1 -1 Time/s kapp/s SD/s Segment 0.024 0.0899 0.0271 1 0.044 0.1133 0.0140 2 0.064 0.1090 0.0094 3 0.084 0.1060 0.0080 4 0.104 0.1040 0.0064 5 0.204 0.0986 0.0020 6 0.404 0.0962 0.0008 7 0.604 0.0951 0.0005 8 0.804 0.0942 0.0003 9 1.004 0.0937 0.0002 10 1.204 0.0932 0.0002 11 1.404 0.0928 0.0002 12 1.604 0.0923 0.0002 13 1.804 0.0919 0.0002 14 2.004 0.0915 0.0002 15 2.204 0.0911 0.0002 16 2.404 0.0907 0.0002 17 2.604 0.0903 0.0002 18 2.804 0.0899 0.0002 19 3.004 0.0896 0.0002 20 3.204 0.0892 0.0002 21 3.404 0.0888 0.0002 22 3.604 0.0884 0.0002 23 3.804 0.0881 0.0002 24 a 12 stopped-flow repetitions

235

Table C.6. Apparent Rate Constants and Standard Deviations Obtained by the 24-Point Sequential Analysis of the Reaction of NC8 (0.1 mM) with OH- (100.0 mM) a in H2O at 298 K (240 nm) -1 -1 Time/s kapp/s SD/s Segment 0.030 0.0900 0.0214 1 0.055 0.0898 0.0091 2 0.080 0.0865 0.0037 3 0.105 0.0850 0.0039 4 0.130 0.0837 0.0033 5 0.255 0.0812 0.0012 6 0.505 0.0812 0.0005 7 0.755 0.0805 0.0005 8 1.005 0.0802 0.0005 9 1.255 0.0799 0.0004 10 1.505 0.0796 0.0004 11 1.755 0.0793 0.0005 12 2.005 0.0790 0.0004 13 2.255 0.0787 0.0005 14 2.505 0.0784 0.0005 15 2.755 0.0781 0.0005 16 3.005 0.0779 0.0005 17 3.255 0.0776 0.0005 18 3.505 0.0773 0.0005 19 3.755 0.0771 0.0005 20 4.005 0.0768 0.0005 21 4.255 0.0766 0.0005 22 4.505 0.0763 0.0005 23 4.755 0.0760 0.0005 24 a 12 stopped-flow repetitions

236

Appendix D. Supplementary Information for Reactions of the 1-Arylnitroethanes with

Hydroxide Ion in Aqueous Solutions

237

4 E.R. = 0.96 2.5 E. R. = 0.90 3 2.0 2 1.5 [p-NO -PNE] = 0.10 mM 2 [m-Cl-PNE] = 0.10 mM [NaOH] = 10.0 mM 1.0 E.R.) - (1 -ln [NaOH] = 20.0 mM -ln (1 - E.R.) (1 -ln in H2 O 1 in H2 O 0.5 298K, 350nm 298K, 288nm 0 0.0 0 5 10 15 20 0 5 10 15 20 25 30 time/s time/s

4 5 E.R. = 0.96 E.R. = 0.98

3 4

3 2 [m-F-PNE] = 0.10 mM [PNE] = 0.11 mM 2 [NaOH] = 50.0 mM -ln (1 - E.R.) (1 -ln

-ln (1 - E.R.) (1 -ln [NaOH] = 20.0 mM 1 in H O in H O 2 2 1 298K, 286nm 298K, 280nm 0 0

0 5 10 15 20 25 30 010203040 time/s time/s

E.R. = 0.94 3

2 [m-Me-PNE] = 0.10 mM [NaOH] = 50.0 mM -ln (1 - E.R.) (1 -ln 1 in H2 O 298K, 280nm 0 0 10203040 time/s

FIGURE D.1. Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE with OH- in H2O at 298 K

238

5 Extent of Reaction = 0.98 Extent of Reaction = 0.88 4 2.25

3 1.50 [p-NO -PNE] = 0.10 mM [m-NO -PNE] = 0.10 mM 2 2 2 -ln (1- E.R.) (1- -ln [NaOH] = 2.0 mM E.R.) (1- -ln [NaOH] = 5.0 mM 0.75 in MeOH:H O = 1:1 in MeOH:H O = 1:1 1 2 2 298K, 395nm 298K, 305nm 0 0.00 0 10203040 0 5 10 15 20 time/s time/s

5 Extent of Reaction = 0.98 4 Extent of Reaction = 0.97 4 3 3 2 2 [p-CF3 -PNE] = 0.10 mM

-ln (1- E.R.) (1- -ln [m-CF -PNE] = 0.10 mM [NaOH] = 5.0 mM E.R.) (1- -ln 3 [NaOH] = 5.0 mM 1 in MeOH:H O = 1:1 1 2 in MeOH:H O = 1:1 298K, 310nm 2 298K, 297nm 0 0 0 10203040 0 1020304050 time/s time/s

4 Extent of Reaction = 0. 94 4 Extent of Reaction = 0.965 3 3

2 2 [p-Cl-PNE] = 0.11 mM [m-Cl-PNE] = 0.11 mM -ln (1- E.R.) (1- -ln [NaOH] = 10.0 mM E.R.) (1- -ln [NaOH] = 10.0 mM 1 1 in MeOH:H2 O = 1:1 in MeOH:H2 O = 1:1 298K, 295nm 298K, 296nm 0 0 0 102030405060 0 1020304050 time/s time/s

FIGURE D.2. Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE with OH- in H2O-MeOH (50/50 vol %) at 298 K 239

4 4 Extent of Reaction = 0.96 Extent of Reaction = 0.97

3 3

2 2 [m-F-PNE] = 0.10 mM

[p-F-PNE] = 0.11 mM E.R.) (1- -ln

-ln (1- E.R.) (1- -ln [NaOH] = 10.0 mM 1 [NaOH] = 20.0 mM 1 in MeOH:H2 O = 1:1 in MeOH:H2 O = 1:1 298K, 284nm 298K, 294nm 0 0

0 10203040 0 1020304050 time/s time/s

4 Extent of Reaction = 0.94 Extent of Reaction = 0.94 3 3

2 2 [m-Me-PNE] = 0.115 mM [p-Me-PNE] = 0.10 mM

-ln (1- E.R.) (1- -ln [NaOH] = 40.0 mM [NaOH] = 40.0 mM E.R.) (1- -ln 1 1 in MeOH:H2 O = 1:1 in MeOH:H2 O = 1:1 298K, 287nm 298K, 287nm 0 0 0 10203040 0 10203040 time/s time/s

Extent of Reaction = 0.87 2.25

1.50 [m-MeO-PNE] = 0.11 mM [NaOH] = 20.0 mM -ln (1- E.R.) (1- -ln 0.75 in MeOH:H2 O = 1:1 298K, 289nm 0.00 0 1020304050 time/s

FIGURE D.2.(continued) Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE - with OH in H2O-MeOH (50/50 vol %) at 298 K

240

Extent of Reaction = 0.975 Extent of Reaction = 0.85 4 2.0

3 1.5

2 1.0 [m-NO2 -PNE] = 0.10 mM [p-NO2 -PNE] = 0.10 mM -ln (1 - E.R.) (1 -ln

-ln (1 - - E.R.) (1 -ln [NaOH] = 5.0 mM 1 [NaOH] = 2.0 mM 0.5 in Dioxane:H2 O = 1:1 in Dioxane:H2 O = 1:1 298K, 410nm 298K, 300nm 0 0.0 0 5 10 15 20 0 5 10 15 20 time/s time/s

Extent of Reaction = 0.96 Extent of Reaction = 0.95 3 3

2 2 [PNE] = 0.11 mM [m-Me-PNE] = 0.10 mM [NaOH] = 50.0 mM -ln (1 - E.R.) - (1 -ln

-ln (1 - E.R.) (1 -ln [NaOH] = 50.0 mM 1 in Dioxane:H2 O = 1:1 1 in Dioxane:H2 O = 1:1 298K, 300nm 298K, 300nm 0 0 0 5 10 15 20 25 30 0 10203040 time/s time/s 3.5 Extent of Reaction = 0.93 3.0 2.5 2.0 1.5 [m-MeO-PNE] = 0.11 mM

-ln (1 - E.R.) (1 -ln [NaOH] = 50.0 mM 1.0 in Dioxane:H2 O = 1:1 0.5 298K, 300nm 0.0 0 5 10 15 20 time/s

FIGURE D.3. Long-time –ln(1 – E.R.) – time profiles for reactions of ArNE with OH- in H2O-dioxane (50/50 vol %) at 298 K

241

0.70 0.14

0.65 0.12 -1 -1 / s

/ s 0.10 0.60 [p-NPNE] = 0.10 mM [m-NPNE] = 0.10 mM app IRCp k [NaOH] = 10.0 mM k [NaOH] = 5.0 mM 0.08 in H O at 298K 0.55 2 in H2 O at 298K 350 nm 0.06 278 nm 0.50 0.04 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.5 1.0 1.5 time/s time/s

0.5 0.35 0.34 0.4 0.33 -1 -1 / s / s 0.3 0.32 IRC IRC [m-CF PNE] = 0.11 mM [m-ClPNE] = 0.10 mM 3 k k 0.31 [NaOH] = 20.0 mM 0.2 [NaOH] = 20.0 mM 0.30 in H O at 298K in H2 O at 298K 2 289 nm 288 nm 0.1 0.29 0.28 0.0 0.2 0.4 0.6 0.8 0.00.20.40.60.81.01.2 time/s time/s

0.30 0.28

-1 0.26

/ s 0.24

IRC [m-MePNE] = 0.10 mM k 0.22 [NaOH] = 50.0 mM

0.20 in H2 O at 298K 280 nm 0.18 0.16 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time/s

- FIGURE D.4. kIRC – time profiles for the reactions of ArNE with OH in H2O at 298 K

242

0.36 0.34 0.34 0.32 0.32 0.30 -1 -1 0.30 [p-NPNE] = 0.10 mM [m-NPNE] = 0.10 mM

/ s 0.28 / s

IRC [NaOH] = 2.0 mM IRC 0.28 [NaOH] = 2.0 mM 0.26 k k in H O:MeOH = 1:1 in H O:MeOH = 1:1 0.26 2 0.24 2 0.24 at 298K, 395 nm at 298K, 305 nm 0.22 0.22 0.20 0.20 0.18 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.5 1.0 1.5 time/s time/s

0.24 0.30

0.22 -1

-1 0.25 / s / s [m-ClPNE] = 0.11 mM IRC 0.20 [p-ClPNE] = 0.11 mM IRC 0.20 k k [NaOH] = 10.0 mM [NaOH] = 10.0 mM 0.18 in H O:MeOH = 1:1 in H2 O:MeOH = 1:1 2 0.15 at 298K, 310 nm at 298K, 296 nm 0.16 0.10 0.0 0.5 1.0 1.5 2.0 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time/s time/s

0.29 0.14 0.28 0.12 0.10 -1 0.27 -1

/ s / s 0.08 0.26 IRC [p-FPNE] = 0.11 mM IRC 0.06 [m-FPNE] = 0.10 mM k 0.25 k [NaOH] = 20.0 mM 0.04 [NaOH] = 5.0 mM in H O:MeOH = 1:1 in H O:MeOH = 1:1 0.24 2 0.02 2 at 298K, 284 nm at 298K, 294 nm 0.23 0.00 0.22 -0.02 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.00.51.01.52.02.53.03.5 time/s time/s

- FIGURE D.5. kIRC – time profiles for the reactions of ArNE with OH in H2O-MeOH (50/50 vol %) at 298 K

243

0.26 0.16

0.24 0.15 -1 -1

/ s 0.22 / s 0.14 [PNE] = 0.10 mM IRC IRC

k [m-CF PNE] = 0.10 mM k 3 [NaOH] = 20.0 mM 0.20 [NaOH] = 5.0 mM 0.13 in H2 O:MeOH = 1:1 in H O:MeOH = 1:1 2 at 298K, 286 nm 0.18 at 298K, 297 nm 0.12

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 time/s time/s

0.24 0.20 0.22 -1 -1 0.18 / s 0.20 / s IRC [p-MeOPNE] = 0.10 mM IRC 0.16 [m-MeOPNE] = 0.11 mM k k 0.18 [NaOH] = 40.0 mM [NaOH] = 20.0 mM in H O:MeOH = 1:1 in H2 O:MeOH = 1:1 0.14 2 0.16 at 298K, 287 nm at 298K, 289 nm 0.12 0.14 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 time/s time/s

0.30 0.28

-1 0.26 [m-MePNE] = 0.12 mM / s

IRC 0.24 [NaOH] = 40.0 mM k in H O:MeOH = 1:1 0.22 2 at 298K, 287 nm 0.20 0.18 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time/s

- FIGURE D.5.(continued) kIRC – time profiles for the reactions of ArNE with OH in H2O-MeOH (50/50 vol %) at 298 K

244

1.2 1.1 1.1

[m-NPNE] = 0.10 mM 1.0 [p-ClPNE] = 0.10 mM -1 1.0 -1 [NaOH] = 5.0 mM [NaOH] = 20.0 mM / s / s 0.9 in H O:Dioxane = 1:1 in H O:Dioxane = 1:1 IRC 2 IRC 2 k 0.9 k 0.8 at 298K, 320 nm at 298K, 320 nm 0.7 0.8 0.6 0.7 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 time/s time/s

2.5 2.0 2.0

-1 [p-MePNE] = 0.10 mM -1 1.5 [p-MePNE] = 0.10 mM 1.5

/ s [NaOH] = 50.0 mM / s [NaOH] = 50.0 mM

IRC in H2 O:Dioxane = 1:1 IRC in H2 O:Dioxane = 1:1 k k 1.0 1.0 at 298K, 320 nm at 298K, 320 nm

0.5 0.5

0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/s time/s

2.0

[PNE] = 0.11 mM -1 1.5 [NaOH] = 50.0 mM / s in H O:Dioxane = 1:1 IRC 2 k 1.0 at 298K, 320 nm

0.5

0.0 0.2 0.4 0.6 0.8 1.0 time/s

- FIGURE D.6. kIRC – time profiles for the reactions of ArNE with OH in H2O-dioxane (50/50 vol %) at 298 K

245

TABLE D.1. Equilibrium and Kinetic Acidities of ArNE in H2O k (M-1s-1) Substituent pK a app a Bordwella This workb m-Me 7.49±0.01 5.42±0.02 5.51±0.07 H 7.39±0.01 6.47±0.06 6.58±0.16 m-F 7.05±0.01 14.2±0.4 15.1±0.3 m-Cl 7.05±0.01 17.5±0.1 17.9±0.1 m-CF3 6.96±0.01 18.0±0.2 21.2±0.8 m-NO2 6.67±0.01 42.7±0.2 46.2±1.6 p-NO2 6.51±0.01 57.9±1.5 71.1±4.4 a Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1971, 93, 511; Bordwell, F. G.; Boyle, W., Jr. J. Am. Chem. Soc. 1972, 94, 3907. b average of three or more spectrophotometric runs at 298 K.

TABLE D.2. Equilibrium and Kinetic Acidities of ArNE in H2O-MeOH (50/50 vol %) k (M-1s-1) Substituent pK a app a Bordwella,b This workc p-MeO d 2.28±0.06 5.49±0.04 p-Me ( 8.55 )d 2.36±0.05 5.66±0.07 m-Me 8.62±0.03 2.54±0.06 6.29±0.63 H ( 8.52 )d 3.53±0.05 7.72±0.27 m-MeO 8.48±0.02 4.36±0.17 10.23±0.14 p-F 8.36±0.02 5.76±0.17 13.50±0.12 p-Cl 8.23±0.01 8.64±0.47 21.00±0.40 m-F 8.22±0.01 10.4±0.3 23.65±0.33 m-Cl 8.20±0.01 12.2±0.4 29.50±0.19 m-CF3 8.12±0.01 17.0±0.4 44.13±2.50 p-CF3 8.05±0.01 18.5±0.8 49.80±2.73 m-NO2 7.73±0.01 43.3±0.7 116.4±3.3 p-NO2 7.49±0.01 72.5±1.4 174.5±3.3 a Bordwell, F. G.; Boyle, W., Jr.; Hautala, J. A.; Yee, K. C. J. Am. Chem. Soc. 1969, 91, 4002; Bordwell, F. G.; Boyle, W., Jr.; Yee, K. C. J. Am. Chem. Soc. 1970, 92, 5926; average of two or more determination at 296±1 K. b Average of three to nine runs at 288 K, determined on a Cary Model 15 recording spectrophotometer. c Average of three to eight runs at 298 K, determined on a Hi-Tech Scientific SF-61 stopped flow spectrophotometer. d Uncertain due to sample decomposition.

246

TABLE D.3. Equilibrium and Kinetic Acidities of ArNE in H2O-dioxane (50/50 vol %) a -1 -1 pKa kapp (M s ) Substituent Shechter a Shechter a Shechter a This work 293 K 303 K 273 K 283 K 293 K 298 K p-Me 10.47 10.47 0.903±0.007 1.95±0.05 4.20±0.00 5.06±0.11 m-Me 10.53 10.53 1.01±0.01 2.27±0.02 4.82±0.05 5.87±0.11 m-MeO 10.38 10.38 1.52±0.01 3.35±0.05 7.50±0.07 9.30±0.02 H 10.29 10.30 1.40±0.04 3.13±0.05 6.58±0.10 8.17±0.07 p-Cl 9.81 9.81 5.12±0.05 10.7±0.1 25.0±0.8 28.15±0.30 p-Br 10.00 10.00 5.12±0.08 10.8±0.1 22.7±1.0 m-Br 9.93 9.93 6.43±0.05 14.2±0.0 28.3±0.1 m-NO2 9.18 9.18 31.2±0.0 68.0±1.2 146±1 142.8±11.0 p-NO2 9.06 9.06 52.5±2.2 119±3 246±4 222.6±8.1 a Fukuyama, M; Flanagan, P. W. K.; Williams, F. T., Jr.; Franinier, L; Miller, S. A.; Shechter, H. J. Am. Chem. Soc. 1970, 92, 4689

247

Appendix E. Supplementary Information for Reactions of Trinitroanisole with Methoxide

Ion in Methanol

248

TABLE E.1. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (15 mM) in MeOH at 293 K -1 -1 -1 time/s kapp/s SD kapp/s SD kapp/s SD Segment 0.015 0.241 0.038 0.214 0.060 0.217 0.093 1 0.028 0.192 0.020 0.197 0.012 0.185 0.021 2 0.040 0.179 0.009 0.178 0.004 0.176 0.015 3 0.053 0.172 0.006 0.174 0.005 0.174 0.009 4 0.065 0.168 0.005 0.169 0.002 0.173 0.008 5 0.128 0.167 0.002 0.169 0.002 0.170 0.004 6 0.253 0.170 0.001 0.172 0.001 0.173 0.002 7 0.378 0.171 0.001 0.174 0.001 0.175 0.001 8 0.503 0.172 0.001 0.175 0.001 0.175 0.001 9 0.628 0.172 0.001 0.175 0.001 0.175 0.001 10 0.753 0.172 0.001 0.175 0.001 0.176 0.001 11 0.878 0.172 0.001 0.175 0.001 0.176 0.001 12 1.003 0.172 0.001 0.175 0.000 0.176 0.001 13 1.128 0.172 0.001 0.176 0.000 0.176 0.001 14 1.253 0.172 0.001 0.176 0.001 0.176 0.001 15 1.378 0.172 0.001 0.176 0.001 0.176 0.001 16 1.503 0.172 0.001 0.176 0.001 0.176 0.001 17 1.628 0.172 0.001 0.176 0.001 0.176 0.001 18 1.753 0.172 0.001 0.176 0.001 0.176 0.001 19 1.878 0.172 0.001 0.176 0.001 0.176 0.001 20 2.003 0.171 0.001 0.176 0.001 0.176 0.001 21 2.128 0.171 0.001 0.176 0.001 0.176 0.002 22 2.253 0.171 0.001 0.176 0.001 0.176 0.002 23 2.378 0.171 0.002 0.176 0.001 0.176 0.002 24

249

TABLE E.2. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (30 mM) in MeOH at 293 K -1 -1 -1 time/s kapp/s SD kapp/s SD kapp/s SD Segment 0.008 0.903 0.087 0.826 0.106 0.837 0.130 1 0.014 0.566 0.029 0.534 0.038 0.527 0.057 2 0.020 0.470 0.021 0.441 0.021 0.445 0.016 3 0.026 0.432 0.012 0.410 0.012 0.410 0.016 4 0.033 0.408 0.011 0.385 0.012 0.392 0.015 5 0.064 0.376 0.005 0.358 0.004 0.356 0.005 6 0.126 0.370 0.003 0.351 0.002 0.350 0.002 7 0.189 0.370 0.003 0.351 0.002 0.349 0.001 8 0.251 0.371 0.002 0.351 0.002 0.350 0.001 9 0.314 0.372 0.002 0.352 0.002 0.351 0.001 10 0.376 0.373 0.002 0.352 0.002 0.351 0.001 11 0.439 0.374 0.002 0.353 0.002 0.352 0.001 12 0.501 0.375 0.002 0.353 0.002 0.352 0.001 13 0.564 0.375 0.002 0.353 0.002 0.352 0.001 14 0.626 0.376 0.002 0.353 0.002 0.353 0.001 15 0.689 0.377 0.002 0.354 0.002 0.353 0.001 16 0.751 0.378 0.002 0.354 0.002 0.353 0.001 17 0.814 0.379 0.002 0.354 0.002 0.354 0.001 18 0.876 0.380 0.002 0.354 0.002 0.354 0.001 19 0.939 0.381 0.002 0.355 0.003 0.354 0.001 20 1.001 0.382 0.002 0.355 0.003 0.354 0.001 21 1.064 0.383 0.003 0.355 0.003 0.355 0.001 22 1.126 0.384 0.003 0.355 0.003 0.355 0.002 23 1.189 0.385 0.003 0.356 0.003 0.355 0.002 24

250

TABLE E.3. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (60 mM) in MeOH at 293 K -1 -1 -1 time/s kapp/s SD kapp/s SD kapp/s SD Segment 0.004 2.899 0.614 3.239 0.260 2.684 1.058 1 0.007 1.781 0.300 1.937 0.106 1.657 0.520 2 0.010 1.338 0.177 1.394 0.058 1.259 0.311 3 0.013 1.126 0.110 1.137 0.042 1.041 0.197 4 0.016 1.004 0.084 1.000 0.033 0.927 0.140 5 0.032 0.802 0.029 0.780 0.010 0.747 0.048 6 0.063 0.741 0.011 0.709 0.003 0.689 0.019 7 0.094 0.729 0.007 0.695 0.002 0.678 0.014 8 0.126 0.724 0.007 0.690 0.002 0.674 0.011 9 0.157 0.723 0.006 0.688 0.002 0.672 0.011 10 0.188 0.722 0.006 0.688 0.002 0.671 0.011 11 0.219 0.722 0.006 0.687 0.002 0.669 0.013 12 0.251 0.723 0.006 0.687 0.002 0.668 0.016 13 0.282 0.723 0.006 0.687 0.002 0.666 0.020 14 0.313 0.724 0.007 0.687 0.002 0.665 0.002 15 0.344 0.725 0.007 0.687 0.002 0.665 0.002 16 0.376 0.726 0.007 0.688 0.003 0.667 0.002 17 0.407 0.726 0.007 0.688 0.003 0.667 0.002 18 0.438 0.727 0.007 0.688 0.003 0.667 0.002 19 0.469 0.728 0.007 0.689 0.003 0.668 0.002 20 0.501 0.729 0.008 0.689 0.003 0.668 0.002 21 0.532 0.730 0.008 0.689 0.003 0.669 0.002 22 0.563 0.731 0.008 0.689 0.003 0.669 0.002 23 0.594 0.733 0.008 0.690 0.003 0.669 0.002 24

251

TABLE E.4. Apparent Rate Constants and Standard Deviations for 3 Sets of Experiments (18 Stopped-Flow Shots Each) on the Reaction of TNA (0.1 mM) with MeO- (120 mM) in MeOH at 293 K -1 -1 -1 time/s kapp/s SD kapp/s SD kapp/s SD Segment 0.002 10.684 0.995 10.111 0.868 10.457 0.832 1 0.003 7.391 0.767 7.236 0.593 7.327 0.659 2 0.005 5.584 0.593 5.430 0.440 5.506 0.480 3 0.006 4.417 0.404 4.282 0.333 4.325 0.358 4 0.008 3.663 0.309 3.525 0.249 3.596 0.284 5 0.015 2.228 0.097 2.094 0.093 2.124 0.085 6 0.030 1.719 0.033 1.573 0.029 1.603 0.031 7 0.045 1.609 0.019 1.458 0.017 1.481 0.018 8 0.060 1.570 0.015 1.413 0.013 1.435 0.016 9 0.075 1.552 0.013 1.390 0.010 1.411 0.013 10 0.090 1.543 0.011 1.378 0.009 1.397 0.012 11 0.105 1.538 0.011 1.369 0.009 1.388 0.011 12 0.120 1.535 0.011 1.363 0.008 1.382 0.010 13 0.135 1.535 0.010 1.359 0.008 1.377 0.010 14 0.150 1.536 0.011 1.355 0.009 1.373 0.010 15 0.165 1.537 0.011 1.353 0.008 1.370 0.010 16 0.180 1.539 0.011 1.350 0.008 1.368 0.010 17 0.195 1.541 0.011 1.348 0.008 1.365 0.010 18 0.210 1.544 0.012 1.347 0.009 1.363 0.010 19 0.225 1.546 0.012 1.345 0.009 1.361 0.011 20 0.240 1.549 0.012 1.343 0.009 1.359 0.011 21 0.255 1.553 0.012 1.342 0.010 1.358 0.011 22 0.270 1.556 0.013 1.340 0.010 1.356 0.011 23 0.285 1.559 0.013 1.339 0.010 1.355 0.012 24

252

0.9

04M15A 0.6 -1 kapp = 0.1653s -ln(1-E.R.) 0.3 [TNA] = 0.0001 M - 0.0 [MeO ] = 15 mM

012345 time/s .

0.75

04M15B 0.50 -1 kapp = 0.1757s -ln(1-E.R.) 0.25 [TNA] = 0.0001 M 0.00 [MeO-] = 15 mM

01234 time/s

FIGURE E.1. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (15 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots. 253

25F30A 0.9 -1 kapp = 0.390s 0.6 -ln(1-E.R.) 0.3 [TNA] = 0.0001 M [MeO-] = 30 mM 0.0 0.0 0.5 1.0 1.5 2.0 2.5 time/s

0.8 25F30B 0.6 -1 kapp = 0.356 s 0.4 -ln(1-E.R.) 0.2 [TNA] = 0.0001 M [MeO-] = 30 mM 0.0

0.0 0.5 1.0 1.5 2.0 time/s

FIGURE E.2. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (30 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots. 254

0.9 26F60A -1 kapp = 0.734 s 0.6 -ln(1-E.R.) 0.3 [TNA] = 0.0001 M [MeO-] = 60 mM 0.0 0.0 0.3 0.6 0.9 1.2 time/s

0.9

26F60B 0.6 -1 kapp = 0.690 s -ln(1-E.R.) 0.3 [TNA] = 0.0001 M [MeO-] = 60 mM 0.0 0.0 0.3 0.6 0.9 1.2 time/s

FIGURE E.3. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (60 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots.

255 1.2

0.9 28F120A -1 kapp = 1.562 s 0.6 -ln(1-E.R.) 0.3 [TNA] = 0.0001 M 0.0 [MeO-] = 120 mM

0.00 0.15 0.30 0.45 0.60 time/s

0.9 28F120B -1 0.6 kapp = 1.338 s -ln(1-E.R.) 0.3 [TNA] = 0.0001 M 0.0 [MeO-] = 120 mM 0.0 0.2 0.4 0.6 time/s

FIGURE E.4. Pseudo-first-order rate plot for the reaction of TNA (0.1 mM) with MeO- (120 mM) in MeOH at 293 K. Each plot represents data obtained from 18 stopped-flow shots.

256

Comments

The data in Tables E.1 to E.4 using a more detailed application of pseudo-first-order kinetics are internally consistent. In all cases the apparent rate constants for the short time segments decrease from a relatively high initial value and approach a plateau (steady-state value). This is characteristic of the reversible consecutive mechanism (Scheme 8-3) and inconsistent with the competitive mechanism in Scheme 8-1.

The phenomenon observed in the previous paragraph cannot be observed from the conventional pseudo-first-order plots in Figure 8-1. The reason for this is that as the reaction period is increased, analysis using 2000 data points over 1 or 4 half-lives, ignore the data at very short times before the first point. For example the time of the first data segments in Figure 8-1 are summarized in the following Table.

- Figure [MeO ]0/mM Half-lives Analysis Time 8-1a 15 1 4 s 8-1b 15 4 15 s 8-1c 120 1 0.5 s 8-1d 120 4 1.9 s

Looking carefully at Figure 8-1c reveals a deviation in the slope at the very

beginning of the reaction while no significant deviations are visible in the other three

cases.

257

Appendix F. Copyright Permissions

258

From: CONTRACTS-COPYRIGHT “[email protected]” Sent: Wed, Feb 8, 2012 at 5:05 AM To: Zhao Li “[email protected]” Subject: FW: Copyright Permission Request February 8, 2012

Dear Dr Li

The Royal Society of Chemistry (RSC) hereby grants permission for the use of your paper(s) specified below in the printed and microfilm version of your thesis. You may also make available the PDF version of your paper(s) that the RSC sent to the corresponding author(s) of your paper(s) upon publication of the paper(s) in the following ways: in your thesis via any website that your university may have for the deposition of theses, via your university’s Intranet or via your own personal website. We are however unable to grant you permission to include the PDF version of the paper(s) on its own in your institutional repository. The Royal Society of Chemistry is a signatory to the STM Guidelines on Permissions (available on request).

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Reproduced by permission of The Royal Society of Chemistry and include a link to the paper on the Royal Society of Chemistry’s website.

Please ensure that your co-authors are aware that you are including the paper in your thesis.

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Publishing Contracts & Copyright Executive Gill Cockhead (Mrs), Publishing Contracts & Copyright Executive Royal Society of Chemistry, Thomas Graham House Science Park, Milton Road, Cambridge CB4 0WF, UK Tel +44 (0) 1223 432134, Fax +44 (0) 1223 423623 http://www.rsc.org

------From: Zhao Li [mailto:[email protected]] Sent: 08 February 2012 06:37 259

To: CONTRACTS-COPYRIGHT (shared) Subject: Copyright Permission Request Zhao Li Dept. of Chemistry and Biochemistry Utah State University Logan, UT 84322-0300 United States Email: [email protected]

February 7, 2012

Royal Society of Chemistry Thomas Graham House Science Park Milton Road Cambridge CB4 0WF Email: [email protected]

To Permissions Editor:

I am preparing my dissertation in the Department of Chemistry and Biochemistry at Utah State University (USU). I hope to complete my degree in the summer of 2012.

An article, “Reactions of the simple nitroalkanes with hydroxide ion in water. Evidence for a complex mechanism”, of which I am first author, and which appeared in Organic & Biomolecular Chemistry, 2011, Issue 12, Page 4563 – 4569, reports an essential part of my dissertation research. I would like permission to reprint it as a chapter in my dissertation. (Reprinting the chapter may necessitate some revision.) Please note that USU sends dissertations to Bell & Howell Dissertation Services to be made available for reproduction.

I will include an acknowledgment to the article on the first page of the chapter, as shown below. Copyright and permission information will be included in a special appendix. If you would like a different acknowledgment, please so indicate.

Please indicate your approval of this request by signing in the space provided, and attach any other form necessary to confirm permission. If you charge a reprint fee for use of an article by the author, please indicate that as well.

If you have any questions, please call me at the number above or send me an e-mail message at the above address. Thank you for your assistance.

Zhao Li 260

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CURRICULUM VITAE

ZHAO LI

Ph.D., Organic Chemistry

Sex: Male 400 Wymount Terrace Date of Birth: June 19, 1982 Provo, UT 84604 Place of Birth: Tianjin, China 801-227-9392 Country of Citizenship: China [email protected]

EDUCATION

 B.S., Chemistry, Nankai University, Tianjin, China, 06/2005 GPA: 3.7/4.0

 Ph.D., Organic Chemistry, Nankai University, Tianjin, China, 06/2011 GPA:3.4/4.0 Advisor: Prof. Jin-Pei Cheng, Ph.D., member of Chinese Academy of Sciences

 Ph.D., Organic Chemistry, Utah State University, Logan, UT, 12/2012 Advisor: Prof. Vernon D. Parker, Ph.D.

Collaborative Doctoral Student of Utah State University and Nankai University, 08/2007 – 06/2011

AWARDS

 Nankai University First-Class Scholarship for freshmen, 2001  Nankai University Third-Class Scholarship, 2002  Nankai University Third-Class Scholarship, 2003  Nankai University Third-Class Scholarship, 2004

LEADERSHIP

 09/2002 – 08/2003, Monitor, Class 2001-3 of Department of Chemistry, Nankai University  05/2006 – 04/2007, Chairman, Graduate Student Council of Department of Chemistry, Nankai University, 270

PROFESSIONAL EXPERIENCE

 Teaching Experience 09/2006 – 07/2007, Nankai University, Department of Chemistry Teaching Assistant for Organic Chemistry 08/2007 – 12/2007, Utah State University, Department of Chemistry and Biochemistry Teaching Assistant for Organic Chemistry Laboratory 01/2008 – 04/2009, Utah State University, Department of Chemistry and Biochemistry Teaching Assistant for General Chemistry Laboratory

 Research Experience 05/2009 – 12/2012, Utah State University, Department of Chemistry and Biochemistry Research Assistant for Prof. Vernon D. Parker Research focuses on the kinetics and mechanisms of some fundamental organic reactions of nitro compounds, such as proton transfer reactions of nitroalkanes and SNAr reactions of trinitroarenes. Some of the reasearch topics are listed below: 1. Development of the new methodology of kinetic data analysis to distinguish reaction mechanisms 2. Kinetics and Mechanisms of proton transfer reactions of nitroalkanes, and exploration of the origin of the nitroalkane anomaly 3. Mechanisms of aromatic nucleophilic substitution reactions of trinitroarenes 4. Isosbestic point study to trace the intermediates 5. Chemical kinetics simulation and computational chemistry 6. Miscellaneous (nitroalkane chemistry, organic synthesis, kinetic isotope effects, hydrogen bonding effects, and solvent effects)

PROFESSIONAL SKILLS

 Sound basis in organic, physical and analytical chemistry, and mathematics  7+ years experience in organic and physical chemistry labs  Professional training in organic synthesis, separation, purification and characterization  Skilled in macro- and micro-scale organic experiments, the operation of vacuum-line, and the techniques for the production and analysis of isotope labeled compounds  Proficient in physical organic chemical research, especially in kinetic experiments and data analysis  Expertise in handling many instruments, such as stopped-flow, UV-vis 271

spectrophotometer, column chromatography, NMR, HPLC, etc  Knowledge of the internet, MS Office, ChemOffice, Origin, MathLab, C, FORTRAN  Excellent analytical and problem-solving skills  Ability in information collection, clarification and extraction  Strong capability in communication and collaboration

SCIENTIFIC PAPERS

Publications:  Vernon D. Parker,* Weifang Hao, Zhao Li and Russell Scow “Non-conventional vs. conventional application of pseudo-first-order kinetics to fundamental organic reactions” Int. J. Chem. Kinet. 2012, 44 (1), 2-12.  Zhao Li, Jin-Pei Cheng,* and Vernon D. Parker* “Reactions of the Simple Nitroalkanes with Hydroxide Ion in Water. Evidence for a Complex Mechanism.” Org. Biomol. Chem. 2011, 9 (12), 4563-4569.  Vernon D. Parker,* Zhao Li, Kishan L. Handoo, Weifang Hao, and Jin-Pei Cheng “The Reversible Consecutive Mechanism for the Reaction of Trinitroanisole with Methoxide Ion” J. Org. Chem. 2011, 76(5), 1250-1256.

In Manuscripts:  Zhao Li, Vernon D. Parker* and Jin-Pei Cheng* “Proton Transfer Reactions of the 1-Arylnitroethanes with Hydroxide Ion in Aqueous Solutions. A Rational Explanation of the Nitroalkane Anomaly, Part II”, to be submitted to J. Org. Chem.  Zhao Li, Vernon D. Parker* and Jin-Pei Cheng* “Isosbestic Points Study of the Proton Transfer Reactions of aliphatic nitroalkanes with Hydroxide Ion in Aqueous Solutions. A Method to Verify the Presence of an Intermediate” to be submitted to J. Phys. Chem, A.  Zhao Li, Xiaosong Xue, Jin-Pei Cheng,* Tapas Kar* and Vernon D. Parker* “The Mechanism of the Nitroalkane Proton Transfer in Water. A Direct Comparison of Experiment with Theory.”  Vernon D. Parker* and Zhao Li “The Validation of Instantaneous Rate Constant 272

Analysis for the Study of Complex Organic Reactions”  Xiaosong Xue, Zhao Li, Jin-Pei Cheng,* Tapas Kar* and Vernon D. Parker* “Hyperconjugation Effect on Nitroalkane Proton Transfer. Relevance to the Origin of the Nitroalkane Anomaly”.  Xiaosong Xue, Zhao Li, Jin-Pei Cheng,* Tapas Kar* and Vernon D. Parker* “The Cyclization of Phenyl 3-(1H-imidazol-4-yl) Proprionate in DMSO and Water. Relevance of the Concepts of Near-Attack Complexes and Hidden Intermediates.”

Conference Poster:  Zhao Li, Jin-Pei Cheng, and Vernon D. Parker* “The Mechanism of the Proton Transfer Reactions between Hydroxide Ion and the Simple Nitroalkanes in Aqueous Solution.” The 33rd Reaction Mechanisms Conference, University of Massachusetts, Amherst, MA, 2010.  Zhao Li, Xiaosong Xue, Jin-Pei Cheng, Tapas Kar and Vernon D. Parker* “A Normal Brönsted Alpha for the Proton Transfer Reactions of Simple Nitroalkanes in Water. A Direct Comparison of Experiment with Theory” The 21st IUPAC International Conference on Physical Organic Chemistry (ICPOC 21), Durham University, UK, 2012.