Computational Studies of Combustion Processes and Oxygenated Species

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COMPUTATIONAL STUDIES OF COMBUSTION PROCESSES AND OXYGENATED SPECIES

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree of Doctor of Philosophy

in the Graduate School of The Ohio State University

Carrigan Jo Hayes, B.S.

****

The Ohio State University 2007

Dissertation Committee: Approved by:

Dr. Christopher M. Hadad, Advisor ______Dr. Matthew S. Platz Advisor Graduate Program in Chemistry Dr. David J. Hart

ABSTRACT

Within this dissertation, we report on explorations of reactive oxygen species with

implications for combustion and atmospheric chemistry. Various computational

approaches, including density functional theory (DFT) and master equation methods,

were used to complete these projects.

The majority of this thesis involves the oxidation pathways of the alkylated

heterocycles that provide a model framework for understanding coal combustion. The

enthalpies and energies of reaction for hydrogen-atom loss and alkyl-group

fragmentations at various temperatures were calculated via density functional theory

(B3LYP/6-311+G**//B3LYP/6-31G*); these results were calibrated against CBS-QB3

calculations. It was suggested that both hydrogen-atom loss and alkyl-group loss reactions will contribute as initiation steps for the high-temperature combustion reactions of these rings. Longer alkyl chains will increase reactivity, and the azabenzene units are more likely to react than the five-membered heterocyclic rings. The initial steps of radical formation are expected to become more favorable at high temperatures.

The oxidation steps of these radicals were shown to be exothermic and exoergic,

as expected. DFT studies (B3LYP/6-311+G**//B3LYP/6-31G*) showed that these

resultant peroxy radicals were more likely to undergo intramolecular reactions to form

bicyclic structures. Furthermore, several pathways seemed feasible and must be

ii considered in rationalizing coal chemistry: formation of either a four-membered or five-

membered ring occurs with similar kinetics and thermodynamics; cyclization at nitrogen

to form a nitroso species has a high reaction barrier but is ultimately quite exoergic. An

internal H-atom transfer can occur on the substituted side chain with a low barrier and

favorable energy of reaction.

We have completed other projects with implications for combustion chemistry

and oxygenated species. 1,5-H transfers proceed readily for n-propylperoxy radical due

to this radical’s ability to adopt a six-membered transition state. This reaction and others

available to this species are of interest due to the ability of n-propylperoxy radical to

serve as a model compound for understanding the combustion of larger hydrocarbon

fuels. Conformational possibilities for this species were explored via B3LYP/6-31G*

and mPW1K/6-31+G** levels of theory to ensure that rotational barriers would not compete with energies of reaction. It was seen that rotamer interconversion occurs with barrier heights of less than 5 kcal/mol, far less than the relevant reaction activation barriers (~20-25 kcal/mol); thus, rotamer interconversion was not expected to affect overall energetics. Building on these results, the unimolecular decomposition of propan-

1-ol-1-peroxy radical was similarly modeled using DFT methods. It was seen than the quantitative energetics of the relevant decompositions were very similar to those of the hydrocarbon analogue, although a wider variety of functionalized products were formed.

Complexes of ethanol with various solvents were modeled to better understand

certain spectroscopic phenomena and potential atmospheric behaviors of oxygenated

species. Experimental work on these complexes had noted a red shift due to

iii complexation of ethanol with benzene that was not seen with any other solvents.

Theoretical spectra were generated using HF/6-31G* and MP2/6-31G* optimizations and

compared well to the experimental spectra. The red shift seen in benzene was attributed

to an interaction of ethanol with the pi system of the benzene ring.

Finally, engine performance varies given the fuel of interest. Hydrogen has often

been proposed as an alternative fuel that would improve engine performance and

minimize harmful emissions. Its use as a fuel additive was explored with n-heptane and

the primary reference fuels (a mixture of iso-octane and n-heptane), using the master equation program CHEMKIN 4.1. It was seen that hydrogen augmentation did increase flame speed and decrease carbon monoxide emissions.

ACKNOWLEDGMENTS

I would like to thank Dr. Christopher Hadad for his advice, support, and guidance over my time at The Ohio State University; I have learned a great deal both from his words as an advisor and his example as a teacher. I thank members of the Hadad group, past and present, for their thoughtful explanations and thorough discussions. I have worked with Reaction Design and McMaster Fuel and am indebted to these companies’ expertise and support, as well as to research support from the NSF-funded Environmental

Molecular Science Institute and the Ohio Supercomputer Center. I have received a

University Fellowship, a Grilly Scholarship, and two GAANN Fellowships; I am grateful to the Graduate School and the Department of Chemistry for these awards.

I thank my family for their encouragement and love, especially my parents, Steve and Karen Hayes; my siblings, Rob and Katie; and my grandparents, Tom and Jeanne

Wright. Although they are too numerous to mention by name, I also thank many uncles, aunts, cousins, and other relatives whose kind support has been a continued source of inspiration throughout my education. In particular, I mention the relatives whom have passed away during my time in graduate school: my aunt, Judy Boling; my great- grandfather, Fred Hines; my uncle, Gary Wright; and my great-aunt, JoAnn Grigsby. I hope to approach my life with the compassion, intellect, humor, and faith that they demonstrated throughout theirs.

VITA

September 2, 1980- Born: Findlay, Ohio

May 20, 2002- B.S. in Chemistry: Ohio Northern University (Ada, Ohio)

2002-2003- University Fellow, Graduate School, The Ohio State University

2004-2005- GAANN Fellow, OSU Department of Chemistry

2002-present- Grilly Scholar, OSU Department of Chemistry

2003-present- Graduate Research and Teaching Associate, OSU Department of Chemistry

PUBLICATIONS

1. Zalyubovsky, S. J.; Glover, B. G.; Miller, T. A.; Hayes, C.; Merle, J. K.; Hadad, C. M. “Observation of the A-X Electronic Transition of the 1-C3H7O2 and 2- C3H7O2 Radicals Using Cavity Ringdown Spectroscopy.” J. Phys. Chem. A 2005, 109, 1308 - 1315.

2. Merle, J. K.; Hayes, C. J.; Zalyubovsky, S. J.; Glover, B. G.; Miller, T. A.; Hadad, C. M. “Theoretical Determinations of the Ambient Conformational Distribution and Unimolecular Decomposition of n-Propylperoxy Radical.” J. Phys. Chem. A 2005, 109, 3637 - 3646.

3. Levering, L. M.; Hayes, C. J.; Callahan, K. M.; Hadad, C. M.; Allen, H. C. “Non-Aqueous Solvation of n-Octanol and Ethanol: Spectroscopic and Computational Studies.” J. Phys. Chem. B, 2006, 110, 6325-6331.

FIELDS OF STUDY

Major field: Chemistry

TABLE OF CONTENTS PAGE Abstract………………………………………………………………………. ii Acknowledgements…………………………………………………………... v Vita………………………………………………………………………….... vi List of Tables…………………………………………………………………. xi List of Figures……………………………………………………………….... xv

CHAPTERS: 1. Chemistry of reactive radical intermediates of combustion and atmospheric reactions………………………………………………… 1

1.1 Introduction…………………………………………………………... 1 1.2 Basic Concepts of Combustion Chemistry…………………………... 1 1.2.1 Free radicals……………………………………………...... 2 1.2.2 Combustion at varying temperatures………………………... 4 1.2.2.1 High-temperature combustion……………………. 5 1.2.2.2 Low-temperature combustion…………………….. 6 1.2.2.3 Negative temperature coefficient (NTC) range…... 9 1.2.2.4 Atmospheric oxidation……………………………. 11 1.2.3 Methods for studying reactive combustion species…………. 15 1.2.3.1 Experimental methods……………………………. 15 1.2.3.2 Computational methods…………………………... 18 1.3 Reactive Radical Intermediates in Combustion Chemistry………….. 21 1.3.1 Aliphatic systems……………………………………………. 21 1.3.1.1 Methane combustion……………………………... 21 1.3.1.2 Ethyl radical + O2...... 24 1.3.1.3 n-Propylperoxy radical…………………………... 27 1.3.1.4 n-Butoxy radical…………………………………. 32 1.3.1.5 1-Pentyl radical…………………………………... 33 1.3.1.6 Larger aliphatic systems…………………………. 33 1.3.2 Aromatic systems……………………………………………. 35 1.3.2.1 Soot formation…………………………………… 35 1.3.2.2 Benzene and toluene……………………………... 36 1.3.2.3 Benzene oxidation………………………………... 38

vii 1.3.2.4 Alkylated aromatics……………………………… 49 1.3.2.5 Heteroaromatic combustion……………………… 51 1.3.2.6 Alkylated heteroaromatics……………………….. 60 1.3.2.7 Peroxy radicals of alkylated heteroaromatics……. 68 1.4 Future Challenges in Combustion Chemistry………………………... 77 1.4.1 Fuel additives………………………………………………... 78 1.4.2 Biodiesel…………………………………………………….. 81 1.5 Conclusions…………………………………………………………... 84 References………………………………………………………………….. 86

2. Combustion Pathways of the Alkylated Heteroaromatics: Bond Dissociation Enthalpies and Alkyl-Group Fragmentations…………... 109

2.1 Introduction………………………...... 109 2.2 Computational Methods……………………………...... 116 2.3 Results………………………………………………………………. 118 2.4 Discussion…………………………………………...... 118 2.4.1 Toluene as reference compound……………………………. 119 2.4.2 Non-alkylated heteroaromatics……………………………... 120 2.4.2.1 Azabenzenes……………………………...... 120 2.4.2.2 Five-membered rings…………………………….. 120 2.4.3 Methyl-substituted heteroaromatics: H-atom loss………….. 121 2.4.3.1 Azabenzenes……………………………...... 121 2.4.3.2 Five-membered rings…………………………….. 125 2.4.4 Ethyl-substituted heteroaromatics: H-atom loss……………. 126 2.4.4.1 Azabenzenes……………………………...... 127 2.4.4.2 Five-membered rings…………………………….. 127 2.4.5 Methyl-substituted heteroaromatics: methyl loss…………... 127 2.4.5.1 Azabenzenes……………………………...... 128 2.4.5.2 Five-membered rings…………………………….. 129 2.4.6 Ethyl-substituted heteroaromatics: ethyl loss………………. 129 2.4.7. General trends………………………………………………. 130 2.4.7.1 Spin density………………………………………. 130 2.4.7.2 Geometry………………………………………… 133 2.4.7.3 Temperature effects……………………………… 134 2.4.7.4 Approximations………………………………….. 140 2.5 Conclusions………………………………………………………… 142 References…………………………………………………………………. 144

viii 3. Combustion Pathways of the Alkylated Heteroaromatics: Peroxy Radical Pathways of the Alkylated Azabenzenes…………………….. 150

3.1 Introduction…………………………………………………………... 150 3.2 Computational Methods……………………………………………… 156 3.3 Results………………………………………………………………... 158 3.4 Discussion……………………………………………………………. 159 3.4.1 Toluene as reference compound……………………………... 159 3.4.2 Methyl-substituted pyridines (picolines)…………………….. 163 3.4.3 Temperature effects for the picolinylperoxy radicals………... 172 3.4.4 Ethyl-substituted pyridines……………… 180 3.4.5 Diazabenzene trends…………………….. 184 3.4.6 Approximations…………………………. 185 3.4.7 Subsequent steps………………………... 186 3.5 Conclusions……………………………………………………...... 188 References………………………………………………………………….. 193

4. Combustion Pathways of the Alkylated Heteroaromatics: Peroxy Radical Pathways of the Five-Membered Heteroaromatics………….. 198

4.1 Introduction…………………………………………………………... 198 4.2 Computational Methods……………………………………………… 203 4.3 Results and Discussion………………………………………………. 205 4.3.1 Furan derivatives……………………………………………. 208 4.3.2 Oxazole derivatives…………………………………………. 218 4.3.3 Pyrrole derivatives…………………………………………... 224 4.3.4 Thiophene derivatives……………………………………….. 227 4.3.5 Overall low-temperature trends……………………………... 230 4.3.6 Heteroatom effects: comparisons to benzylperoxy radical….. 233 4.3.7 Ring size comparison: heteroaromatics……………………... 235 4.3.8 Temperature effects…………………………………………. 236 4.3.9 Ethyl derivatives…………………………………………….. 241 4.3.10 Oscillator vs. rotor approximations………………………… 243 4.4 Conclusions………………………………………………………….. 244 References…………………………………………………………………. 248

ix 5. Combustion Pathways of the Alkylated Heteroaromatics: Reactions of H, O (3P), and HO• with the Alkylated Azabenzenes……………… 252

5.1 Introduction…………………………………………………………... 252 5.2 Computational Methods……………………………………………… 260 5.3 Results and Discussion………………………………………………. 262 5.3.1 Reactions of the picolines……………………………………. 262 5.3.2 Reactions of the alkylated diazabenzenes……………………. 270 5.3.3 Overall trends………………………………………………… 275 5.4 Conclusions…………………………………………………………... 279 References………………………………………………………………….. 281

6. The Multiple Conformations of n-Propylperoxy Radical and Their Implications for Its Unimolecular Decomposition…………………… 286

6.1 Introduction…………………………………………………………... 286 6.2 Computational Methods…………………………………………….... 292 6.3 Results and Discussion………………………………………………. 294 6.3.1 Rotational profiles……………………………………………. 295 6.3.2 Conformer populations………………………………………. 301 6.3.3 Rotational barriers and reaction energetics…………………... 303 6.3.4 Computational approaches…………………………………… 305 6.4 Conclusions…………………………………………………………... 307 References………………………………………………………………….. 309

7. The Unimolecular Decomposition of Propan-1-ol-1-Peroxy Radical: Effects of Functionalization on Peroxy Radical Pathways…………… 313

7.1 Introduction…………………………………………………………... 313 7.2 Computational Methods……………………………………………… 320 7.3 Results and Discussion………………………………………………. 322 7.3.1 Conformations……………………………………………….. 323 7.3.2 Initial H-atom transfers………………………………………. 327 7.3.3 Subsequent decompositions…………………………………. 338 7.3.4 Product distribution and atmospheric implications………….. 342 7.4 Conclusions…………………………………………………………... 346 References………………………………………………………………….. 349

x 8. Non-Aqueous Solvation of n-Octanol and Ethanol: Spectroscopic and Computational Studies………………………………………………... 356

8.1 Introduction…………………………………………………………... 356 8.2 Experimental and Computational Methods………………………….. 360 8.2.1 Raman spectroscopy…………………………………………. 360 8.2.2 Chemicals…………………………………………………….. 360 8.2.3 Computational methods……………………………………… 361 8.3 Results and Discussion………………………………………………. 362 8.3.1 Peak assignments…………………………………………….. 362 8.3.2 Nature of O-H bonds…………………………………………. 366 8.3.3 Computational spectra of ethanol/solvent complexes……….. 367 8.3.4 Rationalization of experimental findings…………………….. 373 8.3.5 Survey of computational methods and basis sets…………….. 374 8.4 Conclusions…………………………………………………………... 377 References………………………………………………………………….. 378

9. The Effects of Hydrogen Augmentation on the Combustion Behavior of Hydrocarbon Fuels: Fuel Blends and Master Equation Analyses…... 383

9.1 Introduction…………………………………………………………... 383 9.1.1 Hydrogen as fuel…………………………………………… 383 9.1.2 Hydrogen as fuel additive………………………………….. 387 9.1.2.1 Generating hydrogen……………………………... 387 9.1.2.2 Methane/H2………………………………………. 388 9.1.2.3 Gasoline/H2………………………………………. 389 9.1.2.4 Diesel/H2…………………………………………. 390 9.1.3 Master equation methods and fuel behavior simulations…... 391 9.2 Computational Methods……………………………………………... 393 9.3 Results and Discussion……………………………………………… 394 9.3.1 Primary reference fuels and hydrogen……………………... 394 9.3.2 n-Heptane/H2 calculations…………………………………. 402 9.4 Conclusions………………………………………………………….. 411 References…………………………………………………………………. 415

Bibliography……………………………………………………………….. 418

LIST OF TABLES

Table Title Page 1.1 Thermodynamic and spin-density information for hydrogen-atom loss reactions of methyl-substituted heteroaromatic rings………………… 63 1.2 Thermodynamic and spin-density information for hydrogen-atom loss reactions of ethyl-substituted heteroaromatic rings…………………... 64 1.3 Thermodynamic information (kcal/mol, 298 K, B3LYP/6- 311+G**//B3LYP/6-31G*) for alkyl group loss reactions of methyl- and ethyl-substituted heteroaromatic rings…………………………… 65 1.4 Comparison of reaction pathway energetics (298 K, kcal/mol) for benzylperoxy radical (B3LYP/6-311+G**//B3LYP/6-31G*)………... 71 2.1 Thermodynamic information and spin density information for hydrogen- loss (C-H homolytic bond cleavage) reactions of methyl-substituted heteroaromatic rings………………………………………. 122 2.2 Comparison of changes in bond lengths (Angstroms) and bond angles (degrees) during the hydrogen-atom loss reactions of toluene and its nitrogen analogue, 2-methylpyridine…………………………………. 123 2.3 Thermodynamic and spin density information for reactions of ethyl- substituted heteroaromatic rings, for hydrogen loss from the CH2 group…………………………………………………………………... 126 2.4 Thermodynamic information for alkyl-group loss reactions of methyl- and ethyl-substituted heteroaromatics………………………………… 128 2.5 Changes in bond lengths (Angstroms) and bond angles (degrees) for hydrogen-loss reaction of representative heteroaromatic ring, 2- methylfuran……………………………………………………………. 133 2.6 Comparison of approximations (harmonic oscillator to hindered rotor), as applied to the thermodynamics of hydrogen-atom loss for methyl- substituted heteroaromatic rings……………………………… 142 3.1 Comparison of DFT (B3LYP/6-311+G**//B3LYP/6-31G*) and CBS- QB3 results for key processes in the reactions possible for benzylperoxy radical………………………………………………….. 161 3.2 Comparison of reaction pathways available to 2-picolinylperoxy radical at 298 K, via B3LYP/6-311+G**//B3LYP/6-31G*…………... 164 3.3 Compiled enthalpies and energies of reaction (kcal/mol) for 3- and 4- picolinylperoxy radical (B3LYP/6-311+G**//B3LYP/6-31G*)……… 170 3.4 Variation in enthalpies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*) for 3- and 4-substituted picolinylperoxy radicals, with increasing temperature……………………………………………….... 179

xii

3.5 Variation in free energies of reaction (B3LYP/6-311+G**//B3LYP/6- 31G*) for 3- and 4-substituted picolinylperoxy radicals, with increasing temperature………………………………………………… 180 3.6 Comparison of free energy profiles (kcal/mol) at 298 K for the picolinylperoxy (methylpyridinylperoxy) and ethylpyridinylperoxy radicals………………………………………………………………… 181 3.7 Free energies of reaction at 298 K (kcal/mol) for reaction pathways available to the peroxy radicals of the diazabenzenes………………… 185 3.8 Free energies of reaction at 298 K (kcal/mol), using rotor approximation in place of harmonic oscillator approximation in calculating the thermal correction to the enthalpy and entropy………. 186 4.1 Free energies of reaction (kcal/mol) with increasing temperature, as calculated via B3LYP/6-311+G**//B3LYP/6-31G*…………………. 211 4.2 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*) over the 298 to 2000 K range, for peroxy radical rearrangement pathways of the methylated furan and oxazole derivatives……………. 214 4.3 Exploration of multiple heteroatom effect through comparison of the methyloxazolylperoxy derivatives to the corresponding methylfuranylperoxy derivative……………………………………….. 222 4.4 Comparing free energies of activation and reaction for 2-substituted methyl peroxy radical derivatives of furan, pyrrole, and thiophene, relative to starting peroxy radicals……………………………………. 234 4.5 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for reaction pathways available to the peroxy radicals of the azabenzenes……………………………………………………………. 236 4.6 Variation in free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298 K) with increasing alkyl substitution (kcal/mol) at 298 K, for the methyl and ethyl-substituted 2- and 3-alkylfuranylperoxy radicals…………………………………………………………………. 242 4.7 Variations in free energies of reaction (B3LYP/6-311+G**//B3LYP/6- 31G*, kcal/mol, 298 K), with varying substitution for the alkylfuranylperoxy, alkylthiophenylperoxy, and alkyloxazolylperoxy radicals. …………………………………………. 243 4.8 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298 K), using the rigid rotor approximation in place of oscillator approximation……………………………………………….. 234 5.1 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for hydrogen-atom (H•) reactions with the picolines (methyl-substituted pyridines), at each relevant site within the parent molecule………………………………………………………………… 262 5.2 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for hydrogen-atom (H•) reactions with the picolines (methyl-substituted pyridines), at each relevant site……………………… 263

xiii 5.3 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for oxygen atom [O (3P)] reactions with the picolines (methyl-substituted pyridines), at each relevant site within the parent molecule……………………………………………………………….. 263 5.4 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for oxygen atom [O (3P)] reactions with the picolines (methyl-substituted pyridines), at each relevant site within the parent molecule………………………………………………………………... 264 5.5 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for hydroxyl radical (HO•) reactions with the picolines (methyl-substituted pyridines), at each relevant site within the parent molecule……………………………………………………………...... 264 5.6 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for hydroxyl radical (HO•) reactions with the picolines (methyl-substituted pyridines), at each relevant site within the parent molecule…………………………………………………………………. 265 5.7 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for the H-atom abstraction pathways and addition pathways available to benzene and pyridine……………………………. 269 5.8 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for the H-atom abstraction pathways and addition pathways available to benzene and pyridine……………………………. 269 5.9 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for reactions of oxygen atom [O (3P)] and the methyl- substituted azabenzenes, at each relevant site within the parent molecule…………………………………………………………………... 270 5.10 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for reactions of oxygen atom [O (3P)] and the methyl- substituted azabenzenes, at each relevant site within the parent molecule…………………………………………………………………. 271 5.11 Free energies of activation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for reactions of hydroxyl radical (HO•) and the methyl- substituted azabenzenes, at each relevant site within the parent molecule…………………………………………………………………... 272 5.12 Free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) for reactions of hydroxyl radical (HO•) and the methyl- substituted azabenzenes, at each relevant site within the parent molecule………………………………………………………………….. 273 6.1 Boltzmann distributions for the five rotamers of n-propylperoxy radical, via their free energy differences (kcal/mol, 298 K) and relative degeneracies, as calculated at the CBS-QB3 and hybrid DFT levels of theory……………………………………………………………………… 302

xiv 6.2 Enthalpies and energies of activation and reaction (kcal/mol) for the scission of ethylperoxy radical into ethene and hydroperoxyl radical, calculated via several methods and basis sets…………………………….. 306

6.3 Enthalpies and energies of activation and reaction (kcal/mol) for the cyclization reaction of n-propylperoxy radical, dissociating into cyclopropane and hydroperoxyl radical, calculated via several methods and basis sets……………………………………………………………… 307 7.1 Bond dissociation enthalpies (298 K, kcal/mol, CBS-QB3, B3LYP/6- 31+G**, and mPW1K/ 6-31+G**) for each unique C─H bond in 1- propanol…………………………………………………………………… 322 7.2 Possible dihedral combinations considered in generating starting conformations of propan-1-ol-1-peroxy radical…………………………... 325 7.3 Populations of the five most common rotamers for propan-1-ol-1-peroxy radical, using H0K data calculated via CBS-QB3 and B3LYP/6-31+G** energies and Boltzmann weighting factors……………………………….. 326 7.4 Enthalpies and free energies of reaction (kcal/mol) at 0 K and 298 K for the unimolecular decomposition of propan-1-ol-1-peroxy radical, calculated at the CBS-QB3 level of theory……………………………….. 329 7.5 Enthalpies and free energies of reaction (kcal/mol) calculated at the mPW1K/6-31+G** level of theory at 0 K and 298 K for the unimolecular decomposition of propan-1-ol-1-peroxy radical………………………….. 330 7.6 Enthalpies and free energies of reaction (kcal/mol) calculated at the B3LYP/6-31+G** level of theory at 0 K and 298 K for the unimolecular decomposition of propan-1-ol-1-peroxy radical………………………….. 332 7.7 Comparison of unimolecular decompositions of respective peroxy radicals. CBS-QB3 enthalpies of reaction at 0K and free energies of reaction at 298 K, relative to the global minimum of the respective starting peroxy radical…………………………………………………….. 337 8.1 Boltzmann weighting factors, as calculated from various energy expressions, using B3LYP/6-31+G**//MP2/6-31G* single-point energies……………………………………………………………………. 371 8.2 O−H bond lengths (Å) and stretching frequencies (cm-1) for each distinct complex, as calculated and scaled (factor of 0.9427) at the MP2/6-31G* level of theory……………………………………………………………... 374 8.3 Relative energies (in kcal/mol) compiled using two distinct basis sets, with represented energies relative to that of the lowest-energy complex within each series…………………………………………………………. 376 9.1 Characteristics of hydrogen as compared to typical hydrocarbon fuels…... 380 9.2 Arrhenius coefficients for the combustion of hydrogen. Units in moles, 3 cm , seconds, and K (A, b); kcal/mol (Ea)………………………………... 381

LIST OF FIGURES

Figure Title Page

1.1 High-temperature methane combustion…………………………….. 6 1.2 Low-temperature methane combustion……………………………... 7 1.3 Typical ignition delay of an alkane fuel as a function of the initial mixture’s temperature………………………………………………. 10 1.4 Flow chart for a typical master equation method…………………… 21 1.5 Conformers of n-propylperoxy radical……………………………… 30 1.6 Initial barriers (kcal/mol) for unimolecular reactions of n- propylperoxy radical………………………………………………... 31 1.7 Reactions of toluene with hydroxyl radical…………………………. 37 1.8 High-temperature oxidation pathways of benzene………………….. 39 1.9 (a) Enthalpies (kcal/mol) leading to 2-oxepinoxy radical via unimolecular rearrangement of phenylperoxy radical. (b) Potential decomposition pathways for phenylperoxy radical………..………... 41 1.10 Unimolecular reaction pathways for phenylperoxy radical...... 43 1.11 Unimolecular decomposition pathways of 2-oxepinoxy radical……. 45 1.12 Most favorable oxidative decomposition pathways for 2-oxepinoxy radical at 298 K and 1250 K………………………………………… 46 1.13 Heteroaromatic compounds of interest in modeling coal combustion………………………………………………………….. 52 1.14 Pyrolysis pathway of pyrrole, via intermediate pyrrolenine...... 56 1.15 Unimolecular pathways available to heteroaromatic peroxy radical; example shown for 2-pyridinylperoxy radical……………………… 58 1.16 Cyanocyclopentadiene……………………………………………… 61 1.17 Variation of reaction free energy with temperature for alkyl C-H hydrogen atom loss in (a) five-membered methyl-substituted heteroaromatic rings and (b) six-membered methyl-substituted heteroaromatic rings………………………………………………… 67 1.18 Unimolecular pathways for 2-picolinylperoxy radical, a representative peroxy radical for alkylated azabenzenes……………. 69 1.19 ΔG298 of reaction versus temperature for the unimolecular pathways of 2-picolinylperoxy radical…………………………………………. 73 1.20 ΔG298 of activation versus temperature for the unimolecular pathways of 2-picolinylperoxy radical………………………………. 74

xvi 1.21 Qualitative depiction of favorable cyclization pathways for representative peroxy radicals of methyl heteroaromatics…………... 76 1.22 Initial reaction steps for fatty ester decomposition………………….. 83 2.1 Heteroaromatic rings of interest……………………………………... 106 2.2 Generic representation of possible radical-generation pathways for the alkylated heteroaromatic rings…………………………………... 111 2.3 Comparison of areas of increased spin densities (α-β) for 2- methylpyridinyl radical and 2-ethylpyridinyl radical………………... 120 2.4 Variation of bond dissociation enthalpy (kcal/mol) with excess spin density at the incipient CH2 radical center, for methyl-substituted heteroaromatic rings…………………………………………………. 126 2.5 Variation of bond dissociation enthalpy (kcal/mol) with excess spin density at the incipient C-H radical center, for ethyl-substituted heteroaromatics……………………………………………………… 127 2.6 Correlation between BDEs for methyl and ethyl-substituted derivatives of the five-membered heteroaromatics...... 128 2.7 Variation of bond dissociation enthalpy (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered methyl- substituted heteroaromatics and (b) six-membered methyl- substituted heteroaromatics………………………………………….. 131 2.8 Variation of bond dissociation enthalpy (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered ethyl- substituted heteroaromatics and (b) six-membered ethyl-substituted heteroaromatics……………………………………………………… 132 2.9 Variation of free energy of reaction (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered methyl-substituted heteroaromatic rings and (b) six-membered methyl-substituted heteroaromatic rings…………………………………………………. 133 2.10 Variation of free energy of reaction (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered ethyl-substituted heteroaromatic rings and (b) six-membered ethyl-substituted heteroaromatic rings………………………………………………… 134 2.11 Comparison of hydrogen-atom loss and methyl-group loss free energies with increasing temperature………………………………... 135 2.12 Comparison of hydrogen-atom loss and ethyl-group loss free energies with increasing temperature………………………………... 136 3.1 Heteroaromatic rings of interest (the azabenzenes)…………………. 146 3.2 Likely pathways for the alkylated aromatic peroxy radicals, using benzylperoxy radical as a model compound………………………… 150 3.3 Numbering scheme for the azabenzylperoxy radicals……………….. 158 3.4 Change in bond lengths with addition of nitrogen atom to the aromatic system……………………………………………………… 161 3.5 Variation in excess spin density via cyclization at the ortho position, for benzylperoxy radical and 2-picolinylperoxy radical…………….. 163

xvii 3.6 H-transfer pathways delineated for each of the three picolinylperoxy radicals………………………………………………………………. 166 3.7 Variation in ΔHrxn with temperature for the pathways available to 2- picolinylperoxy radical………………………………………………. 169 3.8 Variation in ΔGrxn with temperature for the pathways available to 2- picolinylperoxy radical………………………………………………. 170 3.9 Change in ΔHactivation with increasing temperature, for 2- picolinylperoxy radical………………………………………………. 172 3.10 Change in ΔGactivation with increasing temperature, for 2- picolinylperoxy radical………………………………………………. 173 3.11 Subsequent steps available to certain peroxy radical rearrangement products…………………………………………………………….... 183 4.1 Common five-membered heteroaromatic rings and their numbering schemes………………...... 199 4.2 Rearrangement pathways available to a typical peroxy radical derivative of an alkylated five-membered heteroaromatic ring……... 206 4.3 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 2-methylfuranylperoxy radical, shown relative to the starting peroxy radical………………... 209 4.4 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 3-methylfuranylperoxy radical (4.2), shown relative to the starting peroxy radical………….. 210 4.5 Allylic stabilization afforded via the most likely cyclization pathways of 2-methylfuranylperoxy radical (top) and 3- methylfuranylperoxy radical (bottom)……………………………… 216 4.6 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 2-methyloxazolylperoxy radical, shown relative to the starting peroxy radical………………... 219 4.7 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 4-methyloxazolylperoxy radical, shown relative to the starting peroxy radical………………... 220 4.8 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 5-methyloxazolylperoxy radical, shown relative to the starting peroxy radical………………... 221 4.9 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 2-methylpyrrolylperoxy radical, shown relative to the starting peroxy radical………………... 224 4.10 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 3-methylpyrrolylperoxy radical, shown relative to the starting peroxy radical………………... 225 4.11 Free energies of potential steps (B3LYP/6-311+G**//B3LYP/6- 31G*, kcal/mol, 298 K) available to the N-centered radical formed via ortho cyclization / hydrogen-atom transfer in 2- methylpyrrolylperoxy radical………………………………………... 227

xviii 4.12 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 2-methylthiophenylperoxy radical, shown relative to the starting peroxy radical………………... 228 4.13 Free energies (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol, 298K) of the rearrangement pathways for 3-methylthiophenylperoxy radical, shown relative to the starting peroxy radical………………... 229 4.14 Comparison of 2-furanylperoxy radical (A) to 2- methylfuranylperoxy radical (B)…..………………………………… 232 4.15 Peroxy radical pathways resulting in aryl or aryloxy radicals either directly or indirectly, along with pathway resulting in carbonyl- functionalized compound……………………………………………. 237 4.16 Variation in ΔGrxn (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol) with temperature for the pathways available to 2- methylfuranylperoxy radical………………………………………… 239 4.17 Variation in ΔGactivation (B3LYP/6-311+G**//B3LYP/6-31G*, kcal/mol) with temperature for the most energetically favorable pathways available to 2-methylfuranylperoxy radical………………. 240 5.1 Possible pathways for the reaction of hydroxyl radical (HO•) with 2- methylpyridine………………………………………………………. 254 5.2 (a) The azabenzenes. (b) The picolines (methylpyridines) and toluene, model compounds for understanding the chemistry of the azabenzenes with H•, O (3P), and HO•………………………………. 258 5.3 Representation of ring-opening reactions unique to methylpyridazines, when atomic oxygen attacks ortho to the nitrogen atoms……………………………………………………….. 274 5.4 Correlation between the bond dissociation enthalpies (kcal/mol) for hydrogen-atom loss at the methyl group of the alkylated heteroaromatic rings and the corresponding free energy of activation (kcal/mol) for H-atom abstraction at the methyl group by HO•……... 276 5.5 Correlation between the bond dissociation enthalpies (kcal/mol) for hydrogen-atom loss at the methyl group of the alkylated heteroaromatic rings and the corresponding free energy of activation (kcal/mol) for H-atom abstraction at the methyl group by O (3P)…... 277 5.6 Relationship between the free energy of activation (kcal/mol) for H- atom abstraction by HO• at a given position and the free energy of activation (kcal/mol) for addition of HO• to that same position…….. 278 6.1 n-Propylperoxy radical, wherein 1,5-H atom transfer can readily occur via a six-membered ring transition state………………………. 281 6.2 Conformeric possibilities for n-propylperoxy radical……………….. 285 6.3 Rotational profile for C2−C3 bond of n-propylperoxy radical (B3LYP/6-31+G**), as a function of electronic energy (kcal/mol)...... 289 6.4 Rotational profile for C2−C3 bond of n-propylperoxy radical (mPW1K/6-31+G**), as a function of electronic energy (kcal/mol)... 290

xix 6.5 Visual representations of highest-energy rotational conformer for rotation around the C−C−C−O dihedral in n-propylperoxy radical…. 291 6.6 Rotational profile for the C3−O bond of n-propylperoxy radical (B3LYP/6-31+G**), as a function of electronic energy (kcal/mol)… 292 6.7 Rotational profile for the C3−O bond of n-propylperoxy radical (mPW1K/6-31+G**), as a function of electronic energy (kcal/mol)... 293 6.8 Visual representations of highest-energy rotational conformer for rotation around the C−C−O−O dihedral in n-propylperoxy radical…. 293 6.9 Rotational profile for methyl rotation in n-propylperoxy radical, (B3LYP/6-31+G**, kcal/mol)………………………………………. 294 6.10 Initial barrier heights for unimolecular decomposition of n- propylperoxy radical, expressed in terms of ΔH(298 K), kcal/mol, relative to n-propylperoxy radical…………………………………… 298 7.1 Common steps of peroxy radical chemistry…………………………. 309 7.2 Propan-1-ol-1-peroxy radical………………………………………... 317 7.3 Likeliest conformers of propan-1-ol-1-peroxy radical………………. 321 7.4 Isomerization pathways available to propan-1-ol-1-peroxy radical, based on previous work with n-propylperoxy radical……………….. 322 7.5 Initial kinetic barriers for pathways available to propan-1-ol-1- peroxy radical, expressed in terms of ΔH0K (kcal/mol), calculated via CBS-QB3 and DFT (B3LYP/6-31+G** and mPW1K/6- 31+G**) methods……………………………………………………. 328 7.6 Overall potential energy surface for the decomposition of propan-1- ol-1-peroxy radical using ΔH0K (kcal/mol) values calculated at the CBS-QB3 level of theory……………………………………………. 333 8.1 Raman spectra of neat octanol and ethanol………………………….. 362 8.2 Experimental Raman spectra of (a) neat n-octanol, and 0.05x n- octanol in (b) benzene, (c) cyclohexane, and (d) carbon tetrachloride, in the 3550 to 3700 cm-1 region of the free O−H stretch………………………………………………………………... 364 8.3 Experimental Raman spectra of (a) neat ethanol, and 0.05x ethanol in (b) benzene, (c) cyclohexane, and (d) carbon tetrachloride, in the 3550-3700 cm-1 region of the free O−H stretch……………………... 365 8.4 Ethanol:benzene complexes as calculated at the HF/6-31G* (top) and MP2/6-31G* (bottom) levels of theory…………………………. 368 8.5 Ethanol:cyclohexane complexes as calculated at the HF/6-31G* (top) and MP2/6-31G* (bottom) levels of theory…………………… 368 8.6 Ethanol:CCl4 complexes as calculated at the HF/6-31G* (top) and MP2/6-31G* (bottom) levels of theory……………………………… 369 8.7 Gas-phase (a) and PCM (b) calculated Raman spectra, generated via MP2/6-31G* calculations and Boltzmann weighting factors from H0 values (from B3LYP/6-31+G**//MP2/6-31G* energies)…………… 370 9.1 Generalized depiction of the progress of a master equation method... 392

xx 9.2 Variation in flame speed with hydrogen augmentation to PRF combustion mechanism, as predicted by CHEMKIN 4.1…………… 395 9.3 Variation in hydrocarbon fuel consumption (top, iso-octane; bottom, n-heptane) with H2 augmentation, as predicted by PRF mechanism... 396 9.4 Variation in H2 mole fraction as predicted by PRF mechanism, as a function of H2 augmentation (top) and of temperature change (bottom)……………………………………………………………… 397 9.5 Variation in carbon monoxide emissions with H2 augmentation to PRF mechanism……………………………………………………… 398 9.6 Variation in unburned fuel fraction with H2 augmentation to PRF mechanism…………………………………………………………… 398 9.7 Variation in heat production with H2 augmentation to PRF mechanism…………………………………………………………… 399 9.8 Non-linear variation in flame speed at a fixed point (0.15 cm), for H2 augmentation of PRF mechanism………………………………... 400 9.9 Relative overall trends with H2 augmentation to PRF mechanism….. 401 9.10 Variation in flame speed with H2 augmentation to n-heptane mechanism (Φ = 1.2)………………………………………………… 403 9.11 Variation in flame speed at a fixed point (2.4 cm) for H2 augmentation of n-heptane (Φ = 1.2)………………………………... 404 9.12 Variation in n-heptane consumption with increasing H2 augmentation………………………………………………………… 404 9.13 Variation in H2 concentration with increasing H2 augmentation……. 405 9.14 Variation in carbon monoxide emissions with increasing H2 augmentation………………………………………………………… 405 9.15 Variation in net heat production with H2 augmentation to n-heptane.. 406 9.16 Variation in unburned fuel fraction with H2 augmentation to n- heptane (Φ = 1.2)....…………………………………………………. 406 9.17 Relative trends associated with H2 augmentation for n-heptane mechanism (Φ = 1.2)………………………………………………… 407 9.18 Variation of flame speed with equivalence ratio for n-heptane, as calculated experimentally and theoretically…………………………. 409 9.19 Linear variation in fuel-rich (Φ = 2.0) flame speed with H2 augmentation to n-heptane…………………………………………... 410 9.20 Relative trends with H2 augmentation for fuel-rich n-heptane mechanism (Φ = 2.0)………………………………………………… 411

xxi

CHAPTER 1

INTRODUCTION: THE CHEMISTRY OF REACTIVE RADICAL INTERMEDIATES IN COMBUSTION AND THE ATMOSPHERE

1.1. Introduction

Combustion processes convert chemical energy into heat energy, playing several

important roles in today’s society. Oxidation processes provide power to beneficiaries

ranging from automobiles to electrical generators; atmospheric oxidation reactions

impact a wide range of environmental phenomena (i.e., ozone formation, photochemical

smog, and acid rain). To fully understand combustion chemistry, it is necessary to

understand the properties of the common reactive intermediates that participate in these

reactions. Alkyl radicals (R•), alkoxy radicals (RO•), and peroxy radicals (ROO•) constitute the main classes of reactive radical intermediates involved in combustion. The occurrence and stability of the intermediates is governed by the temperature and pressure at which reactions take place. Understanding these complex and dynamic relationships presents challenges for experimentalists and also for theorists. This chapter will first examine the fundamental chemistry that occurs during combustion of a fuel, and then move into an exploration of some key reactive intermediates. In particular, we will focus

1 on the importance of reactive oxygen species to combustion processes, highlighting our

work on the unimolecular dissociative pathways available to the peroxy radicals of alkyl,

aromatic, and heteroaromatic compounds.

1.2. Basic Concepts of Combustion Chemistry

1.2.1. Free radicals. Any type of combustion chemistry is essentially dictated by the

radical intermediates present. Before discussing how this occurs, it is first instructive to

review some key aspects of radical chemistry. Most simply, free radicals are molecules

with unpaired electrons. The lifetimes of these species vary widely given molecular

composition and reaction environment, but the alkyl radicals of interest in combustion

chemistry are highly reactive and thus short-lived. Radicals can vary in their

hybridization (sp3, sp2, or sp), as well as the nature of the orbital in which their unpaired

electron is placed – one dominated by s or p character – and thereby dictating the

geometry around the radical center. Furthermore, a free radical is stabilized by alkyl

substituents on the radical center; tertiary radicals are more stable than secondary

radicals, which are correspondingly more stable than primary radicals. Resonance

stabilization (electron delocalization) also plays a role in radical stability: a radical

adjacent to a π network (i.e., an allylic or benzylic system) can delocalize the unpaired

electron through this system and gain stability.

A radical is an odd-electron molecule, due to an unpaired electron, which can be oriented either spin-up () or spin-down (), leading to two degenerate electronic states as a doublet. This electronic configuration enables reactions that are different from those

2 of closed-shell molecules. The basic steps of a radical chain reaction are familiar from

undergraduate organic chemistry: initiation, whereby a reactive radical species forms;

propagation, the processes by which the radicals react with other molecular species to

generate other radicals; and termination, via the collision of any two radical species to

form one closed-shell molecule, thereby removing radicals from the system. Initiation

can occur either thermolytically (when heat homolytically breaks a molecule’s bond) or

photolytically (when high-energy light homolytically breaks a molecule’s bond). Once a

radical forms, it can undergo a variety of propagation reactions, including hydrogen-atom

transfers, eliminations, additions, unimolecular fragmentations; any reaction step that

begins with a radical reactant and yields a radical product is classified as a chain-

propagating step. Often, in flame chemistry, a reactive hydroxyl (HO•) radical is first

formed, which then reacts with the fuel molecule via an initiation step (R–H + HO• → R•

+ H2O). The ensuing, various propagation possibilities constitute much of the chemistry

of interest in combustion processes; this topic will be revisited shortly.

Bond dissociation enthalpies (BDEs) aid in predicting relative reactivities for

different organic (fuel) molecules. BDEs correspond to the enthalpy change for the

homolytic cleavage of a chemical bond. The more stable the resulting radical is, relative

to the reactant, the more likely the bond is to break. General explanations for radical

stability include alkyl substitution and resonance effects (as noted above); however,

Gronert has recently suggested an alternative explanation, that the potential for release of

1,3 repulsive energy (strain) has the greatest effect on these quantities: i.e., a tertiary

radical is more stable than a primary radical not because of the larger number of alkyl

3 substituents attached to the radical center, but because of the greater magnitude of the

geminal interactions in the parent (more congested) hydrocarbon that are relieved upon

C−H bond cleavage to form the radical.1 Regardless of the origin of the effect, these

BDE quantities are useful in rationalizing initiation steps for given fuels.

Free radicals are involved in a wide variety of reactions, due to their reactivity

and versatility; understanding their behavior as it relates to combustion is a goal of many

experimentalists and theoreticians. Two specific classes of radicals of interest to combustion processes are peroxy (ROO•) radicals and oxy (RO•) radicals; along with

hydroxyl (HO•) radical, many of these radicals are important members in the general

class referred to as reactive oxygen species (ROS).2

1.2.2. Combustion at varying temperatures. The concept behind combustion is

straightforward—when a hydrocarbon fuel reacts with oxygen, the organic component is eventually converted to carbon dioxide and water—but the reality is more complicated.

For instance, the combustion of methane (Reaction 1.1) is often used to teach students how to balance reaction equations:

CH4 + 2 O2 → CO2 + 2 H2O (1.1)

The combustion process for methane requires no fewer than 325 individual mechanistic

steps to be accurately described, rather than the one-step route shown above.3 As such,

incomplete combustion is a common occurrence and reactive oxygen species are

pervasive byproducts of that phenomenon, affecting fuel efficiency, and producing

atmospherically detrimental emissions. Moreover, combustion varies with system

4 temperature, as different oxidative pathways become accessible. By examining the representative cases of methane oxidation over a range of temperatures, this phenomenon becomes clearer.

1.2.2.1. High-temperature combustion. At high temperatures (T > 1000 K), methane oxidation is initiated via hydrogen-atom abstraction by hydroxyl radical, oxygen atom, or hydrogen atom (all of which are species generated in flames). Subsequently, in the most direct oxidative route (Figure 1.1), methyl radical is oxidized to formaldehyde, which then loses a hydrogen atom to form formyl (HCO•) radical.

Figure 1.1: High-temperature methane combustion.

Formyl radical can lose a subsequent hydrogen atom via collisional dissociation or reaction with molecular oxygen, thereby forming carbon monoxide (CO). A final oxidation step via the reaction of CO with hydroxyl radical yields the fully oxidized carbon dioxide as a final product. To fully characterize the overall methane combustion process, additional reactions such as methyl radical recombination and hydrocarbon eliminations must also be considered. In this basic scenario, methyl, methoxy, and formyl radicals are the intermediates of greatest interest; extending beyond this most straightforward case, the reactions of alkyl, alkoxy, and aldehydic radicals are all reactive intermediates of interest in high-temperature fuel combustion.

1.2.2.2. Low-temperature combustion. The low-temperature oxidation of methane (T <

1000 K) presents a more complex reaction scheme (Figure 1.2).

Figure 1.2: Low-temperature methane oxidation.

It can be rationalized as proceeding in two phases.4 Since reactive flame species such as

O(3P), H•, and HO• are not observed at low temperatures, the formation of the initial methyl radical must be achieved instead via an endothermic reaction with molecular oxygen.5 Once methyl radical is formed, it reacts with another oxygen molecule to form

• methylperoxy radical (CH3OO ), which abstracts a hydrogen atom from methane to form methyl hydroperoxide (CH3OOH) and methyl radical. Methyl hydroperoxide can

• • unimolecularly dissociate to produce methoxy (CH3O ) and hydroxyl (HO ) radical.

These last two steps are crucial, as they build up a reactive radical pool. Once a

sufficient amount of methyl, methoxy, and hydroxyl radicals has formed, these species

7 appropriate the initial duty of abstracting H atoms from methane, driving the reaction rate

forward rapidly. Methyl radical is now formed at an appreciable rate and can undergo

oxidation and recombination steps.

More generally, low-temperature combustion relies heavily on the tendency of

radical propagation to yield chain-branching reactions, a phenomenon first explored by

Semenov.6 Semenov’s reaction scheme is most relevant for species with two or more carbons and can be written as:

• • R + O2 → alkene + HO2 (1.2)

• • R + O2 + M → RO2 + M (1.3)

• • RO2 + R−H → RO2H + R (1.4)

• • RO2 → R'CH(=O) + R"O (1.5)

• • HO2 + R−H → H2O2 + R (1.6)

• • RO2H → RO + OH (1.7)

• • R'CH(=O) + O2 → R'C (=O) + HO2 (1.8)

Using this scheme, we can track the original radical through the most likely mechanisms for oxidation at low temperatures that lead to chain-branching. Once formed from the parent molecule (R−H), an alkyl radical (R•) can react with molecular oxygen to form an

• alkene and hydroperoxyl (HO2 ) radical (Equation 1.2), via 1,4-H-atom abstraction.

Alternatively, methylperoxy radicals can be formed following collisional stabilization by

another molecule or atom (M). The branching ratio for these two reactions is highly

pressure-dependent (and thus depends on concentration of M). Once formed, the peroxy

radical can abstract a hydrogen atom from an alkane to form a new radical (Equation 1.4)

8 or dissociate unimolecularly, yielding an aldehyde and alkoxy radical (Equation 1.5); both of these reactions produce a molecule that can participate in a chain-branching

• reaction. Since HO2 is unreactive at lower temperatures, reaction 1.6 is less likely than

• the self-reaction of HO2 resulting in H2O2 and O2. Reactions 1.7 and 1.8 are chain- branching steps, which figure heavily in the exponential increase in radical concentration necessary to achieve ignition for the combustion of a given fuel (R−H).

As shown, peroxy radical chemistry plays a substantial role in low-temperature processes, as opposed to the alkoxy radical chemistry of high-temperature combustion.

Thus, the peroxy radicals constitute an important class of reactive intermediates with significant implications for combustion and atmospheric reactions.

1.2.2.3. Negative temperature coefficient (NTC) phenomenon. In terms of temperature regions, low-temperature combustion occurs over the range 298–550 K, whereas high- temperature combustion mechanisms dominate at temperatures over 1000 K.

Intermediate temperatures, from 550 to 700 K, demonstrate an unusual phenomenon called the negative temperature coefficient (NTC), which is observed for methane and larger hydrocarbon fuels.7 As shown in Figure 1.3, when the correct alkylperoxy radical chemistry is included in a fuel’s combustion mechanism, a NTC range exists (Figure 1.3, plot C) and an increase in temperature causes a decrease in reaction rate (i.e. a longer time to ignition).8 This phenomenon can be rationalized via an examination of the low- temperature combustion mechanism.

Figure 1.3: Typical ignition delay of an alkane fuel as a function of the initial mixture’s temperature. Three different kinetic models are shown: (a) High temperature chemistry only; i.e., no peroxy radical chemistry. (b) Same as (a), but the “Q•OOH” chain- branching channel of the peroxy radicals has been considered. (c) Same as (b), but the • • concerted elimination of RO2 to olefin + HO2 has been considered. (Figure courtesy of Dr. Timothy Barckholtz, ExxonMobil Research and Engineering.)

Again, a crucial step in achieving the combustion of hydrocarbon fuels involves

the unimolecular dissociation of an alkyl hydroperoxide (ROOH) into alkoxy (RO•) and hydroxyl (HO•) radicals, i.e., chain-branching. The alkylperoxy radical leading to an alkyl hydroperoxide (Equation 1.4) is in equilibrium with the reactants, alkyl radical and molecular oxygen (O2) (reverse of Equation 1.3). As the temperature increases, entropy

favors the reactants, so that the alkylperoxy radical concentration will be minimized, and

therefore, so will the alkyl hydroperoxide concentration. Thus, the chain-branching step

cannot drive the oxidation forward, and the ignition time will increase. Moreover, for a

hydrocarbon with two or more carbons, molecular oxygen will instead abstract a

10 hydrogen atom from the alkyl radical, yielding an alkene and (notoriously unreactive)

• hydroperoxyl (HO2 ) radical (Equation 1.2). The NTC regime will persist until the temperature increases sufficiently to allow for high-temperature, chain-branching pathways. At high-temperatures, NTC is no longer relevant and the ignition rate increases with increasing temperature once again.

1.2.2.4. Atmospheric oxidation. The chemistry of the troposphere overlaps with low-

temperature combustion, as one would expect for an oxidative environment.

Consequently, the concerns of atmospheric chemistry overlap with those of combustion

chemistry. Monks recently published a tutorial review of radical chemistry in the

troposphere,9 while Atkinson and Arey have compiled a thorough database of

atmospheric degradation reactions of volatile organic compounds, which addresses these

issues in far greater detail than is possible for the scope of this chapter.10 We can extend the low-temperature combustion reactions (Equations 1.4 and 1.5), whereby peroxy radicals would have the capacity to react with prevalent atmospheric radicals, such as

NO, NO2, and NO3 (collectively known as NOx):

• • • • RCH2O2 + NO → RCH2O + NO2 (1.9)

• • RCH2O2 + NO + M → RCH2ONO2 + M (1.9a)

• • RCH2O2 + NO2 + M → RCH2OONO2 + M (1.10)

• • RCH2O2 + HO2 → RCH2OOH + O2 (1.11)

• • RCH2O2 + HO2 → RCHO + H2O + O2 (1.11a)

• • • • RCH2O2 + RCH2O2 → RCH2O + RCH2O + O2 (1.12)

11 • • RCH2O2 + RCH2O2 → RCHO + RCH2OH + O2 (1.12a)

• • • • RCH2O2 + NO3 → RCH2O + NO2 + O2 (1.13)

Oxidation in the atmosphere begins photolytically with radiation from the sun

rather than thermolytically; thus, atmospheric chemistry differs between day and night.

In the daytime, the most common initiation step involves photolysis of ozone by the sun’s ultraviolet light, leading to hydroxyl (HO•) radical generation:

1 1 O3 + hυ → O( D) + O2( Δg) (1.14)

1 • O( D) + H2O → 2 HO (1.15)

Once hydroxyl radical is formed, it can abstract hydrogen atoms from hydrocarbons (in

the atmosphere, a hydrocarbon is generally referred to as a volatile organic compound, or

VOC) to generate alkyl radicals, which can react similarly to those in low-temperature

combustion. VOCs are emitted into the atmosphere via both natural and anthropogenic

(man-made) processes. Again, since peroxy radical concentrations are pressure-

dependent, these species can revert back to reactants if they are not collisionally

stabilized. Once formed, the peroxy radicals have longer lifetimes than HO• radical and

maintain larger concentrations in the atmosphere; common reactions of peroxy radicals include self-reactions to yield two carbonyl-functionalized species and O2 (Equations

• 1.12 and 1.12a); reactions with HO2 to yield alkylhydroperoxides, aldehydes, H2O, and

O2 (Equations 1.11 and 1.11a); and reactions with NOx species to yield alkoxy radical and

nitrate moieties. NOx reactions are of significant interest for these latter species because

• • they decompose into RO and NO2 . Alkoxy radicals can react with oxygen to yield

aldehydes; moreover, after H-atom transfer, the weak aldehydic C−H bond is readily

12 • abstracted to yield an acyl radical that can react with O2 or NO2 in succession to form

peroxyacylnitrates (RC(=O)ONO2 or PANs). PANs have various detrimental effects; they are lachrymators and demonstrate mutagenic effects.11 Moreover, these PANs are

long-lived and can act as reservoirs for NOx and VOCs, traveling far from their points of origin, thus increasing their lifetime and geographical impact.

At night, when the sun’s radiation is minimal, the dominant oxidant is nitrate

• • • radical (NO3 ). This oxidant’s chemistry differs from HO radical in that NO3 prefers to react with unsaturated compounds via addition to one of the carbons of the π-system, rather than by hydrogen-atom abstraction:

• • NO2 + O3 → NO3 + O2 (1.16)

• • NO3 + CH3CH=CH2 → CH3 CH═CH2ONO2 (1.17)

• • CH3 CH═CH2ONO2 + O2 → CH3CH(OO )CH2ONO2 (1.18)

• • As shown, NO3 radical leads to different chemistry than does HO radical; the peroxy

radical can decompose to yield several products, including acetaldehyde, formaldehyde,

1,2-propanediol dinitrate (PDDN), nitroxyperoxypropyl nitrate (NPPN) and α-

nitrooxyacetone. The reactions of the peroxy radicals with NOx species can lead to

highly functionalized (and oxidized) organic compounds.

• The interplay of HO , peroxy radicals, VOCs, and NOx species has substantial

implications for tropospheric air quality. For instance, VOCs, NOx, and sunlight result in

poor visibility from ozone as well as aerosol formation, together denoted as

photochemical smog, which can lead to health effects in sensitive individuals. Normally,

we think of reductions in either class of compounds as beneficial to the atmosphere.

13 However, reducing VOC emissions only impacts ozone concentration in high-NOx areas.

Moreover, in VOC-sensitive areas, reductions in NOx may lead to the overproduction of

ozone. We can examine a simplified scheme12 for ozone production:

• • 3 NO2 + hυ → NO + O( P) (1.19)

3 O( P) + O2 + M → O3 + M (1.20)

• • In an ideal troposphere, O3 would react with NO yielding NO2 , and ultimately

regenerating O3 (Equations 1.19 and 1.20), thus no over-production of ozone could occur.

However, in the presence of VOCs, the resultant peroxy radicals formed can compete

• • with O3 and instead react with NO to form excess NO2 , thus resulting in the formation

of excess ozone. This is just one example of the complexity of atmospheric chemistry;

peroxy radicals and NOx have substantial implications for reaction with climate gases,

acid rain formation, and other aspects of air quality. Saunders et al.13 and Jenkin et al.14 have provided a wealth of information on the tropospheric degradation of aliphatic and aromatic VOCs. Additionally, the interested reader may wish to consult References 7-9 for further discussion of these important topics.

An additional concern in the commercial applications of combustion chemistry involves understanding and minimizing the production of harmful emissions (such as carbon monoxide, carbon dioxide, and the oxides of sulfur (SOx), in addition to NOx) in combustion processes. Carbon dioxide increases the amounts of greenhouse gases in the atmosphere and contributes to global warming, while NOx and SOx (oxidized derivatives

of nitrogen and sulfur) can be transformed in water aerosols resulting in acid rain (via

HNO3 and H2SO4, respectively). Another concern involves the formation of soot

14 particles that can have severe respiratory effects. Many studies in combustion chemistry

seek to reduce the production of these harmful byproducts.15

1.2.3. Methods for studying reactive combustion species

1.2.3.1. Experimental methods. Experiments performed in the 1960s and 1970s used a

variety of approaches to detect molecular species and determine rate coefficients for the elementary steps that comprised hydrocarbon combustion. Many of these experimental methods are still widely used in combustion studies today. We will briefly discuss these methods as well as surveying some of the more sophisticated methods developed in recent decades.

In combustion experiments, there are two key considerations: first, generating a

flame; and second, detecting the species of interest. Gaseous flows in a flame can be classified as laminar (streamlined layers) or turbulent. While these flames can be analyzed directly, it is less confounding to study flame chemistry through controlled

generation of reactive species in one of a wide variety of experimental apparata.

One such device is the shock tube.16 This cylindrical apparatus has both a high- pressure region filled with an inert gas and a low-pressure region that contains the reactants of interest—fuel only if pyrolytic processes are being examined, fuel and oxidizer if combustion processes are being examined— separated by a thin membrane.

By rupturing the membrane, a high-pressure shock wave travels down the low-pressure region and is reflected back on a microsecond time scale. The system temperature

15 increases rapidly enough to yield high-temperature chemistry and is rapidly quenched for

clean analysis.

Other techniques simulate post-ignition flame processes. In the flow reactor,

reactants of interest enter the reactor at one end and travel through a constant-temperature region. Ideally, all concentrations and temperatures are consistent across the cross- section of the reactor, so that all movement is in one direction and wall reactions are minimized. A similar approach involves the use of crossed molecular beams,17 wherein two molecular beams are directed into one another; the area of collisional intersection demonstrates chemistry that can occur in flames.

Additionally, specific flame species of interest can be directly generated.

Radicals can be generated either photolytically (via light) or thermolytically (via heat).

Laser-based methods are used to photolytically generate radicals. However, not every

radical of interest can be generated from a convenient precursor; moreover, radicals

generated via photolytic methods have excess internal energy, which increases the

potential of their side reactions. Likewise, pyrolytic sources can be used with a wider

range of species, but often necessitate a long residence time (ms) for radicals in the

heating zone, giving high probabilities for radical-radical reactions and radical-wall

reactions. These drawbacks have been circumvented via novel instrumentation in certain

cases. For instance, Chen et al. developed a hyperthermal pyrolytic nozzle18 that works

on a shorter time scale (μs) and generates thermally cold radicals via a jet expansion; this

nozzle has been coupled with several targets and techniques by various researchers.19

16 In terms of coupling flame generation and detection methods, several

combinations are common. Generally, shock tubes are coupled with IR and UV

absorption and gas chromatography (GC) detectors, while flow reactors are used in

tandem with GC, electron spin resonance, and resonance fluorescence detection.

More advanced techniques are also available. For instance, mass spectrometry

(MS) can be used by converting neutral radicals to ions, via chemical ionization and

electron impact; these ions are then separated and detected according to their mass-to-

charge ratios (m/z). The primary drawback of this method is that it cannot directly

discern between isomers; structural isomers have identical m/z ratios, but may behave

unique chemically. Moreover, when MS is coupled with a flame-generating system, the

probe location must be chosen carefully, as the species population can vary greatly given

the distance from the flame.

Instrumental methods have become more sophisticated to face these challenges.20

In particular, Westmoreland and Cool have developed a flame-sampling mass spectrometer that has provided several revelations in terms of relevant molecular intermediates in combustion.21 Their set-up couples a laminar flat-flame burner to a mass

spectrometer. This burner can be moved along the access of the molecular beam, to obtain spatial and temporal profiles of common flame intermediates. By using a highly tunable synchrotron radiation source, isomeric information on selected mass peaks can be obtained. This experiment represents a huge step forward in the utility of MS in combustion studies: lack of isomer characterization had previously prevented a full accounting of the reaction species and pathways.

17 When paired with an appropriate radical target, laser-based methods can serve

either diagnostically, to discern which intermediates are present in a flame, or

analytically, to explore the kinetics and dynamics of elementary steps of interest. Laser-

induced fluorescence (LIF) and Raman spectroscopy (RS) are two typical diagnostic

techniques; the former explores electronic transitions of a radical of interest, while the

latter explores structural aspects of a species via observation of changes in its

polarizability. Laser flash photolysis is a common kinetic technique, in which a radical

precursor is generated via a laser pulse, and the resultant radicals react with a target of

interest; the rate of this reaction can be thus extrapolated by monitoring decreasing radical concentration over time. Many laser techniques are currently available and can provide a wealth of information on the structural, vibrational, and electronic properties of reactive radical intermediates. Several reviews of the use of lasers in combustion chemistry have been compiled, including those by Wolfrum,22 Crosley,23 and Eckbreth.24

1.2.3.2. Computational methods. Computational and experimental methods clearly

benefit from a symbiotic relationship in combustion studies.25 Theoretical calculations

can propose potential pathways yielding empirically-observed intermediates by providing

reaction energies and rate coefficients of elementary reactions, thereby guiding

experiments. Moreover, theoretical calculations can supplement some gaps caused by

limitations in experimental approaches: the vast majority of analytical techniques fail to

distinguish between structural isomers and to identify discrete intermediate species, both

18 of which are important objectives in delineating overall combustion behavior. Finally,

modeling can identify species to look for experimentally.

Quantum chemical calculations are the most accurate theoretical methods

available for studying the structures, energies, and elementary reactions for molecules. It

is possible to determine the structure, energy, and geometrical parameters (i.e.,

vibrational frequencies, electronic states, rotational constants) for reactants, transition

states and products of a chemical reaction. With this information, the enthalpy (H),

entropy (S), and free energy (G) at specified temperatures can be estimated and reaction barriers and energies predicted. Furthermore, since we can calculate reaction barriers,

absolute reaction rate coefficients can be calculated using transition state theory (TST).26

Tk ≠ Γ= TTk )()( B e Δ− 0 BT)/kG( (1.21) TST h

≠ T is the absolute temperature, h is Planck’s constant, kB B is Boltzmann constant, and ΔG 0 is the free energy barrier height relative to reactants at infinite separation. The temperature dependent factor Γ(T) represents quantum mechanical tunneling and the

Wigner approximation27 to tunneling through an inverted parabolic barrier:

2 1 ⎛ hvi ⎞ T 1)( +=Γ ⎜ ⎟ (1.22) 24 ⎝ BTk ⎠

where νi is the imaginary vibrational frequency representing the TS barrier’s curvature.

Transition state theory yields rate coefficients at the high-pressure limit (i.e.,

statistical equilibrium) For reactions that are pressure dependent, more sophisticated

methods such as RRKM28 rate calculations coupled with master equation29 calculations

19 (to estimate collisional energy transfer) allow for estimation of low-pressure rates. Rate

coefficients obtained over a range of temperatures can be used to obtain two- and three-

parameter Arrhenius expressions:

⎛ −E ⎞ ⎜ a ⎟ k(T) = Ae⎝ RT ⎠ (1.23)

⎛ −E ⎞ ⎜ o ⎟ k(T) = AT me⎝ RT ⎠ (1.24)

Common methods for exploring the energetics of elementary reaction steps

include ab initio30 and density functional theory (DFT).31 As computational speeds have

increased, use of higher levels of theory have allowed for more accurate prediction of

properties and reactions for reactive radical intermediates, further advancing our understanding of combustion chemistry.

Using these methods, the elementary reaction steps that define a fuel’s overall

combustion can be compiled, generating an overall combustion mechanism. Current

combustion software allows a user to provide a mechanism for a specific fuel and select

other parameters of interest, along with a reactor model that simulates a particular

reaction environment via a given application code (Figure 1.4).32 One such application

code can simulate a flame in this fuel, thus providing a wealth of information about a

flame’s speed, key intermediates, and dominant reactions. Computational fluid dynamics

can be combined with detailed chemical kinetic models to also be able to simulate

turbulent flames and combustion environments.

While theoretical calculations generally have been used to supplement experimental findings, they also hold enormous promise for fully discerning the potential

20 energy surfaces of relevant combustion pathways, as well as identifying and exploring the chemistry of relevant reactive intermediates.

KINETIC MECHANISM

THERMODYNAMIC REACTOR MODEL RESULTS DATA

TRANSPORT DATA

Figure 1.4: Flow chart for a typical master equation method.

1.3. Reactive Radical Intermediates in Combustion Chemistry

1.3.1. ALIPHATIC SYSTEMS

1.3.1.1. Methane combustion. The simplest hydrocarbon, methane, has posed a wealth of challenges to experimentalists and theoreticians seeking to discern its combustion mechanism. These reactions have been explored in a wide variety of contexts over the

21 past several decades. We have discussed these briefly; the interested reader is referred to

the reviews cited in our previous discussion chemistry for further details. Due to the scope of this chapter, we are primarily interested in these reactions insofar as they

• provide useful benchmarks for the reactions of larger alkylperoxy (RO2 ) and alkyloxy

(RO•) systems. With respect to the reactive intermediates present in methane combustion

and their implications for larger systems, Lightfoot has published a review on the

atmospheric role of these species,33 while Wallington et al. have provided multiple

overviews of gas-phase peroxy radical chemistry.34 Lesclaux has provided multiple

reviews of developments in peroxy radical chemistry.35 Batt published a review of the

gas-phase decomposition reactions available to the alkoxy radicals.36

Notably, the Gas Research Institute’s mechanism (GRI-MECH) for methane combustion is well-established, drawing on research from several groups over several decades to define and calibrate kinetic and thermodynamic data for each elementary reaction step. Additional mechanisms37 for methane oxidation are also available and

updated periodically to include the most recent data.

• • Methoxy (CH3O ) and methylperoxy (CH3O2 ) radicals have been subjected to

substantial study. Zaslonko et al. have reviewed several reactions involving the methoxy

radical.38 More specifically, several experimental methods have been employed in

studying this species. As early as fifty years ago, methoxy radical was an experimental

target in mass spectrometric studies by Lossing.39 Burcat and Kudchadker used IR

vibrational spectra of methanol at varying temperatures to extrapolate the ideal gas

properties of methoxy radical.40 Ruscic and Berkowitz used photoionization mass

22 41 spectrometry to determine the ionization potential (IP) and heat of formation (ΔHf) of methoxy radical. Martinez et al. used laser-induced fluorescence (LIF) to determine the

• • temperature and pressure dependence of the rate coefficients for CH3O + NO2 over the

250 to 390 K temperature and 50 to 600 Torr pressure ranges.42 Wollenhaupt et al.

examined the same reaction using pulsed laser photolysis (PLP).43 Computationally,

Carter and Cook completed an extensive assessment on theoretical approaches for

methoxy radical,44 while Page explored the kinetics of its unimolecular decomposition.45

Subsequent studies have focused on methoxy radical’s reactivity with a variety of

46 47 • 48 • molecules: Pan et al. and Sun et al., with NO2 ; Pang et al., with NO . Gomez et

al.49 have modeled the addition and H-atom abstraction reactions of methoxy radical with

various hydrocarbons.

In early studies of methylperoxy radical, Simonaitis and Heicklin50 observed its

• • 51 reaction with NO and NO2 , while Cox and Tyndall used molecular modulation spectroscopy to supplement these findings, and Kan and Calvert studied the water vapor

• 52 dependence of the CH3O self-reaction. More recently, Wallington et al. obtained

absorption spectra of methylperoxy and other alkylperoxy radicals, over the 200-400 nm

range.53 Tyndall et al. explored the self-reaction of methylperoxy radical via Fourier-

Transform Infrared (FT-IR) spectroscopy, while Ghigo et al. have modeled the reaction

energy surface computationally.54 Their findings complemented an earlier flash

photolysis (FP) study by Lightfoot et al.55 Lesar et al. completed a quantum mechanical

• • 56 investigation of the reaction of CH3O2 with NO . Biggs et al. explored the reaction of

•57 • methylperoxy radical with NO3 as a possible source of night-time HO radical.

23 • Atkinson and Spillman have explored the kinetics of CH3O2 using cavity ring-down

spectroscopy (CRDS), confirming previous findings by Hunziker58 and Pushkarsky.59

Enami et al. explored the kinetics of the reaction between bromine monoxide (BrO•) and

methylperoxy radical.60 Together, these experimental and computational investigations provided mechanistic insights, rate constants, pressure dependences, branching ratios, etc. for the creation and validation of the 325-step GRI-MECH for methane combustion.

1.3.1.2. Ethyl radical + O2. Intramolecular reactions become increasingly important as

• the size of the alkyl chain increases. Ethylperoxy (CH3CH2O2 ) radical is a target of

significant interest because it can undergo intramolecular rearrangement via a low-strain,

5-membered ring transition state structure. Historically, ethyl radical has been implicated

as a discrete intermediate in many reactions. While early experimental studies of ethyl

radical suggested that this species reacted bimolecularly with O2 to yield ethene

• 61 (H2C=CH2, C2H4) and hydroperoxyl (HO2 ) radical, subsequent observation of other

products such as acetaldehyde and oxirane implied a more complex mechanism. In 1975,

Hickel62 affirmed that this initial view of ethyl radical oxidation was incomplete, with

support by Dechaux and Delfosse63 in 1979. Rather, it was deemed likely that ethyl

radical oxidation proceeded through a Semenov-type mechanism (Equation 1.3), in which

ethylperoxy radical is an intermediate, formed by collisional cooling, which could

transfer a hydrogen atom intramolecularly and decompose via multiple pathways.

Subsequent experimental work bolstered the likelihood that ethylperoxy radical was an

ethane oxidation intermediate. Baldwin postulated in 1986 that molecular oxygen adds to

24 ethyl radical to form ethylperoxy radical, which then undergoes concerted H-atom

transfer and elimination to yield ethene and hydroperoxyl radical.64 These and other

experimental findings have been summarized in several reviews, including those of

Fish,65 Walker,66 and Pilling et al.67

• The small size of the CH3CH2 + O2 system makes high-level computational exploration of its reaction energy surface tractable. Rienstra-Kiracofe et al. have

• provided an excellent review of the advances made in ab initio modeling of the CH3CH2

68 + O2 potential energy surface over the past several years. These authors also

summarized their own high-level calculations, noting the five most plausible pathways for the ethyl radical + O2 reaction, four of which involve the unimolecular

decomposition/rearrangement of ethylperoxy radical.

• • C2H5 + O2 → C2H4 + HO2 (1.25)

• • • C2H5 + O2 → CH3CH2OO → CH2CH2OOH

• → c-CH2CH2O + HO (1.26)

• • • • C2H5 + O2 → CH3CH2OO → CH3 CHOOH → CH3CHO + HO (1.27)

• • • • C2H5 + O2 → CH3CH2OO → CH2CH2OOH → C2H4 + HO2 (1.28)

• • • C2H5 + O2 → CH3CH2OO → C2H4 + HO2 (1.29)

Equation 1.25 accounts for the NTC range observed for the ignition of ethane.

Essentially, these reactions are refinements of the Semenov mechanism, since unimolecular reactions are important pathways in the oxidation of ethane.

25 Due to its importance to hydrocarbon combustion as a model alkylperoxy radical,

ethylperoxy radical continues to be the subject of experimental studies. Xing et al. used

time-resolved, negative-ion mass spectrometry to explore the reaction of ethylperoxy radical and nitric oxide.69 In separate works, Matricq and Szente explored the kinetics of

ethylperoxy’s reaction with acetylperoxy radical70 and NO71 using transient diode laser

absorption and time-resolved ultraviolet (TR-UV) spectroscopy. Atkinson and Hudgens

have used ultraviolet cavity-ringdown spectroscopy (CRDS) to perform kinetic studies on

the ethylperoxy radical self-reaction,72 while Rupper et al. used CRDS to explore the

• 73 A˜ ← X˜ electronic transition of CH3CH2O2 . Hasson et al. used FT-IR and high-

performance liquid chromatography (HPLC) with fluorescence detection to study the

• • 74 reaction of CH3CH2O2 with HO2 , while Mah et al. produced a mid-IR spectrum of this

species.75

• Ethoxy radical (CH3CH2O ) has enjoyed considerable interest as well. Choi et al.

explored its photodissociation dynamics via photofragment translational spectroscopy,76 while Faulhaber et al. pursued the same goal using photofragment coincidence imaging.77

Computationally, Matus et al. performed CCSD(T) calculations78 to generate quantities

of interest for this radical, including computing a heat of formation (–2.7 ± 0.8 kcal/mol)

via atomization energies.

The development of an ethane combustion mechanism provides a historical

context for understanding some overall trends of alkyl radical combustion. An

understanding of the likely pathways for this small system is useful in modeling

26 chemistry of larger systems, as can be observed from an examination of some other

reactive radical intermediates.

• 1.3.1.3. n-Propylperoxy radical (CH3CH2CH2O2 ). In longer chain hydrocarbon radicals, isomerization reactions become more important; these pathways compete with bimolecular oxidation reactions and can impact ignition rates at low temperatures. For instance, n-propylperoxy radical can undergo several unimolecular dissociations/rearrangements:79

• • CH3CH2CH2OO → CH3CH2CH2 + O2 (1.30)

• • CH3CH2CH2OO → CH3CH=CH2 + HO2 (1.31)

• • CH3CH2CH2OO → CH3CH2CH OOH (1.32)

• • CH3CH2CH2OO → CH3CH CH2OOH (1.33)

• • CH3CH2CH2OO → CH2CH2CH2OOH (1.34)

Reversion to reactants (Equation 1.30) is straightforward; similarly, the concerted H-atom

transfer and elimination pathway (Equation 1.31), observed for ethylperoxy radical can

• also occur for CH3CH2CH2O2 . However, multiple isomerization pathways (Equations

1.32, 1.33, 1.34) are now possible because the length of the alkyl chain has increased. In

particular, the 1,5-H-atom transfer occurs via a six-membered ring transition state, thereby minimizing ring strain. Rearrangement reactions lead to a more complex mixture of products. Extrapolating from our knowledge of the ethylperoxy radical pathways, these isomerization products can decompose into propene, propanal, and other oxidation

27 products. The preferences of n-propylperoxy radical will impact overall propane

combustion.

Because n-propylperoxy radical is small and can undergo low-barrier rearrangements, it is important to understand its possible rearrangement products; these findings have implications for larger hydrocarbons. DeSain et al. studied the production of hydroperoxyl radical via the reaction of n-propyl radical with O2 and proposed an

activation barrier of 26.0 kcal/mol for Reaction 1.31;80 moreover, they have also

observed sizable amounts of HO• radical, likely following one of the unimolecular H-

atom transfer steps.81 Zalyubovsky et al. examined the A˜ ← X˜ transition of

• 82b CH3CH2CH2O2 (using CRDS) and detected several of its rotational isomers at 298 K.

• • Chow et al. explored the kinetics of CH3CH2CH2O2 + NO via high-pressure chemical

ionization mass spectrometry (CIMS).83 Kaiser explored the production of propene from

• the CH3CH2CH2 + O2 reaction as a function of temperature and pressure and posited that

• chemically activated CH3CH2CH2O2 was an intermediate, resulting from the addition

reaction’s exothermicity.84 Computationally, DeSain et al.85 performed QCISD(T)

• studies to explore the 1,4- and 1,5-H-atom transfer reactions for several RO2 systems

• • (including CH3CH2CH2O2 ), generating RRKM/master equation rates to model HO2 and

HO• production. Naik et al.86 performed a similar study using quantum RRK rates to

yield rates for hydroperoxyl radical production in the n-propyl + O2 system. Chen and

Bozzelli have completed ab initio and DFT studies on the thermochemical and kinetic

parameters of the n-propyl + O2 reaction; they hypothesized that low-temperature ignition

• for this system results from intramolecular H-transfer reactions of CH3CH2CH2O2

28 followed by addition of a second oxygen molecule making it capable of forming products

that undergo chain-branching.87

• Our group has examined the conformations of CH3CH2CH2O2 , as well as its

possible unimolecular decomposition pathways.88 n-Propylperoxy radical conformations

are described by two torsion angles: CC–CO in a trans (t) or gauche (g) orientation and

CC–OO in a trans (T) or gauche (G) orientation. Energy profiles for these torsions were generated computationally, minima were obtained, enantiomers were noted, and five

unique conformers were obtained (Figure 1.5). These conformers could rapidly

interconvert, as the highest torsional barrier is predicted to be less than 5.0 kcal/mol.

Using the CBS-QB3 theoretical method,89 the 298 K distribution of rotamers was

calculated to be 28.1, 26.4, 19.6, 14.0, and 11.9 % for the gG, tG, gT, gG’, and tT

conformers, respectively. Therefore, all five conformers will be present as predicted experimentally by Zalyubovsky et al.82b

Figure 1.5: Conformers of n-propylperoxy radical, named according to the conformational preferences around the central C−C bond, then around the C−O bond. Figure courtesy of John Merle (J. Phys. Chem. A 2005, 109, 3637-3646). Reprinted with permission of J. Phys. Chem. A.

• The unimolecular reactions of CH3CH2CH2O2 were studied in detail (Figure 1.6);

complete potential energy surfaces were generated using both DFT (B3LYP/6-31+G(d,p)

and mPW1K/6-31+G(d,p))31,90 and CBS-QB3 methods. As expected, 1,5-H transfer

(Equation 1.34) occurs with the lowest barrier, followed by simultaneous 1,4-H transfer

• and HO2 expulsion (Equation 1.31). The overall decompositions for each H-atom transfer to yield decomposition products were modeled. It was shown that, although the

• 1,5-H-transfer reaction has the lowest barrier, the resultant CH2CH2CH2OOH cannot

easily undergo further unimolecular rearrangements. Rather, the 1,4-H atom transfer

routes (Equations 1.31 and 1.33) encounter lower barriers in subsequent steps. This

30 pathway for n-propylperoxy radical parallels those for the decomposition of ethylperoxy

radical.68

Figure 1.6. Initial reaction barriers for unimolecular reactions of n-propylperoxy radical. Figure courtesy of John Merle (J. Phys. Chem. A 2005, 109, 3637-3646). Reprinted with permission of J. Phys. Chem. A.

The CBS-QB3 potential energy surface accounts for the various experimentally- observed products, including hydroperoxyl radical, propene, HO•, propanal, and oxirane

• (c-C3H6O). The activation barrier for simultaneous 1,4-H transfer and HO2 expulsion,

obtained via calculations, compared well to the experimentally-observed barrier (26.0

kcal/mol) of DeSain et al.80,81 This work provides some ramifications for larger

alkylperoxy radicals: multiple conformers of long alkylperoxy radicals are likely to play a

31 role in the overall oxidation chemistry and dictate consideration for correct treatment of

thermochemistry; at lower temperatures (T < 500 K), unimolecular reactions dictate

peroxy radical chemistry.

• 1.3.1.4. n-Butoxy radical (CH3CH2CH2CH2O ). Just as n-propylperoxy radical is the

smallest peroxy radical that can undergo the 1,5-H-atom transfer, n-butoxy radical is the

smallest alkoxy radical that can do so, while pentyl radical is the smallest alkyl radical

with this potential. Similarly, these species are often used as models to understand the

chemistry of larger alkoxy radical and alkyl radical systems.

n-Butoxy radical exists in multiple conformer forms and can undergo a facile 1,5-

H-atom transfer. Vereecken and Peters91 exhaustively examined this possibility, via DFT

calculations and TST rate coefficients, to recommend a rate coefficient of 1.4 x 105 s-1, which agreed well with the experimental rates of both Atkinson92 and Hein et al.93

Vereecken and Peters used multiple approaches for deriving their multirotamer transition- state theory expressions, and demonstrated consistency through all of these. Ferenac et al. examined this unimolecular isomerization (1,5-H shift) for n-butoxy radical and its functionalized derivatives, noting substantial substituent effects (more dependent on substitution patterns than on the functional groups themselves).94 Lendvay and Viskolcz examined unimolecular reactions available to n-butoxy radical via ab initio and RRKM calculations and noted that, while 1,5-isomerization was the fastest route, fragmentation reactions would compete at combustion temperatures.95 This finding was corroborated

by exhaustive quantum chemical/RRKM dynamics calculations by Somnitz and

32 Zellner.96 Jungkamp et al. generated an exhaustive atmospheric mechanism for n-butane

via DFT and ab initio methods, proposing that n-butoxy radical will react primarily via

1,5-H transfers to ultimately form 4-hydroxy-1-butanal, while 2-butoxy radical will tend

to decompose via β-scission to ethyl radical and acetaldehyde.97 Cassanelli et al.

completed relative rate studies of 1-butoxy radical using FT-IR spectroscopy, noting that

reaction with oxygen competed with isomerization.98

• 1.3.1.5. 1-Pentyl radical (CH3CH2CH2CH2CH2 ). For pentyl radical, 1,5-H transfer can

occur regardless of whether further O2 oxidation occurs. Thus, this reaction has

implications for low-temperature combustion, as this (unimolecular) isomerization can

directly compete with the bimolecular reaction with O2. Most simply, n-pentyl radical

can quickly isomerize to iso-pentyl radical; each of these radicals can undergo β-scission reactions to yield a new alkyl radical + alkene:

• • • C3H7 + H2C=CH2 n-pentyl ' iso-pentyl

• H2C=CHCH3 + C2H5 (1.35)

Several experimental studies, over the past several decades, have modeled the overall

combustion of this system.99 Jitariu et al. have calculated unimolecular rates for

reactions of pentyl radical (i.e., intramolecular H-atom transfer, β-scission, and

elimination) noting that isomerizations have lower barriers than β-scissions.100

1.3.1.6. Larger aliphatic species. In general, the trends predicted by n-propylperoxy

radical, 1-butoxy radical, and n-pentyl radical provide good benchmarks for

33 understanding the chemistry of longer chain radicals.101,102 For instance, the 1,5-H-atom

transfer and the 1,4-H-atom transfer concurrent with elimination provide two important

routes with implications for both low and high-temperature combustion. These

possibilities constitute an important sub-class of the reactions included in comprehensive

mechanisms103 for the corresponding parent compound (i.e. propane,104 butane,105 and pentane). Also, developing larger mechanisms by substituting reaction data for similar, smaller species is a common practice in mechanism development (referred to as lumping106); thus, the reactions of these model compounds have parallels in the

chemistry of larger fuels (in particular, n-heptane107 and iso-octane,108 which together

constitute the primary reference fuels used to model gasoline combustion,109 as well as n-

hexadecane, which shows promise for understanding diesel oxidation110). Chemistry

taking place through 5- and 6-membered ring transition states is consistently favored

kinetically over larger and smaller membered ring transition states.

Gasoline and diesel fuels are two aliphatic hydrocarbon fuels that merit further

discussion.111 These fuels are primarily used in different types of combustion

environments: gasoline, in a spark-ignition (SI) engine, and diesel, in an autoignition

engine. A spark-ignition engine relies on a four-stroke internal combustion process,

involving the reciprocating piston, the intake valve, the exhaust valve, and a spark plug.

In terms of the mechanism of combustion, a spark plug ignites the compressed fuel-air

mixture, and the resultant flame ideally propagates smoothly across the engine cylinder.

The speed at which the flame propagates is dependent on the fuel used. In a diesel

engine, ignition relies on compression of the fuel until the autoignition temperature can

34 be reached; no spark ignition is used, and no flame propagation occurs, and thus fewer emissions are involved. Similarly, autoignition temperature varies between given fuels.

Even from this general overview, it is clear that the efficiency at which either type of engine operates depends heavily on fuel identity. Common metrics for understanding the ignitability of gasoline and diesel fuel are referred to as the octane number and the cetane number, respectively. Essentially, octane number refers to the volume percent of iso-octane in a given gasoline sample; cetane number refers to the volume percent of cetane (n-hexadecane) in a given diesel sample. In practice, the octane and cetane numbers refer to the practical efficiency of a given fuel to that of iso-octane and n- hexadecane, respectively. Wallington et al. have recently provided an excellent tutorial review of these and other related topics involving chemistry’s many roles in automotive fuels and engines.

1.3.2. AROMATIC SYSTEMS

1.3.2.1. Soot formation. Before we examine the oxidation pathways available to aromatic systems, it is first instructive to review the most notorious role of these compounds in combustion chemistry: their propensity to lead to soot-formation. Soot is a byproduct of fuel-rich combustion, and soot particles can affect respiration and general health in humans.112 Soot production is a result of polycyclic aromatic hydrocarbon

(PAH) formation in flames: as reactive hydrocarbon radical intermediates combine to grow and propagate, they can also cyclize into rings, which ultimately yield large networks of aromatic rings.113 To work towards minimizing harmful soot emissions, it is

35 important to understand the mechanisms by which soot forms. Generally, the first

cyclization step, whereby a benzene ring is formed from acyclic radical species, has been

postulated to occur by one of two steps based on acetylene (C2H2) experiments: (1) the

• reaction of acetylene with either 1,3-butadien-1-yl radical (H2C=CH–CH=CH ) or buta-1-

• • en-3-yn-1-yl radical (HC≡C–CH=CH ); (2) propargyl radicals (HC≡C–CH2 ) self- reaction, followed by H-atom transfers. More recently, cyclopentadiene has also been implicated as a likely precursor to benzene formation.114

Once the initial benzene ring has cyclized, it can undergo sequences of H-atom

abstraction followed by acetylene addition, to yield polycyclic aromatic hydrocarbons

(PAHs). This is known as the H-abstraction-C2H2-addition (HACA) process, proposed

by Frenklack and Wang.115 As an aromatic species aggregates to a size over 500 amu, it

adopts a particulate form and can coalesce with other PAHs to further increase in size.

When many of these particles agglomerate, they form soot.116 Efforts to minimize soot

production are widespread. Notably, decreasing the carbon content relative to oxidizer

concentration in a fuel/oxidizer mixture decreases the amount of soot formed.

1.3.2.2. Benzene and toluene. In addition to their roles in soot formation, aromatic

compounds undergo oxidation processes unique from acyclic saturated hydrocarbons.

Benzene and toluene are common fuel additives; they reduce undesirable autoignition

events (engine knock), thereby, increasing a fuel’s octane rating. Therefore, aromatic oxidative decompositions have implications for combustion and atmospheric chemistry.

The C–C and C–H bonds present in aromatic hydrocarbons are substantially stronger than

36 those of alkanes, due to their sp2 hybridized carbons. When we consider the combustion reaction of an unsaturated species such as benzene or toluene, a new initiation step is

possible. A reactive radical (for instance, HO•) may either abstract a hydrogen atom or

add directly to the ring’s π-system, generating an allylic-type radical system: two

competing pathways (Figure 1.7).

+H2O

+HO H

HO H

Figure 1.7. Reactions of toluene with HO• radical. HO• can abstract a benzylic hydrogen atom or add to the aromatic ring at the ipso, ortho, meta, and para positions relative to the methyl group. Each resultant radical can decompose by various pathways, depending on temperature and pressure.

Both pathways contribute to the combustion chemistry of aromatic species; HO• addition

to the aromatic ring is the more prevalent at 298 K.117 In a mono-alkyl-substituted

37 aromatic species, such as toluene, abstraction of a hydrogen atom from the side chain can

compete with HO• addition at positions ipso, ortho, meta, or para to the side chain. Thus,

the possibilities for oxidative initiation and subsequent peroxy radical reactions increase.

1.3.2.3. Benzene oxidation. Of the aromatic hydrocarbons, the oxidative pathways of

benzene have been studied most exhaustively. Fujii et al.118 proposed a global

mechanism, in the early 1970s in which the C−H bond of benzene is broken to form the

• phenyl (C6H5 ) radical that subsequently reacts with molecular oxygen to form the

• phenylperoxy (C6H5OO ) radical:

• • • C6H5 + O2 → C6H5OO → 2CO + C2H2 + C2H5 (1.36)

Although greatly simplified, this model demonstrates the importance of phenylperoxy

• radical (C6H5OO ) as a reactive intermediate and accounts for some of the major combustion products. However, several other mechanistic intermediates (C3, C4, and C5 hydrocarbons) were also observed.

Subsequently, Glassman’s mechanism for benzene combustion accounted for

• several more products, proposing that phenoxy (C6H5O ) radical was the chief reactive

intermediate driving the combustion of benzene. The stepwise mechanism for benzene

119 • combustion began with H-atom loss to form a phenyl radical (C6H5 ), then proceeded through reaction with O2 and then carbon monoxide expulsion to form cyclopentadienyl

• (c-C5H5 ) radical, which could react with O2 and expel CO again to form smaller

hydrocarbon species (Figure 1.8). However, this model still over-predicted the formation

of phenyl, phenoxy, and cyclopentadienyl radicals; moreover, it failed to account for

38 additional experimentally observed products (i.e. furan, pyranyl radical, and oxo-

butadiene).120

+HO2

O2 +O(3P)

+CO

O2 +O(3P)

+CO

Figure 1.8: High-temperature oxidation pathways of benzene, as proposed by Glassman.

The tendency of the benzene combustion mechanism to substantially overestimate

the formation of phenoxy radical suggested either flaws in the kinetic data involving

• C6H5O or incompleteness of the combustion mechanism. Subsequent work verified the

• kinetics and energetics used in modeling C6H5O decomposition. In separate studies, Liu

et al.121 and Olivella et al.122 used ab initio and DFT models, along with RRKM rate

39 coefficients, to confirm the data for these pathways. (More recently, these data were also

borne out in a quantum mechanical/RRKM study by Hodgson et al.123)

Consequently, the benzene oxidation mechanism was further developed by

considering additional decomposition and oxidation steps. Sethuraman et al. proposed

that phenyl radical decomposition can occur by either of two key pathways:124 β-scission

of phenyl radical or by breakdown of the phenylperoxy radical formed by oxidation of

phenyl radical (Figure 1.9). Using PM3 calculations,125 which were ultimately verified

by DFT studies,126 Carpenter predicted that another species, 2-oxepinoxy radical (3 in

Figure 1.9b), is an important intermediate due to its relative stability, formed via a spirodioxiranyl intermediate (2 in Figure 1.9b) from phenylperoxy radical. Pathway A in

Figure 1.9b is the thermodynamically preferred pathway at temperatures increasing up to

432 K, while pathway B has an entropic benefit at higher temperatures. While pathway

B essentially matched the traditional view of benzene combustion, pathway A introduced a new route for phenylperoxy radical, which could resolve discrepancies observed using previous models.

40 O O O O (a) O O O

PM3/UHFa 0.0 26.1 5.5 ------69.0

DFTb 0.0 27.2 22.6 11.3 46.1 -10.5 - 48.1

(b)

Figure 1.9. (a) Enthalpies (kcal/mol) leading to 2-oxepinoxy radical formation via unimolecular rearrangement of phenylperoxy radical. PM3/UHF = ΔHf and DFT (B3LYP/6-311+G(d,p)//B3LYP/6-31G(d)) = ΔH298 (b) Potential decomposition pathways for phenylperoxy radical, A involving 2-oxepinoxy radical, and B involving oxygen atom loss. Figure courtesy of Steven Kroner (J. Am. Chem. Soc. 2005, 127, 7466 – 7473). Reprinted with permission of J. Am. Chem. Soc.

41 This supposition was validated by experimental studies that demonstrated the

prevalence of different reactive oxygen species at different temperatures. Using cavity-

ringdown spectroscopy, Yu and Lin studied the reaction of phenyl radical and oxygen,

noting that phenylperoxy radical was the only adduct formed at temperatures ranging up

to 473 K;127 Venkat et al. completed flow reactor studies of benzene combustion at 1200

K and identified phenoxy radical as a key intermediate.119

Our group has completed several studies of key reactions for some relevant

reactive intermediates in benzene oxidation. Barckholtz et al. examined the oxidation

pathways of several aromatic species, using benzene as a benchmark.126a General models

were proposed for aromatic hydrocarbon and heterocycle oxidation (namely: benzene,

pyridine, furan, and thiophene) in preparation for more specific studies of each relevant

species. Carbon-centered radicals at each relevant position underwent exoergic

oxidation, and the resulting peroxy radical unimolecular decomposition pathways were

delineated. It was proposed that these peroxy radicals could undergo rearrangements that

make them of significant atmospheric interest.

A subsequent study examined phenylperoxy radical in greater detail. Fadden et

al.126b identified five possible unimolecular decomposition pathways for phenylperoxy

radical (Figure 1.10): via oxygen atom loss to form phenoxy radical (Figure 1.10, route

A); via a dioxiranyl radical species (Figure 1.10, route B); via a dioxetanyl radical

intermediate (Figure 1.10, route C), via a 1,3-peroxy radical species (Figure 1.10, route

D), and via a p-phenylquinone radical intermediate (Figure 1.10, route E). These routes

were examined using DFT (B3LYP/6-31G(d)) and ab initio (CASSCF) structures, with

42 high-level CAS-MP2, and UCCSD(T) single-point energies. Formation of the dioxetanyl species was predicted to be most favorable based on ΔG298 energies. This radical could

unimolecularly decompose to produce smaller species, including cyclopentadienyl and

pyranyl radicals, as well as acyclic oxygenated species, that are experimentally observed.

At higher temperatures (T > 500 K), the entropic benefit afforded via oxygen atom loss

becomes a contributing factor, and pathway A is the major decomposition route.

Moreover, route B leads directly to 2-oxepinoxy radical (3 in Figure 1.9b), which is

potentially an important intermediate in low-temperature benzene oxidation.

+O(3P)

O O A O O B

C O D O E H

O H O O

O H

Figure 1.10. Potential unimolecular reaction pathways for phenylperoxy radical.

43 The stablility of 2-oxepinoxy radical qualified it as a target for further theoretical

and experimental study. The calculations of Barckholtz et al.126a allowed the refinement

of a feasible energetic pathway toward 2-oxepinoxy radical; these DFT calculations

supplemented the semi-empirical work of Carpenter and also proposed a triradical

intermediate between the dioxiranyl and oxepinoxy species (Figure 1.10a).

Consequently, the unimolecular decomposition of 2-oxepinoxy radical (3 in

Figure 10b) was thoroughly modeled by Fadden et al. using DFT (B3LYP) methods.128

Gibbs free energy profiles (T = 298 to 1250 K) were generated. A wide range of decomposition pathways were examined, which could account for typical experimentally- observed products (Figure 1.11). Notably, the delineated decomposition pathway did not require the generation of cyclopentadienyl radical. Cyclopentadienone is a commonly observed product in benzene combustion, and most mechanisms presume that cyclopentadienyl radical is its most likely precursor. However, it was shown that 2- cyclopenten-1-yl radical (19 in Figure 1.11), a feasible source of cyclopentadienone, could be formed from the 2-oxepinoxy radical. These computer pathways supported the experimental results of Pfefferle and coworkers,137b in their work on the low-temperature

combustion of benzene, in which C2, C3, and C4 hydrocarbons were observed without

formation of C5 constituents.

Figure 1.11. Unimolecular decomposition pathways of 2-oxepinoxy radical (1). The relative free energies (298 K, kcal/mol) at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level are shown for each intermediate relative to 1, and each free energy of activation is relative to the reactant for that specific step. Figure courtesy of Michael Fadden (J. Phys. Chem. A, 2000, 104, 8121 -8130.) Reprinted with permission of J. Phys. Chem. A.

2-Oxepinoxy radical is highly stabilized by its unique structure; Mebel et al. determined, via PUMP3/6-31G(d)//UHF/ 6-31G(d) calculations, that it would have a

• relative enthalpy of ΔH0 = –91.8 kcal/mol as compared to phenylperoxy (C6H5O2 ) radical.129 The stability of this species suggests that it will be fairly long-lived, and thus

could undergo reactions of atmospheric interest, such as the addition of molecular

45 oxygen. Merle and Hadad studied the oxygen-initiated decomposition of 2-oxepinoxy

radical using both DFT and CBS-QB3 calculations.130 Calculations predicted that from T

= 298 to 750 K, O2 addition routes compete with unimolecular decomposition (Figure

1.12); for T > 750 K, however, the entropic penalty associated with the O2 addition step

causes the unimolecular decomposition of 2-oxepinoxy radical to be more favored.

O O O O O2 O2 O O O O A B O O

O O

O O O O +O(3P) O

O O +CO2 O O O

+O(3P) O

O H

3 +CO2 +O( P)

O O

+CO2 + H

Figure 1.12. Most favorable oxidative decomposition pathways for 2-oxepinoxy radical, at 298 K (path A) and 1250 K (path B).

The most stable O2 addition adduct below T = 1250 K is 6-peroxyoxepinone

(route A in Figure 1.12), which can cyclize to form a 1,4-peroxy intermediate which

subsequently releases CO2 to form a 5-oxopentanalyl radical. This species can cyclize

and fragment, yielding formyl radical, furan, and carbon dioxide. Above T = 1250 K, the

dissociative pathway (route B in Figure 1.12) afforded by 2-peroxyoxepinone’s loss of

oxygen atom becomes more favorable.

Even though 2-oxepinoxy radical (3 in Figure 9b) may be an important

intermediate in benzene oxidation, no confirmatory experimental evidence exists.

Recently, Kroner et al. published an experimental study of the gas-phase acidity of

131 2(3H)-oxepinone (C6H6O2), obtained via flowing-afterglow mass spectrometry. They postulated that this quantity could be used along with a thermodynamic cycle to determine the heat of formation of 2-oxepinoxy radical:

– + C6H6O2 → C6H5O2 + H ΔHacid (1.37)

– • – – C6H5O2 → C6H5O2 + e EA (C6H5O2 ) (1.38)

H+ + e– → H• –IP (H) (1.39)

• • C6H6O2 → C6H5O2 + H BDE = ΔHacid + EA − IP (1.40)

• • ΔHf (2-oxepinoxy radical, C6H5O2 ) = BDE + ΔHf (H ) − ΔHf (C6H6O2) (1.41)

A value of ΔHacid = 352 ± 2 kcal/mol was determined for equation 1.37. This

experimental evidence could ultimately be valuable in conclusively identifying 2-

oxepinoxy radical as a reactive species of interest.

47 The overall pathways of benzene oxidation and the decompositions of possible

intermediates have been well characterized via theoretical methods. Thus far, we have

discussed these species mainly in the context of their oxidation mechanisms, but

phenylperoxy and phenoxy radicals have also been investigated as individual

experimental targets.

• The chemistry of phenoxy (C6H5O ) radical has been of interest for several

decades. Benson et al. proposed the first rate coefficient for its unimolecular

decomposition,132 while Lin and Lin provided information on the Arrhenius parameters

for the reaction.133 Experimental and theoretical studies have examined the electronic states,134 molecular vibrational frequencies,135 and spin density, as well as thermal and

oxidative decomposition.136 Benzene combustion mechanisms rely heavily on the

inclusion of phenoxy radical data;118,,119 137 additionally, phenoxy radical decomposition

reactions are necessary in the mechanisms for combustion of several other species,

including propane,138 butane,139 and anisole.140 More notoriously, phenoxy radical has

recently been implicated in routes to dioxin and polychlorinated naphthalenes; several

theoretical studies have been completed on these potential reactions.141 Finally, the roles

of phenoxy radical in flame chemistry,142 emissions,143 and other aspects of

combustion144 have been compiled in several reviews.

Phenylperoxy radical has similarly been a topic of experimental and theoretical

interest. Tokmakov et al.145 calculated a potential energy surface for phenyl radical and

O2 using ab initio G2(MP2) calculations. Weisman and Head-Gordon used time-

dependent density functional theory (TD-DFT) calculations to examine the effect of

48 substituents on the phenylperoxy radical UV-vis absorption spectrum.146 Lin and Mebel

used ab initio methods to study the phenoxy radical + O-atom reaction.147 Just et al. have

examined the A˜ ← X˜ electronic transition of phenylperoxy using CRDS.148 Tonokura et

al.149 used CRDS to study the visible absorption spectrum of the phenyl radical, as well as the kinetics of its reaction with O2. Krauss and Osman examined the UV absorption

• 150 spectra of vinylperoxy radical (H2C=CHO2 ) and phenylperoxy radicals.

Phenylperoxy radical, originally assumed to be a factor in low-temperature

combustion only, has actually been shown to play a substantial role in dictating the

overall combustion trends of benzene. Just as the isomerizations and eliminations of the

alkylperoxy radicals significantly affected their overall combustion pathways,

rearrangements and other intramolecular pathways available to phenylperoxy radical

similarly impact the overall progress of benzene combustion. This knowledge can be

extrapolated to more complex aromatic species.

1.3.2.4. Alkylated aromatics. Like benzene, toluene (C6H5CH3) is a common constituent

of gasoline. Much of the literature concerning toluene’s oxidation focuses on a global

mechanism for understanding its combustion. Emdee et al.151 proposed that toluene’s

combustion mechanism is most sensitive to its reaction with O2 to form benzyl radical

• • (C6H5–CH2 ) and HO2 . Dagaut et al. proposed that toluene oxidation is initiated by

benzylic H-atom abstraction by O2 to form the benzyl radical, which can unimolecularly

decompose to acetylene and cyclopentadienyl or react with an additional O2 and

unimolecularly decompose to phenyl and formyl radicals (via benzaldehyde, (C6H5–

49 C(=O)H).152 Pitz et al. generated a comprehensive mechanism for toluene combustion in

varying settings, due to its widespread use as a fuel additive.153 El Bakali et al. noted an

overall similarity between the chemistry of benzene and the chemistry of toluene, based

on their oxidation mechanisms.154 Ethylbenzene has also been the subject of mechanistic studies,155 most recently by Ergut et al.156

As mentioned previously, the low-temperature oxidation of toluene is proposed to

begin with either of two steps; if hydroxyl radical is present, HO• can abstract a benzylic

hydrogen atom or add directly to the aromatic ring. Once a radical is generated on the

aromatic ring or side chain of toluene, rapid oxidation can occur. The resulting peroxy

radical has several viable pathways available. Atkinson compiled data on low-

• temperature atmospheric reactions for both the benzyl radical and the C6H5–CH3/HO adduct. Andino et al. modeled the atmospheric oxidation of toluene and disubstituted xylenes, noting that several cyclized peroxy radical rearrangement products were energetically stable.157

• Additionally, studies have focused on benzylperoxy radical (C6H5CH2O2 ), although this is a less common target than phenylperoxy radical because HO• addition to

the aromatic ring is more dominant than H-atom abstraction of the benzylic C–H bond.

Elmaimouni et al. studied the equilibrium for benzylperoxy radical and benzyl radical +

O2 over the temperature range 393-433 K, extrapolating the addition reaction enthalpy to

be –20.1 kcal/mol at 298 K, and the free energy to be 11.4 kcal/mol.158 Fenter et al.

performed a kinetic study159 using the same equilibrium at 760 torr with a temperature

-13 range of 298─398 K, proposing a rate kf(T) = (7.6 ± 2.4) x 10 exp[(190 ± 160)/T(K)]

50 3 -1 -1 4 -1 cm molecule s , equilibrium Kp = 6.3 ± 0.2 x 10 atm , and reaction enthalpy ΔH298 =

–21.8 kcal/mol. Buth et al. used a flow reactor coupled to mass spectrometric detection

160 11 3 -1 -1 in a comparable study, determining kf = (4.44 ± 1.3) x 10 cm molecule s and Kp =

57,200 bar-1 at 298 K. Noziere et al. monitored the reaction of benzylperoxy radical with

hydroperoxyl radical using flash photolysis/UV absorption and continuous

photolysis/FTIR.161 El Dib et al. performed a flash photolysis kinetics study of the self-

reaction of benzylperoxy radical.162

It was again observed that rearrangement pathways comprise a substantial portion

of the oxidation routes for alkylated aromatics.10,157 Since this phenomenon is mainly

due to peroxy radical reactivity rather than of the identity of the parent compound, it is

clear that comparable rearrangements would be factors for polycyclic aromatic

hydrocarbons (PAHs), as well as for N-, O-, and S-containing heteroaromatic rings and

their alkylated derivatives.

1.3.2.5. Heteroaromatic combustion. Considering additional functionalities in an

aromatic ring allows for conclusions with implications for coal chemistry. Coal is a vital

fossil fuel; about 50% of the US is dependent on coal for electric power generation, and its use accounts for 90% percent of Ohio’s electrical power. Current engineering efforts are underway to maximize coal’s energy potential while minimizing harmful

163 environmental emissions (i.e., Hg, SOx, NOx, and CO2).

Unlike hydrocarbon-based fuels like methane and gasoline, coal has never been

subjected to a comprehensive mechanistic analysis due to the complexity of its molecular

51 structure. However, the fact that coal’s complex structure consists of monocyclic units

can be exploited: aromatic hydrocarbons and heteroaromatic rings are recurring units in

coal’s structure, even while the overall structure varies geographically. Understanding

low and high-temperature oxidation reactions for these subunits and their reactive radical

intermediates will facilitate a better understanding of their chemistry in combustion.

Heteroaromatic compounds (Figure 1.13) have been used as models for

understanding coal chemistry in several pyrolytic studies.

H N O S O 5 2 2 2 2 4 3 3 3 N Pyrrole Furan Thiophene Oxazole N N N N 2 N 2 2

3 3 5 N N 4 4 4 Pyridine Pyridazine Pyrimidine Pyrazine

Figure 1.13. Heteroaromatic compounds of interest in coal combustion.

The azabenzenes (N-containing heteroaromatics) have historically been used most often;

their pyrolysis has been shown to proceed through reactive radical intermediates,

although the identity of these intermediates can vary with reaction conditions.164 Using a shock tube, Mackie et al. observed the pyrolytic decomposition of pyridine,165 noting that

52 three initial radicals derived from C−H bond scission: o-pyridinyl, m-pyridinyl, and p-

pyridinyl. Of these, o-pyridinyl radical was dominant and was observed to yield

cyanoacetylene (N≡C–C≡CH) through a ring-opening process, while m- and p- pyridinyl radicals formed HCN as a major product, via a less discernable pathway.

Similarly, Kiefer et al. studied the pyrolysis of pyrazine, pyrimidine, and pyridine;166 all

were observed to undergo ring-scission to yield 2-cyanovinyl radical (•CH=CH–C≡N),

which accounts for several combustion products upon decomposition, including HCN,

N≡C–C≡CH, and acetylene. 2-Cyanovinyl radical has been identified in several

pyrolytic studies of the azabenzenes, originally via the shock-tube study of Doughty et

al.164f,g These authors proposed that the relative position of the nitrogen atoms in the ring

substantially impacts the reactivity of that ring toward pyrolysis: i.e., pyrazine dissociates

more quickly than pyrimidine. Overall, the azabenzenes demonstrate increased reactivity

relative to benzene; their C–H BDEs range from 93 to 98 kcal/mol, compared to

benzene’s C–H BDE of 112 kcal/mol.167 The smallest C–H BDEs occur at positions

ortho to nitrogen (although being a C–H bond that is twice ortho to N (as in pyrimidine)

does not render a further lowering of the BDE). Kikuchi et al,168 Mackie et al.,169 and

Jones et al.170 have attributed this phenomenon to the nitrogen atom’s in-plane lone pair

electrons interacting with the lone pair electron on the carbon center of the radical,

thereby reducing the strength of the C-H bond via radical product stabilization.

The oxidative decomposition of the azabenzenes has not been studied in such

great detail. Tabares et al. studied the reaction of pyridine with O-atom, noting a

decrease in reactivity relative to benzene. 171 Alfassi et al. studied the formation and

53 reactivity of pyridylperoxy radicals in solution.172 Eisele postulated that the presence of

ions derived from pyridine and picoline in the troposphere implicates these species as atmospherically significant.173 Yeung and Elrod explored this claim via chemical

ionization mass spectrometry to study the reactions of HO• with pyridine, the picolines, the lutidines, and the ethylpyridines, and postulated that pyridinated compounds could indeed have substantial implications on tropospheric ion content.174 As with toluene, the

reaction of HO• with pyridine and alkylated pyridines is likely to proceed either via HO• addition to the aromatic ring or hydrogen-atom abstraction from a C–H bond. The new radicals can unimolecularly decompose or undergo reaction with O2. These reactions

have been modeled for toluene and the hydrocarbon analogues by Andino et al.157

Heteroaromatic compounds have the potential to add O2 at the ring nitrogen and thus

175 176 form NOx species, leading to excess tropospheric ozone and acid rain.

The five-membered heteroaromatic (furan, oxazole, pyrrole, and thiophene) are of

additional interest. Besides their role in coal combustion, these have been implicated as

emissions of biomass burning,177 residential fires,178 waste tire burning,179 cigarette smoking,180 and motor vehicles.181 Bruinsma et al. examined the pyrolysis of

heteroaromatic rings most commonly found in coal volatiles,182 determining a rank of

increasing pyrolytic reactivity: thiophene < benzene < pyridine < pyrrole <

cyclopentadiene < furan; they also noted that an additional, fused aromatic ring has a

stabilizing effect, especially for pyridine and furan. Cullis and Norris also studied the

pyrolytic processes of the heteroaromatics, yielding methane and benzene as major

products, via hydrocarbon radical intermediates. Qualitative product analysis revealed

54 that these heteroaromatics decomposed by similar mechanisms regardless of identity; the

heteroatoms were generally not present as major combustion products; they were lost as

water, hydrogen sulfide, or hydrogen cyanide.183 Braslavsky and Heicklen extensively

reviewed the thermal and photochemical decomposition of heteroaromatic compounds.184

Klein et al. studied variations in heteroaromatic C–H BDEs for substituted aromatic compounds.185

In particular, furan and pyrrole, as well as their methylated derivatives, have been

common targets of pyrolytic studies. Pyrolysis of furan and its methylated derivatives

has been shown to lead to products, including carbon monoxide, acetylene, acetaldehyde,

propyne, and allene. Grela et al. observed that methylated furan is likely to undergo C–O

• bond scission, yielding either benzene and water, via the biradical C(CH3)=CH–

• 186 CH=C(CH3)O , or isomerizing prior to decomposition to produce CO and C5H8.

Organ and Mackie also suggested that the biradical intermediate was the most likely intermediate.187 The mechanism has since been re-evaluated. Fulle et al. noted that the

major decomposition products of unsubstituted furan were formed via one of two

188 pathways, one which resulted in C2H2 and ketene (H2C=C=O), and one which led to propyne and carbon monoxide; Sendt et al. confirmed these pathways and proposed that they were achieved via 1,2-H transfer in the original furan molecule, which lead to cyclic carbene intermediates.189

The pyrolysis of pyrrole produces a variety of products: hydrogen cyanide,

propyne, allene, acetylene, cis-crotonitrile, and allyl cyanide, among them. Lifshitz et al.

hypothesized that pyrrole undergoes 1,2-bond (N–C) cleavage, then an internal H-atom

55 transfer to yield a radical intermediate that can isomerize to either cis-crotonitrile or allyl

cyanide, or dissociate to HCN and propyne.190 Bacskay et al. completed quantum

chemical comparisons of the isoelectronic pyrrolyl and cyclopentadienyl radicals; they

hypothesized that pyrrolyl radical is formed via C–H bond scission in the intermediate

pyrrolenine (2H-pyrrole) rather than directly via N–H bond cleavage (Figure 1.14).191

Mackie et al. explained a similar finding, postulating that it was the formation of pyrrolenine that dictated the rate at which pyrrole pyrolysis occurred.192

H N H H N N CH2

Figure 1.14. Likely pyrolysis pathway of pyrrole, via intermediate pyrrolenine.

While most studies have focused on the pyrolytic unimolecular decomposition of

these mono-heteroaromatic compounds, our group has explored their oxidative

decomposition. As with benzene, where phenylperoxy radical plays a major role in

dictating oxidation pathways, we hypothesize that the peroxy radicals derived from

heteroaromatic rings are reactive species of considerable interest for combustion and

atmospheric reactions.

Barckholtz et al. surveyed a variety of computational methods and basis sets to

select an appropriate theoretical model for study of these molecules, finding that density

56 functional theory (DFT) provided a good balance of accuracy and computational

economy.193 This study also validated the use of heteroaromatic monocyclic rings as

constructive models for their polycyclic analogues (by extension, this finding could also

confirm the similarities between the chemistry of coal and these smaller model

compounds). Bond dissociation enthalpies were compiled for a variety of poly-

heteroaromatic rings; the resulting values were compared to the corresponding mono-

heteroaromatics. For example, for benzofuran, the C2–H BDE is 117.8 kcal/mol, which

is 0.6 kcal/mol less than the corresponding C2–H BDE in furan. These calculations

showed that increasing the number of rings in the compound did not have a substantial

effect on BDE, except for a C–H bond adjacent to a bridgehead junction and for which an

electronegative heteroatom was present on the other side of the bridgehead. Even in such

cases, the deviation between the monocyclic analogue and the polycyclic derivative was

only ~ 2 kcal/mol.

In separate DFT studies, Fadden et al. examined the rearrangement pathways

(Figure 1.15) of peroxy radicals from azabenzenes194 and five-membered heteroaromatic rings.195 It was observed that each azaphenylperoxy radical can lose molecular oxygen

(1.2 → 1.1), rearrange to a dioxiranyl species (1.2 → 1.3) or a dioxetanyl species (1.2 →

1.4), or lose atomic oxygen (1.2 → 1.5). Other unimolecular decomposition pathways

afforded to alkylperoxy radicals (i.e. H-atom transfer and β-scission) are not possible for their aromatic analogs.

57 O N

1.3

N O

N O N 1.4a H O +O2

1.1 1.2 N O

1.4b

N O

+O(3P)

1.5

Figure 1.15. Unimolecular pathways available to heteroaromatic peroxy radicals; example shown for 2-pyridinylperoxy radical.

From the calculated energies, several main conclusions were drawn. Loss of O2 is less endoergic than loss of O-atom for most heteroaromatic peroxy radicals; two exceptions are 3-pyridinylperoxy radical, which mimics phenylperoxy radical in this aspect of its reactivity as well as many others, and 3-pyridazinylperoxy radical, in which the oxy

58 radical is a σ-radical (2A') and maintains aromaticity not observed in the peroxy radical.

Dioxiranyl formation is generally less endoergic than O2 and O-atom loss at 298 K;

however, at temperatures greater than 500 K, the entropic contributions reverse the stabilities. Dioxetanyl intermediates are more strained and, therefore, unstable intermediates; a few exceptions are observed for compounds in which an alkyl chain is adjacent to a ring nitrogen and cyclization can form stable nitrosyl radicals (as for

Pathway 1.4b for 2-pyridinylperoxy radical), but these reactions still incur high reaction barriers.

Similar routes are available to peroxy radicals of O-, S-, N-, and O,N-containing

five-membered ring heteroaromatics. The kinetic and thermodynamic parameters for the

viable arylperoxy radical unimolecular dissociation steps were calculated for the

furanylperoxy radicals; the effect of a second heteroatom was examined by a comparable

approach for the oxazolylperoxy radicals. Thermodynamic parameters for these reactions

were compared to those of the pyrrolylperoxy and thiophenylperoxy radicals. For

smaller heteroaromatic peroxy radicals, loss of O-atom to form the corresponding aryloxy

radical is preferred at 298 K to other decomposition routes. Dioxiranyl formation (Figure

1.15, Pathway 1.3) competes thermodynamically with oxygen atom loss (Figure 1.15,

Pathway 1.5) in some cases and is universally more favorable than O2 loss (Figure 1.15,

Pathway 1.1). The dioxetanyl route (Figure 1.15, Pathway 1.4) is disfavored for 5- membered ring heteroaromatic peroxy radicals, often due to formation of an anti-Bredt

double bond in the ring system. As with the azabenzenes, the dissociative pathways

became more favorable than rearrangements at high temperatures.

59 Overall, reactivity of the heteroaromatic peroxy radicals was shown to depend

heavily on ring size. For azabenzylperoxy radicals, losing an oxygen atom is

substantially unfavorable, and reversion to reactants (aryl radical + O2) is a more likely

dissociation pathway; the peroxy radical of the five-membered ring heteroaromatics can

lose oxygen atom at a lower cost. For both sets of arylperoxy radicals, isomerization

pathways are important at low temperatures. Additionally, intramolecular cyclizations

compete with O-atom loss, and some cyclizations lead to nitroso radicals, creating

implications via possible NOx formation. As with phenylperoxy radical, the

azabenzylperoxy radicals have lower barriers for rearrangement than for loss of oxygen

atom, and consequent products will influence overall combustion pathways.

1.3.2.6. Alkylated heteroaromatics. Substantially fewer studies have been published for the reactions of alkyl-substituted heteroaromatics, though these species demonstrate

comparable promise for elucidating coal combustion chemistry. Several references

discussed in the previous section contain information on methylated heteroaromatic rings.

Mackie and coworkers completed experimental196,197 and theoretical198 studies of the pyrolytic decomposition of 2-picoline (2-methylpyridine). They concluded that decomposition proceeded mainly through o-pyridinyl and 2-picolinyl radicals. The former tended to decompose predominantly to yield cyanoacetylene, while the latter favored decomposition to a cyano-functionalized cyclopentadiene (Figure 1.16).

60 CN

Figure 1.16. Cyanocyclopentadiene.

Fifteen years later, this pyrolytic study remains the most comprehensive for an

alkyl-substituted heteroaromatic compound, despite the authors’ hypothesis that the

alkylated derivatives actually provided a better model for fuel-bound nitrogen (FBN) than

did unsubstituted heteroaromatic rings, which have been more common targets.193-199

Kinetic studies are more common in the literature: Frerichs et al. examined the reaction of the picolines with oxygen atom,199 while Yeung and Elrod studied reactions of HO• with pyridine and its methyl- and ethyl-substituted derivatives. Both groups noted that the presence of nitrogen did not demonstrably affect the species’ chemistry; generally, reactivity is comparable to toluene.

The oxidation pathways for alkylated heteroaromatics start with the formation of

a radical species, via hydrogen-atom or alkyl-group homolytic bond cleavage. We

calculated these BDEs for methyl and ethyl-substituted derivatives of several key

heteroaromatics (Tables 1.1─1.3).200 Few of these experimental values exist;201 therefore, we also briefly examined the chemistry of benzylperoxy radical, because it is a hydrocarbon analogue for methylated heteroaromatics and an experimental target.

Calculations at the CBS-QB3 level closely replicated toluene’s experimentally- determined geometry, spectroscopic information, and bond dissociation enthalpy;

61 additionally, DFT (B3LYP) calculations replicated the qualitative trends predicted by the

CBS-QB3 calculations – quantitatively, the DFT calculations consistently underpredicted the BDEs and reaction energies relative to CBS-QB3.

X CH3 X CH2

+ H

ΔH298 ΔG298 (α - β) Methyl B3LYP CBS Experimental B3LYP CBS BDE Toluene 1 86.7 90.6 88.0-90.3b 79.4 83.8 0.72 Pyrrole 2 83.1 86.1 75.3 78.9 0.63 3 86.8 90.1 78.9 82.4 0.74 Furan 2 83.1 86.3 75.3 78.6 0.60 3 87.4 90.5 79.5 82.7 0.73 Thiophene 2 85.2 86.5 84.2 79.1 0.60 3 87.0 89.9 88.1 82.2 0.71 Oxazole 2 86.4 89.9 78.7 82.3 0.64 4 88.1 91.1 80.2 83.3 0.63 5 84.5 87.9 76.6 80.1 0.72 Pyridine 2 88.2 92.0 96.0c 80.5 84.7 0.73 3 87.0 91.0 79.6 83.7 0.72 4 87.9 91.6 80.6 84.6 0.74 Pyridazine 3 88.9 93.3 81.3 85.8 0.76 4 87.6 91.7 80.5 84.6 0.75 Pyrimidine 2 89.5 93.1 82.4 86.7 0.73 4 89.3 92.7 81.9 85.5 0.75 5 87.5 91.4 80.7 84.7 0.72 Pyrazine 2 88.0 92.3 80.5 85.0 0.72 b Reference 155 c Reference 170

Table 1.1. Thermodynamic and spin density information for hydrogen-atom loss reactions of methyl-substituted heteroaromatic rings. Enthalpies and energies in kcal/mol, obtained at the B3LYP/6-311+G**//B3LYP/6-31G* (designated as B3LYP) and CBS-QB3 (designated as CBS) levels. See Figure 1.13 for structures and numbering.

X CHCH X CH2CH3 3

+ H

ΔH298 ΔG298 (α - β) Ethyl B3LYP CBS Experimental B3LYP CBS BDE Ethylbenzene 1 83.9 88.1 85.4-86.9b 75.2 79.7 0.68 Pyrrole 2 80.8 84.6 72.2 75.9 0.61 3 83.8 87.7 75.3 78.9 0.71 Furan 2 80.1 83.9 71.6 75.5 0.57 3 84.2 87.9 75.4 79.1 0.69 Thiophene 2 79.8 83.8 71.1 75.2 0.55 3 83.5 87.1 74.4 78.1 0.67 Oxazole 2 82.4 86.5 74.1 78.4 0.61 4 84.5 88.3 76.0 79.9 0.68 5 81.5 85.6 73.0 77.1 0.60 Pyridine 2 84.2 88.1 75.2 80.0 0.67 3 82.9 85.6 74.8 77.2 0.69 4 83.7 87.2 74.5 78.7 0.69 Pyridazine 3 84.7 90.1 77.6 83.1 0.68 4 83.7 88.7 75.1 79.7 0.68 Pyrimidine 2 84.2 89.0 76.1 80.9 0.69 4 83.9 88.5 75.7 80.4 0.70 5 84.3 89.1 74.9 80.5 0.66 Pyrazine 2 83.8 90.2 75.1 81.4 0.68 b Reference 115.

Table 1.2. Thermodynamic and spin density information for hydrogen-atom loss reactions of ethyl-substituted heteroaromatic rings. Enthalpies and energies in kcal/mol, obtained at the B3LYP/6-311+G**//B3LYP/6-31G* (designated as B3LYP) and CBS- QB3 (designated as CBS) levels. See Figure 1.13 for structures and numbering.

64 Methyl ΔH298 ΔG298 Ethyl ΔH298 ΔG298 Pyrrole 2 106.1 89.3 2 101.1 87.1 3 104.3 87.7 3 99.1 85.6 Furan 2 108.8 92.1 2 103.9 89.9 3 105.7 89.1 3 100.6 86.8 Thiophene 2 103.9 87.3 2 99.1 85.3 3 100.9 84.2 3 95.6 81.6 Oxazole 2 109.8 93.3 2 104.9 91.1 4 106.9 90.3 4 102.1 88.3 5 110.8 94.1 5 105.9 92.1 Pyridine 2 94.1 77.9 2 89.3 75.5 3 98.3 82.1 3 93.4 79.4 4 97.6 81.7 4 92.7 78.9 Pyridazine 3 96.2 79.7 3 91.4 77.7 4 97.1 81.2 4 92.2 78.6 Pyrimidine 2 97.4 81.5 2 92.5 78.8 4 90.3 74.1 4 89.7 75.9 5 99.7 84.1 5 94.9 81.1 Pyrazine 2 94.9 78.5 2 87.1 72.3

Table 1.3. Thermodynamic information (kcal/mol, 298 K, B3LYP/6- 311+G**//B3LYP/6-31G*) for alkyl-group loss reactions of methyl and ethyl- substituted heteroaromatic rings.

65 The reactivity of methyl- and ethyl-substituted azabenzenes was explored by

calculation of the homolytic BDEs and free energies for alkyl C–H hydrogen-atom and

alkyl side-chain fragmentation. These values were analyzed as a function of heteroatom,

ring size, side chain length, spin density, and temperature. Furthermore, the impact on the

thermodynamic values derived from the harmonic-oscillator approximation was

analyzed, by treating side-chain torsions as hindered rotors. At 298 K, loss of hydrogen-

atom to form a benzylic-like radical is roughly 10 kcal/mol more favorable than loss of

the alkyl group, regardless of ring size or heteroatom; this trend is consistently exhibited

over a wide temperature range (T = 298 – 2000 K), although both reactions become

increasingly favorable with increasing temperature, due to entropic effects on the free energy (Figure 1.17). Spin densities for heteroaromatic radicals correlate well with the

BDE values: the more diffuse the spin density, the lower the corresponding BDE. This is most dramatic for the five-membered ring heteroaromatics. Both the harmonic oscillator and hindered rotor treatments give comparable values for reaction enthalpies and free energies. The ethyl derivatives have lower reaction enthalpies and free energies than methyl derivatives.

(a) (b)

Figure 1.17. Variation of reaction free energy (kcal/mol) with temperature (K) for alkyl C–H hydrogen-atom loss in (a) five-membered ring methyl-substituted heteroaromatic rings and (b) six-membered ring methyl-substituted heteroaromatic rings.

With respect to predicting the chemistry of larger heteroaromatic systems (such as those in coal), these calculations suggest that both hydrogen-atom and alkyl-group loss can contribute in initiation reactions to the combustion of coal; the subsequent oxidation pathways of both the aromatic peroxy radicals (previously explored194,195) and the

alkylated aromatic peroxy radicals are of interest. Reactivity will likely increase with

increasing alkylation of a subunit, and the azabenzene units are more likely to react than

the five-membered heteroaromatic rings. The initial steps of radical formation are

67 expected to become more favorable at higher temperatures, primarily due to entropic

considerations.

1.3.2.7. Oxidative decomposition of alkylated heteroaromatics. Upon formation of

alkylated heteroaromatic radicals, these species can rapidly react with O2 to form various

peroxy radicals. Again, it seems likely that these resultant reactive species will have an

impact on overall combustion processes. Benzylperoxy radical was initially explored

computationally to obtain a qualitative picture of peroxy radical decomposition for

species containing both alkyl and aromatic components; these findings were then

extended to peroxy radicals of methyl- and ethyl-substituted azabenzylperoxy radicals.202

The alkyl chains of these species are large enough than conformeric considerations are a concern. We performed calculations to analyze rotational profiles for alkyl group torsions to isolate the most stable conformation. Furthermore, in all cases, rotation of the dihedral angle occurred with a barrier less than ~5 kcal/mol. As shown in Figure 1.18, alkylated heteroaromatic peroxy radicals (1.2) can revert to reactants (1.1), or cyclize via attack of the side chain’s terminal O at a position ipso (1.3) or ortho (1.4) to the alkylperoxy chain. Oxygen atom loss can occur (1.5). Given the presence of the exocyclic methylene group, isomerization via H-atom transfer (1.6) can occur from a methylene carbon to the terminal peroxy oxygen; this cannot occur in the non-alkylated parent compounds. Additionally, entire side chain loss (as dioxirane in the case of methyl substituted aromatics) is possible (1.7).

68 O N O N 1.3 O 1.4a

O H

OO O

N N CH 2OO N N CH2O +O2 1.4b 1.2 1.1

N CH2O +O(3P)

N O + O 1.5

N CHOOH N CHO 1.7 + HO

1.6

Figure 1.18. Unimolecular pathways for 2-picolinylperoxy radical, a representative peroxy radical for alkylated azabenzenes.

Calculated kinetic and thermodynamic values for unimolecular decomposition of benzylperoxy radical and 2-picolinylperoxy radical (2-methylpyridinylperoxy radical) at

298 K are presented in Table 1.4 (representative structures shown in Figure 1.18). The energies for decomposition of these two compounds are similar: bicyclic ring formation at the ortho carbon (pathway 1.4) occurs with a barrier of ~30 kcal/mol; ipso cyclization

(pathway 1.3) occurs with a barrier of ~35–40 kcal/mol; internal H-atom transfer

(pathway 1.6) occurs with a barrier of ~40 kcal/mol. The added functionality afforded by

69 the nitrogen atom in 2-picolinylperoxy radical allows a cyclization resulting in a stable

N–O radical after O–O bond scission (pathway 1.4b), which has potential for yielding

precursors to NOx chemistry; however, this process has a substantially high barrier (~50 kcal/mol) and is unlikely to be a factor at atmospheric temperatures. While the

qualitative trends were replicated between benzylperoxy radical and 2-picolinylperoxy

radical, the latter has slightly higher reaction barriers and energies in nearly every case,

which can be attributed to the relative stabilization of the allylic systems in the cyclized derivatives. CBS-QB3 calculations helped demonstrate that the DFT (B3LYP) approach provides good qualitative predictions for the energetic trends. The trends for 2- picolinylperoxy radical were similar for other picolinylperoxy radicals, as well as peroxy radicals of alkylated diazabenzenes (i.e., pyridazine, pyrimidine, and pyrazine). It was observed that the presence of a second ring nitrogen has little effect on either the identity

or energetics of the preferred pathways. Likewise, the ethyl analogs favored similar

reaction pathways, with energies of activation and reaction varying by only ~ 2 kcal/mol

between the methyl and ethyl analogues. When present, the disparities in the reaction

energetics were rationalized via consideration of the inductive effects caused by the

nitrogen atom(s) and varying amounts of geometric strain introduced in the

rearrangement pathways.

Benzylperoxy radical B3LYP CBS-QB3 Experiment ο ο ο ο ο ο ΔΗ ΔG ΔΗ ΔG ΔΗ ΔG 1.2 → 1.1 -16 -5.5 -22.7 -12.2 -20.1a, -21.8b -12.2

TS(1.2-1.3) 35.7 37.2 30.1 31.7 1.2 → 1.3 33.2 34.2 25.8 26.9 TS(1.2-1.4a) 33.5 35.6 29.7 31.8 1.2 → 1.4a 35.6 23.7 14.6 15.1 TS(1.2-1.6) 37.9 38.9 38.4 39.2 1.2 → 1.5 56.5 47.3 61.9 52.5 a a 1.2 → 1.6 -33.9 -35.4 1.2 → 1.7 53.7 42.9 55.8 45.3 a Geometry could not be optimized.

2-Picolinylperoxy radical B3LYP CBS-QB3 ΔΗ ΔG ΔΗ ΔG 1.2 → 1.1 16.3 6.5 22.7 13.2 TS(1.2-1.3) 37.1 39.4 31.0 33.4 1.2 → 1.3 34.2 35.7 26.1 27.9 TS(1.2-1.4a) 30.4 33.2 25.6 28.7 1.2 → 1.4a 20.6 23.2 13.2 16.0 TS(1.2-1.4b) 47.1 49.8 1.2 → 1.4b -5.8 -4.1 1.2 → 1.5 61.6 53.0 TS(1.2-1.6) 38.0 39.4 37.6 39.2 1.2 → 1.6 -24.7 -33.6 -23.7 -32.4 1.2 → 1.7 49.2 38.7

Table 1.4. Comparison of reaction pathway energetics (kcal/mol) for benzylperoxy radical and 2-picolinylperoxy radical at 298 K, via B3LYP/6-311+G**//B3LYP/6-31G*. All enthalpies and free energies are relative to the peroxy radical (1.2); when preceded by TS, the relative data are the enthalpy and free energies of activation. Where applicable, 1.4a refers to cyclization at a ring carbon and 1.4b refers to ortho cyclization at nitrogen.

Figure 1.19 shows that with increasing temperature, formation of 1.1, 1.5, and 1.7

benefit entropically and become substantially exoergic reactions. Formation of 1.3 and

1.4a exhibit little entropic benefit. As shown in Figure 1.20, the reaction barriers also gain little entropically. Formation of 1.4b has a similarly small entropic benefit but maintains a high reaction barrier, such that any NOx formation via this process is

expected to be minimal except at extremely high temperatures. Formation of 1.6 exhibits

a precipitous drop in its barrier and is the dominant processes at T ≈ 1250 K. This last

reaction is of considerable interest given its relevance to both low-temperature and high-

temperature combustion, since it essentially constitutes a dissociative rearrangement

pathway. Both the direct and indirect decomposition intermediates (1.1, 1.5, 1.6, and 1.7)

will play a substantial role in combustion as temperatures rise above 298 K, as peroxy

radicals, themselves reactive oxygen species, demonstrate the potential to generate

reactive O-atom and hydroxyl radical.

Figure 1.19. ΔGrxn versus temperature for the unimolecular pathways of 2- picolinylperoxy radical. 1.2 → 1.3 denoted by open diamond; 1.2 → 1.4a denoted by solid square; 1.2 → 1.4b denoted by open triangle; 1.2 → 1.5 denoted by dash; 1.2 → 1.6 denoted by x; 1.2 → 1.7 denoted by solid diamond. All energies calculated at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level of theory.

Figure 1.20. ΔGactivation versus temperature for unimolecular pathways for 2- picolinylperoxy radical. Activation energy for 1.2 → 1.3 denoted by open diamond; activation energy for 1.2 → 1.4a denoted by solid square; activation energy for 1.2 → 1.4b denoted by open triangle; activation energy for 1.2 → 1.6 denoted by x. All energies calculated at the B3LYP/6-311+G(d,p)//B3LYP/6-31G(d) level of theory.

The overall chemistry of alkylated azabenzylperoxy radicals was consistent regardless of alkyl substitution or number of nitrogen atoms. The picolinylperoxy radicals provide excellent models for the chemistry exhibited by this larger class of species. Moreover, aromatic hydrocarbons can themselves predict several aspects of this

74 chemistry, the exception being those processes involving oxidation or rearrangement with

ring nitrogens.

When this approach is extended to alkylated derivatives of the five-membered

heteroaromatic rings,203 the energetic trends could be considered in light of ring size and

heteroatom effects. In general, the same six pathways are available, such that

rearrangements and dissociations are observed to contribute to the chemistry of these

species. Many trends are consistent between both sets of alkylated heteroaromatics: increasing alkyl substitution leads to small stabilization of reaction barriers and energies.

Increasing temperature leads to a shift in preference for the dissociation pathways.

However, a difference was observed for smaller rings: while cyclizations are favored pathways at 298 K regardless of parent ring size, alkyl-substituted heteroaromatic peroxy radicals of the five-membered rings cyclize in such a manner as to generate an allylic radical system (cyclizing at a position either ipso or ortho to the side chain). On the other hand, alkylheteroaromatic peroxy radicals of the six-membered rings preferred to form five-membered rings via ortho cyclization, due to their increased stability over spirodioxetane structures (which would result from ipso cyclization). This general trend is represented in Figure 1.21.

75 N N CH2OO O

O O

CH2OO

Figure 1.21. Qualitative depiction of favorable cyclization pathways for representative peroxy radicals of methyl heteroaromatics (top: pyridine, and bottom: furan). Cyclization for the alkylated six-membered heteroaromatics is driven by the thermodynamic stability of the resulting ring, while cyclization for the alkylated five-membered heteroaromatics is dictated by which pathway allows the generation of a stable allylic radical system.

Heteroatom identity also has an impact on the reactions of interest. Oxygen, nitrogen, and sulfur atoms affected heteroaromatic chemistry to slightly different quantitative extents (though qualitative trends were consistent), and the effect of multiple heteroatoms (as in oxazole) led to small differences in reaction energetics. Notably, the pyrrole, oxazole, and thiophene derivatives reacted to form various species wherein their heteroatoms are oxidized, and these effects were unique to each heterocycle. Thus, data for aromatic hydrocarbon species are useful in estimating the energetics of these species, but cannot completely predict their chemistry, due to the propensity of increasing functionalization to lead to different products and pathways.

76 Relative to non-alkylated heteroaromatic peroxy radicals,194,195 we observed that

alkylated species demonstrated a greater affinity for intramolecular reactions, due to the length and flexibility of their side chains. Dissociative reactions were less favorable for alkylated derivatives, due to a reduction of aromatic character. Our studies have provided important details for the oxidative decomposition of alkyl-substituted heteroaromatic rings in particular, pathways originating with peroxy radicals along with their reactivity over a wide temperature range. We have shown that the alkylated five- membered heteroaromatics demonstrate certain unique tendencies in their reactivity.

Given the differences in reactivity between the five- and six-membered heteroaromatics, as well as between the alkylated and non-alkylated heteroaromatics, it seems likely that the chemical behavior of coal could vary somewhat depending on the abundance and nature of the cyclic subunits present in its structure. However, these discrepancies are mainly limited to the variety of products formed via combustion rather than the overall kinetics and thermodynamics of the relevant processes.

1.4. Future Challenges in Combustion Chemistry

In closing this chapter, it seems logical to highlight some of the most recent

progress in combustion chemistry. Alternate forms of energy and methods of combustion

are continually being developed, thereby continuously invoking new challenges for

experimentalists and theoreticians. Some alternatives involve new combustion processes,

as in the case of homogenous-charge compression-ignition (HCCI)204 chemistry, which

depends on auto-ignition (low-temperature) chemistry within a homogenous gas mixture

77 (unlike a spark-ignition engine). This new combustion method has the potential to

increase fuel efficiency and decrease harmful emissions.205,206 One significant issue with

HCCI is adequately controlling fuel ignition during the compression stroke of the engine; this is essentially a kinetics problem, requiring understanding of the reaction rates and mechanisms of the radical species generated by the fuel. Thus, reactions normally associated with low-temperature combustion and often treated cursorily in oxidative mechanisms can have a greater impact on combustibility.

For the purposes of this chapter, we are most interested in the implications of the

changing energy landscape for the reactive pathways involved. As the natures of the fuel used in everyday life change, the reactive radical intermediates formed in their combustion will also change. We will examine the context of two classes of relevant fuel developments.

1.4.1. Fuel additives. Oxygenated molecules have long been used to augment gasoline

formulations. For instance, since the elimination of tetraethyl lead (Pb(C2H5)4), oxygenates have been used as gasoline additives to reduce harmful carbon monoxide emissions and increase a fuel’s octane rating. The most prominent oxygenate has been methyl tert-butyl ether (MTBE); however, this additive has since been flagged as a potential carcinogen and odorous component that can taint water supplies.207 Moreover,

MTBE necessitates the use of the industrial side-product, isobutene, for its generation,

further competing with crude oil supplies for a value-added product.

78 As the downsides to MTBE use became more apparent, ethanol emerged as an

attractive alternative oxygenate. It did not demonstrate the negative health effects of

MTBE, and moreover, it could be produced from renewable (biomass) fuels.208

Compared to MTBE, ethanol has a higher oxygen-to-carbon ratio. Ethanol has been used primarily as a gasoline additive; however, in the years since the Energy Policy Act of

1992,209 a shift has occurred, such that current manufacturers are building cars with the capacity to run on fuel blends of 85% and 95% ethanol, along with a small amount of

gasoline – these fuels are often referred to as E85 or E95, respectively. (However, some

engine modifications are necessary for vehicles to run effectively on blended fuels with

greater than 20% ethanol.) This advance has been hampered by the general lack of

availability of ethanol at fueling stations, a shortage that is being gradually remedied.

Currently, the cost benefits of using ethanol over gasoline are substantial, but the

availability of the former is still limited.210

Ethanol itself demonstrates several drawbacks as an alternative fuel, despite its increasing availability. Most notably, ethanol absorbs water. Thus, it cannot travel

through existing gasoline pipelines, as the water could subsequently separate and freeze

during colder temperatures, and possibly bursting the pipelines; moreover, ethanol is also corrosive.211 Thus, ethanol has to be transported via other means (a fact which,

ironically, generally necessitates the use of gasoline, diesel or other fuel and results in a

higher cost that negates one monetary benefit of using ethanol as a fuel). Moreover,

ethanol evaporates relatively quickly, and so in warmer temperatures, it must be blended

carefully.212

79 Butanol possesses the chemical benefits of ethanol while avoiding its drawbacks.

Its use is considerably less temperature-sensitive: it is six times less evaporative than ethanol, and it is not corrosive, so can be shipped via existing fuel pipelines.213 In terms

of fuel benefits, due to its higher number of carbons, it has higher energy content

(110,000 Btu/gallon) than ethanol (84,000 Btu/gallon), and is comparable to gasoline

(115,000 Btu/gallon); it can also be generated more easily from biomass than can

ethanol.214 Unlike ethanol, it can be used as a direct replacement for gasoline rather than as an additive therein, since butanol’s air/fuel ratio is comparable to that of gasoline.215

Finally, butanol’s primary combustion byproduct is carbon dioxide; it avoids formation

216 of the pollutants NOx, SOx, and carbon monoxide. Thus, butanol is a potential fuel of

substantial interest.

Studies have been completed specifically on combustion processes of ethanol and

butanol, and several of the peroxy and oxy radical species have been examined.92-105

Marinov proposed an exhaustive mechanism for ethanol’s combustion.217 Cavalli et al.

examined the initial reaction of HO• radical with 1-butanol by FTIR spectroscopy,218 and

Chen et al. studied the anodic oxidation of this species.219 Recent experiments by

McEnally and Pfefferle led them to propose that butanol combustion primarily occurs via a complex fission reaction rather than H-atom abstraction.220

While we have discussed the historical background of the main gasoline

oxygenates, it is worthwhile to note that several other species have been discussed in this

context as well. Notably, it has been shown that simply adding oxygen to a given

combustion environment does not in itself achieve soot reduction; the role of the oxygen

80 within the structure of the oxygenate plays a major part. For instance, Westbrook et al.

completed a modeling study on the effect of various oxygenated hydrocarbons on soot production.221 They saw a significant reduction in the number of alkynyl radicals serving

as soot precursors in a diesel flame via the inclusion of alcohol (ROH) and ether (ROR’)

additives, but noted a lesser effect when esters (RCO2R’) were included. This is due to

the fact that esters can readily fragment to generate CO2, so that their oxygen atoms are

not involved in the processes that can affect soot reduction. Similarly, Sinha and

222 Thomson studied three C3 oxygenated hydrocarbons - isopropyl alcohol, dimethoxy

methane (DMM), and dimethyl carbonate (DMC) − all in comparison to propane, and noting different effects for each. DMM and DMC lack C–C bonds. Thus, the concentration of the alkenyl and alkynyl radicals necessary to form benzene and larger aromatic hydrocarbons was correspondingly smaller in these species, and soot production drops. Nag et al.223 have postulated that the identity of a given oxygenate contributes to the resultant balance of CO and CO2 in the radical pool; CO has a greater propensity for

PAH reduction than does CO2. The implications for power output and efficiency are

important as well, since a significant amount (~33%) of the eventual heat is generated by

• the conversion of CO to CO2 in the combustion environment (usually mediated by HO radical). The structure of an oxygenate has notable implications for both its reactivity and its propensity for the formation of emissions.

1.4.2. Biodiesel. Having alluded briefly to biomass compounds in the previous section, as sources for ethanol and butanol, we turn now to the potential of these species as

81 fundamental alternatives to fossil fuels. In 1912, Rudolf Diesel presciently stated, “The

use of vegetable oils for engine fuels may seem insignificant today. But such oils may in

the course of time become as important as petroleum and the coal tar products of the

present time.” Biodiesel can be produced from a variety of sources, 224 including animal fats (on small scales), algae, and vegetable oils: the fuel itself is produced via esterification of these lipids with methanol or ethanol. In terms of the overall benefits

and sources of fuels, several reviews are currently available. As early as 1987, Schwab et

al. reported on the potential of vegetable oils for forming diesel fuels.225 More recently,

Graboski and McCormick,226 Srivastava and Prasad,227 and Lin et al.228 have reviewed

the fuel properties (emissions, engine performance, etc.) of these species. Ma and Hanna

have compiled a review of the general benefits of biodiesel chemistry.229

The emergence of biofuels as potential energy sources demands a mechanistic

approach comparable to those currently in use for hydrocarbon compounds. Biofuels are

commonly esters (RCO2R’) of large long-chain fatty acids, so their reactivity will depend on more factors than these extant mechanisms. Kulkarni and Dalai have summarized mechanistic aspects of biodiesel chemistry, with respect to waste cooking oil.230

Thermolytic decomposition can yield alkanes, alkenes, ketones, esters, and small acids.

Oxidative decomposition leads to highly functionalized peroxy radicals, which then can add a hydrogen atom to form hydroperoxides, ultimately decomposing to aldehydes, hydrocarbons, and acids; additionally, these peroxy radicals might dimerize or oligomerize if excess oxygen is present. Hydrolytic reactions comprise an additional possibility: triglycerides readily decompose to glycerol, monoglycerides, diglycerides,

82 and free fatty acids (FFA), in the presence of water. Zhenyi et al. have completed

thermodynamic calculations on the pyrolysis of vegetable oils, postulating that, for a

given ester, the key initiation step proceeds via breaking of the alkyl (sp3) C–O bond.231

We can summarize the different possible initiation routes for a given triglyceride, familiar from our previous discussions (Figure 1.22). Even from this basic view, it is clear that several classes of reactive radical intermediates will play a role in biofuel combustion: alkyl (sp3) and alkenyl (sp2) radicals are readily formed, as well as peroxy

radicals and functionalized derivatives of each of these original species.

+ OH OH

H2O O

-H O

heat low T O O +CH3 2

O O

O O + O CH2CH3

Figure 1.22. Initial reaction steps for fatty acid ester decomposition, represented by ethyl butanoate, which can decompose via thermolysis (pyrolysis), oxidation, or hydrolysis.

Mechanism development traditionally depends on the inclusion of data for

relevant, smaller compounds; that philosophy will apply in this case, where the reactions

of both small hydrocarbons and small esters are of interest. Mechanisms for methyl

232 butanoate (CH3CH2CH2CO2CH3) have been developed by Gail et al. and Curran et

al.;233 the latter notes the negative temperature coefficient (NTC) range demonstrated by this species, suggesting that future work may benefit by exploring comparisons to

hydrocarbon chemistry. Good and Francisco have modeled the tropospheric oxidation

234 mechanism of methyl formate (HCO2CH3). Metcalfe et al. derived combustion

235 mechanisms for C5H10O2 ethyl and methyl esters, using CBS-QB3 calculations.

Recent studies by Glaude et al.,236 Schwartz et al.,237 and Sarathy et al.238 have provided

experimental information on larger esters, in an effort to model further reactions with

implications for biofuel combustion. This area is of significant interest, and it is expected

that the next few years will provide a more thorough understanding of the important species and relevant mechanisms involved in biofuel combustion.

1.5. Conclusions

In the course of this chapter, we have provided a historical context for understanding combustion chemistry as it applies to some of the most fundamental hydrocarbon compounds. We have explored the implications of these processes for larger and increasingly functionalized molecules. These species can be used to model the

84 chemistry of petroleum and coal, in addition to smaller hydrocarbon fuels. Combustion

is a complex topic, such that both theoretical and experimental methods are useful in

exploring chemistry with implications for high-temperature oxidation and low-

temperature atmospheric reactions. In particular, the master equation methods developed

over the past few decades can consider the collective chemistry of thousands of

elementary steps to predict the overall oxidation of a given fuel; the kinetics and

thermodynamics of each of these elementary steps can be generated via experiment or

computational modeling.

Reactive oxygen species and other radical intermediates dictate the oxidative

decomposition of fuels. We have noted that peroxy radical intermediates provide an

enormous amount of flexibility in the combustion of a given compound, specifically in

the unimolecular steps available to that compound. In an instructive display of the

interaction of experimental and theoretical techniques, rearrangement pathways of the

peroxy radicals have been modeled computationally and provide justification for several

unexpected products.

At the start of the twenty-first century, efforts are underway to decrease society’s

dependence on fossil fuels. It is clear that alternate energy forms will bring with them their own sets of reactive radical intermediates and revisit the important intermediates seen from smaller model compounds, as we consider future challenges in combustion

chemistry. We expect that advances in experimental techniques and computational

approaches will correspondingly be developed in the years ahead.

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108

CHAPTER 2

COMBUSTION PATHWAYS OF THE ALKYLATED HETEROAROMATICS: BOND DISSOCIATION ENTHALPIES AND ALKYL-GROUP FRAGMENTATIONS

2.1 Introduction

Coal is a valuable fossil fuel, accounting for the majority of America’s electrical

power generation, and it is likely to become even more useful in the years ahead, as natural gas and oil reserves dwindle.1 The actual structure of a given coal specimen

varies greatly with geography;2 however, aromatic hydrocarbons and heteroaromatic

rings (Figure 2.1), both alkylated and non-alkylated, are recurring components, the

proportions of which differ between regions and samples.3

The practice of using the reactions of these individual rings to better understand

the overall chemistry of the complex structure of coal has been widespread over the past

few decades. In separate studies, Mackie et al. and Kiefer et al. have examined shock

tube studies of pyridine, the picolines (methyl-substituted pyridines), pyrazine, and

pyrimidine to better understand the thermal decompositions of coal units.4 These studies

have focused only on pyrolysis; thus, the understanding of the oxidative decompositions

of these heteroaromatics are still of interest. Moreover, Eisele established the presence of

109

pyridine and picoline ions in the troposphere, such that the low-temperature oxidation

pathways of these species are also relevant and could have implications for atmospheric

processes.5 These heteroaromatic rings have the potential to be oxidized at the nitrogen

6 atom and thus form NOx species, which can subsequently react to over-produce

tropospheric ozone and contribute to acid rain.7

H N O S O 5 2 2 2 2 4 3 3 3 N Pyrrole Furan Thiophene Oxazole N N N N 2 N 2 2

3 3 5 N N 4 4 4 Pyridine Pyridazine Pyrimidine Pyrazine Figure 2.1. Heteroaromatic rings of interest.

Our group has devoted much time to the study of these coal constituents.

Barckholtz et al. completed an exhaustive survey to select an appropriate computational method for study of these relatively large molecules; density functional theory (DFT)8 was shown to balance accurate results with computational economy to the greatest extent.9 This study also allowed the determination of a crucial conclusion, that the

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monocyclic heteroaromatic rings do provide constructive models for comparison to their

polycyclic analogues, via comparisons of sp2 C-H bond dissociation enthalpy (BDE) values in polycyclic compounds with the corresponding BDE in the relevant monocyclic ring. The vast majority of these calculations showed that increasing the number of rings in the compound affected the BDEs by less than 1 kcal/mol, and thus the smaller rings provide worthy, computationally-prudent models for the larger systems. Moreover, it was shown that heteroatoms in the six-membered rings provided stabilization for the resulting radical, such that pyridine and other heteroaromatic rings had lower BDE values than did benzene alone.

The combustive pathways of these heteroaromatics have also been explored, at

multiple temperatures. Fadden et al. saw that there were considerable differences

between the pathways of the five-membered heteroaromatics’ peroxy radicals and the

azabenzenes’ peroxy radicals;10 the former could lose atomic oxygen at a relatively low

energetic cost, while for the six-membered rings, losing atomic oxygen was substantially

more unfavorable, to the extent that dissociation back to the aromatic radical and

molecular oxygen was preferable. For both sets of compounds, intramolecular

cyclizations competed with oxygen loss, and some of these cyclizations did lead to

nitroso compounds, which have implications both for NOx formation and as

carcinogens.11

Computational and experimental methods clearly benefit from a symbiotic

relationship in combustion studies: calculations can propose pathways for empirically-

observed intermediates, and experiments can verify the accuracy of the calculated

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energies and rate coefficients. Combustion models have been proposed for several

classes of molecules, including alkyl hydrocarbons and aromatic species.

To this point, little has been published on the subject of alkylated heteroaromatic

rings, though these species demonstrate comparable promise for elucidating coal

chemistry. Notably, Mackie and coworkers completed both experimental12,13 and

theoretical14 studies of the pyrolytic decomposition of 2-picoline (2-methylpyridine).

However, more than a decade later, this remains the most exhaustive study of an

alkylated heteroaromatic ring’s combustion pathway, although the authors hypothesized

that these actually provided a better model for fuel-bound nitrogen (FBN) than did

unsubstituted heteroaromatic rings, which have been more common targets.- The kinetics

of the methyl-substituted azabenzenes’ initial reactivities have been explored more

frequently: Frerichs et al. examined the reaction of the picolines with atomic oxygen,15 while Yeung and Elrod completed a study of hydroxyl-radical’s reactions with pyridine and its methyl and ethyl substituted derivatives.16 Both groups noted similarities

between the alkylated azabenzenes and the reactivity of toluene.

Unsurprisingly, with respect to toluene and the other alkylated aromatic

hydrocarbons, more references are available. Both experimental and theoretical studies

have been completed on the combustion processes of toluene. Most recently, Pitz et al.

published a comprehensive mechanistic study using shock-tube techniques;17 earlier studies had dealt specifically with improving predictions of some of the key intermediates therein.18 Computationally, substituent effects are a popular area of study as well as the

overall mechanism: the hydrogen-atom loss and subsequent atmospherically relevant

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reactions of toluene have been studied via semi-empirical methods19 and the B3LYP

functional.20 Nam et al. completed a DFT study of toluene and its para and meta-

substituted derivatives, observing how substituents on the methyl group itself further

impacts the bond dissociation enthalpies of these species.21 Ethylbenzene has been

subjected to several studies; both its pyrolysis22 and its reactions with atomic oxygen,23 fluorine radical,24 hydrogen atom,25 hydroperoxyl radical,26 and benzyl radical27 have

been studied. These hydrocarbon compounds can provide references for energies and

likely pathways for the corresponding alkylated heteroaromatic rings.

Of greatest interest to this particular work are the bond dissociation enthalpies

(BDEs) of toluene and ethylbenzene. Besides their use as reference compounds for the

substituted heteroaromatics, they are also of interest as intermediates in the HACA (H-

28 abstraction-C2H2-addition) pathway to soot formation. A necessary first step in any

combustion pathway is generation of a radical species that can be subsequently oxidized,

and this homolytic cleavage is represented quantitatively via BDEs. The BDEs of

toluene’s methyl group and ethylbenzene’s benzyl position have been experimentally

determined by several methods, including flowing-afterglow mass spectrometry, shock

tubes, and photoacoustic calorimetry; these were recently compiled by Muralha et al.29

The BDE values calculated for toluene varied from 88.0 kcal/mol30 to 90.3 kcal/mol,31 with the majority of results falling in the 89.5-90 kcal/mol range. With ethylbenzene, the resulting radical saw stabilization from the additional alkyl group, so its BDE was lower, ranging from 85.4 kcal/mol to 86.9 kcal/mol.,32 ,33

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In general, bond dissociation enthalpies are useful quantities in terms of

predicting relative reactivities for different compounds, reflecting the enthalpy change for

homolytic cleavage of a given bond. The more stable the resulting radical, the more

likely a bond is to break. General explanations for radical stability include alkyl

substitution and resonance effects; Gronert has recently suggested an alternative

explanation, that the potential for release of 1,3-repulsive energy (strain) has the greatest effect on these quantities: i.e., a tertiary radical is more stable than a primary radical not because of the larger number of alkyl substituents in the radical, but because of the greater magnitude of the geminal interactions in the parent hydrocarbon that are relieved upon C−H bond cleavage.34

The BDEs of the alkylated heteroaromatics are expected to reflect the resonance

stability of the formed radicals via conjugation to the aromatic system and the

stabilizing/destabilizing role of the relevant heteroatom(s). Hydrogen-atom loss seems to

be the most likely initiation step in the combustion of the alkylated heteroaromatic rings,

although other pathways, such as loss of the alkyl group, are also plausible (Figure 2.2).35

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X X CH3 X CH2

+CH 3 + H

X X CHCH X CH2CH3 3

+CH2CH3 + H

Figure 2.2. Generic representation of possible radical-generation pathways for the alkylated heteroaromatic rings.

These cleavage pathways will be chain-propagating for the combustion process and may dominate at higher temperatures due to the favorable entropic term.

Just as alkylated aromatic rings are widespread in petroleum compounds, alkylated heteroaromatic rings are prevalent in coal compounds, and their combustion pathways are thus noteworthy. Thus, the hydrogen-atom loss reactions and alkyl-radical loss reactions for the methyl and ethyl-substituted five- and six-membered heteroaromatic rings will be explored via DFT methods, with the goal of further elucidating the chemistry of the larger heterocyclic systems found in coal. Additionally, the DFT results will be calibrated against CBS-QB3 data, with the intent of validating the B3LYP method as an economical method with which to further explore the oxidative pathways of the consequent radicals.

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2.2 Computational Methods

All geometry optimizations, vibrational frequency calculations, and single-point

energy calculations were completed with Gaussian 9836 and 0337 at the Ohio

Supercomputer Center. The B3LYP/6-31G* hybrid density functional theory (DFT)38 level was used for all geometry optimizations and vibrational frequency calculations.

Single-point energies were calculated at the B3LYP/6-311+G** level, using six Cartesian d functions with the scf=tight option; it has been shown that there is a small basis set effect with more polar systems,9,39 so this larger basis set was selected to compensate for

that effect. CBS-QB3 calculations40 were also performed to validate the DFT method for

these particular systems.

Vibrational frequencies were calculated for each stationary point to characterize

these structures as minima or transition states. The unscaled vibrational frequencies were

used to calculate the thermodynamic corrections to the enthalpy and free energy. Once

obtained, zero-point vibrational energy corrections were scaled by a factor of 0.9806.41

The overall enthalpy at each temperature was determined from the single-point energy, the thermal correction to the enthalpy, and the scaled zero-point energy, while the overall free energy at each temperature also included the entropic correction to the free energy.

Transition states were connected to reactants and products by either using intrinsic reaction coordinate (IRC)42 searches or displacing the relevant geometries by

±10% along the reaction coordinate characterized by the imaginary vibrational frequency,

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then carefully optimizing (opt = calcfc) these resulting geometries to their corresponding

minima.

For the doublet radical species and many transition states, spin contamination

() was negligible (no greater than 0.80). The DFT methods employed in this work have demonstrated an ability to minimize spin contamination for the radicals of interest,

keeping the computed values near the expected value of 0.75. Spin densities were

obtained for the hydrogen-loss radicals using the natural population analysis (NPA)

method.43

Because flame processes are some of the reactions of interest for these

compounds, it is necessary to see how these species react at higher temperatures. The

enthalpies of both the parent compounds and the resultant radicals were calculated from

298 to 2000 K via the temperature-dependent term:44

=Δ trans + rot + vib )()()()( + RTTHTHTHTH

3 3 i / kThv −1 )( ++=Δ ∑ i evNhRTRTTH )1( +− RT 2 2 i

The summation takes place over all 3N-6 normal modes. For each compound, the scaled

zero-point energy and enthalpy contribution were computed at various temperatures via the given equations and added to the B3LYP total energy, to obtain the bond dissociation enthalpies as a function of temperature. A similar approach was used with calculation of the entropic corrections, to determine the free energies of reaction over the same temperature range.45

To reduce potential errors in the thermodynamic values arising from treating all

vibrations according to the harmonic-oscillator rigid-rotor approximation, low-energy

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torsions in the alkylated species were also treated as hindered rotors,46 and the resulting

energetics were compared to those from the original calculations.

2.3 Results

Several alkylated heteroaromatic rings were examined: pyrrole, furan, thiophene,

oxazole, pyridine, pyrimidine, pyridazine, and pyrazine (Figure 2.1). Bond dissociation

enthalpies (BDEs) and energies were compiled for the benzyl C−H BDE in both the methyl and ethyl derivatives of these compounds, as were the corresponding spin densities in the derived radicals. Enthalpies and free energies of reaction for loss of the attached alkyl groups were also documented. BDE values were then analyzed both as a function of excess spin density on the major radical center of interest and of temperature.

Finally, the harmonic oscillator and rigid rotor approximations were compared.

2.4 Discussion

Several trends can be observed from the enthalpic and free energy data; for

simplicity’s sake, these trends will be discussed in terms of their relative bond

dissociation enthalpies. Moreover, the nomenclature used will indicate that all radicals

are located on the benzylic position of the compound; that is, 2-methylpyridinyl radical

• will be used as an abbreviation for 2-methylpyridin-2’-yl (c-C5H4N-CH2 ) radical, throughout the remainder of the paper.

With respect to the different methods, the hydrogen-loss BDE values were

calculated and tabulated for both the CBS-QB3 and B3LYP calculations. The DFT

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enthalpies and energies of reaction were consistently 3−4 kcal/mol lower than the CBS results (which were themselves comparable to experimental results, where available); thus, the qualitative trends were duplicated between methods. The majority of the comparative discussion will refer back to the B3LYP geometries and energies.

2.4.1 Toluene as reference compound

The BDE and geometry of toluene were both explored, along with the substituted heteroaromatic rings. Since more information is available for toluene, it can serve as a standard for evaluating the accuracy of the computational approach, which can then be applied to the heteroaromatic rings as well.

As shown in the Supporting Information, the B3LYP/6-31G* method matched experimental values for toluene’s geometry very well: both the C-C and C-H bond lengths are reproduced when compared to the spectroscopic work of Amir-Ebrahimi et al.,47 and the rotational constants similarly match up. The vibrational frequencies, also reported in the Supporting Information, saw a comparable correspondence.

Comparable information on the benzyl radical was not readily available; however, it can be inferred from the bond dissociation enthalpy of toluene, as both parent and radical must necessarily be geometrically correct to give an accurate BDE value. The

CBS-QB3 calculations predict a BDE of 90.6 kcal/mol, matching well with the experimental data (a range of 88.0 – 90.3 kcal/mol). The B3LYP/6-311+G**//B3LYP/6-

31G* energies ultimately provide a calculated BDE of 86.7 kcal/mol; the 4 kcal/mol difference from the CBS-QB3 calculation is consistent throughout the heteroaromatic

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rings studied, such that qualitative trends are reproduced. The slight underestimate is

common to the DFT approach and is seen in other work in this area.9

2.4.2 Non-alkylated heteroaromatics

2.4.2.1 Azabenzenes: Just as this work uses toluene and ethylbenzene as benchmarks for

the alkylated heteroaromatic rings, previous work on the unsubstituted heteroaromatic rings has shown several trends in their BDEs relative to that of benzene. With respect to the azabenzenes, it was seen that the presence of one or more nitrogen atoms within the aromatic ring directly affected those compounds’ BDEs. In particular, the BDE at the C-

H bond adjacent to nitrogen was consistently seen to be around 4−5 kcal/mol lower than benzene’s C-H BDE, a phenomenon attributed to nitrogen’s ability to lend greater resonance stabilization to the heterocyclic radical. At the non-nitrogen-adjacent positions, the C-H BDE was comparable to that of benzene itself.

2.4.2.2 Five-membered rings: Prior work on the unsubstituted five-membered heteroaromatic rings has shown that their combustion pathways are most likely to begin with decomposition or isomerization of the ring itself, rather than loss of hydrogen atom.

This is due to the geometric perturbation introduced by forming a radical centered on the

aromatic ring, which is reflected in the higher C−H BDE values compared to benzene.

Furthermore, unlike the azabenzenes, there is no distinct preference of H-abstraction from position 2 over position 3; again, due to geometric factors, the heteroatoms are unable to stabilize the radical to the degree seen in the six-membered rings.

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Shifting focus to the alkylated heteroaromatic rings, it seems probable that the

chemistry here could differ substantially, since these H-loss reactions will not create a

radical center within the aromatic ring itself, but rather on the attached alkyl group. This

proves to be the case, as these trends differ from those of the unsubstituted compounds.

2.4.3 Methyl-substituted heteroaromatics: Hydrogen-atom loss

2.4.3.1 Azabenzenes: The methyl-substituted azabenzenes vary in their BDEs from 86.3

to 92.6 kcal/mol, with an average value of 87.2 kcal/mol, higher than toluene’s value of

86.7 kcal/mol (Table 2.1). The experimental work of Doughty and Mackie on 2- methylpyridine14 did provide a tangential reference point here; their proposed C−H BDE

was 96 kcal/mol, compared to the calculated value of 88.2 kcal/mol via B3LYP (92.0

kcal/mol via CBS-QB3). Calculations were seen to underestimate the BDE by a slightly

greater margin than in toluene’s case. The authors noted that the heat of formation for

their 2-picolinyl radical was an estimate, which would extend to the extrapolated BDE of interest and could explain this discrepancy. Losing hydrogen from the attached methyl group rather than from the ring itself means that the resultant radical is not directly on the ring, and not as directly stabilized by nitrogen’s additional resonance effects. Moreover,

the trend of the ortho-substituted compound’s BDE being lower than the other substituted

compounds is not duplicated here: in fact, 2-methylpyridine and 3-methylpyridazine both

have substantially higher BDEs than their counterparts, and 2-methylpyrimidine’s BDE

value is near the highest value for the pyrimidine derivatives.

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X CH3 X CH2

+ H

Table 2.1: Thermodynamic information and spin density information for hydrogen-loss (C-H homolytic bond cleavage) reactions of methyl-substituted heteroaromatic rings. a

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Both geometries and spin densities were examined to discern the origin of these effects. The geometry changes involved are minimal, as shown (Table 2.2). Virtually the same changes occur for toluene losing a hydrogen atom from the methyl group as for 2- methylpyridine.

1 1 6 6 CH3 CH2 N CH3 N CH2 5 5 6 6 1 1 2 2 + H + H 4 2 4 2 5 3 5 3 3 3 4 4

Bond Lengths Parent Radical Change Parent Radical Change C6-C1 1.401 1.427 0.026 N1-C2 1.345 1.372 0.027 C1-C2 1.401 1.427 0.026 C2-C3 1.401 1.425 0.024 C2-C3 1.396 1.389 -0.007 C3-C4 1.394 1.389 -0.005 C3-C4 1.396 1.403 0.007 C4-C5 1.393 1.399 0.006 C4-C5 1.396 1.403 0.007 C5-C6 1.396 1.405 0.009 C5-C6 1.396 1.389 -0.007 C6-N1 1.337 1.326 -0.011 C1-Cmeth 1.512 1.407 -0.105 C2-Cmeth 1.509 1.408 -0.101 Bond Angles Parent Radical Change Parent Radical Change C6-C1-Cmeth 121.4 121.4 0 N-C2-Cmeth 116.3 117.2 0.9 C2-C1-Cmeth 120.1 121.4 1.3 C3-C2-Cmeth 121.7 121.6 -0.1 C1-Cmeth-H 110.5 121.2 10.7 H-Cmeth-C2 111.8 C1-Cmeth-H 110.1 121.2 11.1 H-Cmeth-C2 110.4 119.6 9.2 C1-Cmeth-H 112.3 H-Cmeth-C2 110.4 121.3 11.1

Table 2.2. Comparison of changes in bond lengths (Angstroms) and bond angles (degrees) during the hydrogen-atom loss reactions of toluene and its nitrogen analogue, 2-methylpyridine.

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Spin density (population) appears to be the most logical candidate for rationalizing these

trends. From the relative electron distribution (α-β) between benzyl radical and 2-

methylpyridinyl radical (Figure 2.3), it can be seen that 2-methylpyridinyl radical

localizes its electron density on the CH2 carbon to a greater extent than benzyl radical;

correspondingly, benzyl radical sees more electron density delocalized through the ring

and a resultant stabilization. In particular, the excess spin density is localized on the

positions ortho and para to the attached methyl group, and the nitrogen of 2-

methylpyridinyl radical bears less spin density than does the corresponding carbon in

benzyl radical. Similar trends were seen for the other methyl-substituted heteroaromatics

(and will be discussed subsequently), although this is the most direct comparison

possible. Interestingly, the ethyl-substituted heteroaromatic rings’ trends are reversed

relative to ethylbenzene.

0.178 (0.215) 0.730 (0.718) 0.177 0.672 (0.196) (0.684)

0.214 0.236 (0.215) 0.229 0.198 (0.242) (0.224) (0.208)

Figure 2.3. Comparison of areas of increased spin densities (α-β) for 2-methylpyridinyl radical and 2-ethylpyridinyl radical. The top number refers to the α-β value for that particular position; the bottom number, in parentheses, refers to the corresponding α-β value for the hydrocarbon equivalent (toluene and ethylbenzene, respectively).

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2.4.3.2 Five-membered rings: In another marked difference from the unsubstituted

heteroaromatic rings, the five-membered, methyl-substituted heteroaromatic rings

consistently demonstrate BDEs lower than any of their six-membered counterparts,

including toluene. Because the radical center is removed from the ring, the geometric

perturbations that affected the unsubstituted compounds are no longer a major concern.

Moreover, loss of hydrogen atom from the methyl group forms an allylic radical, which

can now maintain the planarity necessary for delocalization.

The 2-methyl-substituted, five-membered heteroaromatic rings have lower BDEs

than their 3-methyl-substituted counterparts. Presumably, the trend seen in the

unsubstituted azabenzenes helps to rationalize the results seen here: the compounds in

which the methyl group is ortho to the heteroatom are more able to exploit the additional

resonance stability afforded by nitrogen, oxygen, and sulfur relative to carbon.

Heteroatom identity does not have a large effect on energetics for the five-

membered rings, the only set of compounds for which the heteroatom was varied. The 2-

methyl-substituted heteroaromatic rings, in particular, have virtually identical BDEs. In the methyl derivatives of oxazole, the heteroaromatic containing both nitrogen and oxygen, it appears that the nitrogen has a more stabilizing effect than oxygen on the resulting radical, as the 4-methyl derivative (ortho to nitrogen) has a lower BDE than the

2-methyl derivative (ortho to oxygen).

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2.4.4 Ethyl-substituted heteroaromatics: Hydrogen-atom loss

Overall, the ethyl-substituted heteroaromatic rings have considerably lower BDEs than their methyl counterparts; the additional alkyl group serves to stabilize the radical derived from hydrogen-atom loss, regardless of ring size, by 4 to 5 kcal/mol (Table 2.3).

Table 2.3: Thermodynamic and spin density information for reactions of ethyl- a substituted heteroaromatic rings, for hydrogen loss from the CH2 group.

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2.4.4.1 Azabenzenes: The BDE values for the ethyl-substituted azabenzenes actually

encompass the value calculated for ethylbenzene (83.9 kcal/mol), as they range from 81.8

to 84.7 kcal/mol. The narrower range and lack of any trend relative to ethylbenzene

suggest that the additional methyl group present stabilizes all of the relevant radicals to a comparable extent.

2.4.4.2 Five-membered rings: The same trend seen with the methyl-substituted heteroaromatics is repeated here: the 2-substituted compounds have substantially lower

BDEs, again due to their increased proximity to the stabilizing heteroatom. Moreover, these compounds demonstrate more of a heteroatom effect, although it is a slight trend: the larger the heteroatom, the lower the BDE. Presumably, polarizability effects in stabilizing the radical might become more visible as the number of electrons in the molecule increase.

2.4.5 Methyl-substituted heteroaromatic rings: Methyl loss

Scission of the Cring-Calkyl bond for all of these compounds leads to an in-plane,

sp2 aromatic radical, localized in the σ system of the aromatic ring. It was expected that

the thermodynamics of these reactions would compare well to those for H-atom loss from

the unsubstituted heteroaromatic rings, and this was confirmed to be the case (Table 2.4).

Moreover, the thermochemistry for the loss of these alkyl groups was considerably more

endothermic and endoergic, in all cases, than hydrogen-atom loss.

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Methyl ΔH298 ΔG298 Ethyl ΔH298 ΔG298 Pyrrole 2 106.1 89.3 2 101.1 87.1 3 104.3 87.7 3 99.1 85.6 Furan 2 108.8 92.1 2 103.9 89.9 3 105.7 89.1 3 100.6 86.8 Thiophene 2 103.9 87.3 2 99.1 85.3 3 100.9 84.2 3 95.6 81.6 Oxazole 2 109.8 93.3 2 104.9 91.1 4 106.9 90.3 4 102.1 88.3 5 110.8 94.1 5 105.9 92.1 Pyridine 2 94.1 77.9 2 89.3 75.5 3 98.3 82.1 3 93.4 79.4 4 97.6 81.7 4 92.7 78.9 Pyridazine 3 96.2 79.7 3 91.4 77.7 4 97.1 81.2 4 92.2 78.6 Pyrimidine 2 97.4 81.5 2 92.5 78.8 4 90.3 74.1 4 89.7 75.9 5 99.7 84.1 5 94.9 81.1 Pyrazine 2 94.9 78.5 2 87.1 72.3 a Enthalpies and energies in kcal/mol, obtained at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory.

Table 2.4: Thermodynamic information for alkyl-group loss reactions of methyl- and ethyl-substituted heteroaromatics.a

2.4.5.1 Azabenzenes: Loss of the methyl group was seen to be around 10 kcal/mol more endothermic than loss of hydrogen, for any given position in these compounds.

Moreover, when the methyl group in question was ortho to nitrogen (as with 2- methylpyridine compared to the other pyridine derivatives, and 3-methylpyridazine

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compared to 4-methylpyridazine), the corresponding C-C BDE was even lower, due to

the stabilizing effects of the adjacent nitrogen. With the pyrimidine derivatives, the trend

is still evident; 4-methylpyrimidine, with its methyl group between two nitrogens, has a

substantially lower BDE than any other in this group.

2.4.5.2 Five-membered rings: The trends seen for hydrogen-loss reactions are non-

existent here. As seen in earlier work by our group9 and others,48 any stabilizing effects of the nearby heteroatom are negated by the geometric strain introduced by forming a ring-centered radical: the BDE at the 2-position is generally 2 to 3 kcal/mol higher than at

the 3-position. No definite heteroatom trends are evident, and the oxazole derivatives

demonstrate that the presence of two heteroatoms does not lead to greater reactivity at any one position.

2.4.6 Ethyl-substituted heteroaromatic rings: Ethyl loss

The ethyl-substituted compounds (Table 2.4) have the same trends as the methyl

derivatives and so will not be discussed further, save to note that the BDE values are

again around five kcal/mol lower than those of the methyl compounds, probably due to

the increased stability of the primary ethyl radical over the methyl radical.

2.4.7 General trends

2.4.7.1 Spin density: The spin densities were calculated via Natural Population Analyses

at the B3LYP/6-311+G**//B3LYP/6-31G* level. Excess spin density (α – β) was

determined for each of the incipient CH2 radical centers, and BDE was plotted as a

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function of this quantity (Figure 2.4). A comparable graph of BDE as a function of excess spin density was completed for the ethyl-substituted compounds (Figure 2.5).

Figure 2.4. Variation of bond dissociation enthalpy (kcal/mol) with excess spin density at the incipient CH2 radical center, for methyl-substituted heteroaromatic rings. Data for the five-membered heteroaromatic rings are denoted by closed circles; data for the six- membered heteroaromatic rings are denoted by open squares.

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Figure 2.5. Variation of bond dissociation enthalpy (kcal/mol) with excess spin density at the incipient C-H radical center, for ethyl-substituted heteroaromatics. Data for the five-membered heteroaromatic rings are denoted by closed circles; data for the six- membered heteroaromatic rings are denoted by open squares.

The spin density generated at the incipient radical correlated well with the BDE regardless of ring size or substitution, suggesting that the more localized a resulting radical will be, the larger the BDE value (or the more that electron delocalization will stabilize a given radical, the lower the BDE for its corresponding parent compound will be). The ethyl derivatives saw a slightly lower degree of correlation (R2 = 0.79) than did

the methyl derivatives (R2 = 0.84).

The correlation between the methyl and ethyl derivatives’ respective bond

dissociation enthalpies, for all the heteroaromatic rings considered together, was minimal.

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With the azabenzenes, the ethyl derivatives were far more uniformly stabilized than their

methyl counterparts; their correlation was thus poor. When only the five-membered rings

were considered (Figure 2.6), a substantially higher correlation was seen (R2 = 0.78).

Figure 2.6. Correlation between bond dissociation enthalpies for methyl and ethyl- substituted derivatives of the five-membered heteroaromatics.

2.4.7.2 Geometry: Several geometric changes occurred within these compounds, which can be understood by examining a representative reaction (Table 2.5) with 2-methylfuran.

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1 1 5 O 5 O 2 2 CH3 CH2 + H 4 4 3 3

Compound Radical Change in bond length O-C2 1.371 1.390 0.019 C2-Cmeth 1.479 1.377 -0.102 C2-C3 1.364 1.411 0.047 C3-C4 1.436 1.411 0.025 C4-C5 1.359 1.373 -0.14 C5-O 1.366 1.361 -0.005 Cmeth-H 1.097 1.083 -0.14

Compound Radical Change in bond angle O-C2-Cmeth 116.64 118.93 2.29 C3-C2-Cmeth 133.82 133.17 -0.65 H1-Cmeth-C2 111.57 H2-Cmeth-C2 111.57 120.93 9.36 H3-Cmeth-C2 109.87 120.06 10.19 H1-Cmeth-H2 108.17 H2-Cmeth-H3 107.36 119.01 11.65 H3-Cmeth-H1 108.16

Table 2.5. Changes in bond lengths (Angstroms) and bond angles (degrees) for hydrogen-loss reaction of representative heteroaromatic ring, 2-methylfuran.

In terms of bond lengths, the main change occurred in the bond between the furan ring

and alkyl chain, which shorted substantially as the bond took on more π character in the corresponding π radical. Bonds within the ring lengthened to some extent. With respect to bond angles, the O-C2-Cmeth angle increased slightly, and the H-Cmeth-C2 angles

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increased substantially, as hybridization at the radical center changed from sp3 to sp2.

The analogous geometries of interest for the other heteroaromatics are summarized in the

Supporting Information. What is most significant is that, for these alkylated aromatics, the ring itself was relatively unperturbed, relative to previous studies in which the new radical was located directly on the heteroaromatic of interest.9

2.4.7.3 Temperature effects: Calculations were completed to examine the changes in

hydrogen-loss BDE at combustion temperatures for these compounds. As shown

(Figures 2.7 and 2.8), minor quantitative changes (increases of roughly 4 kcal/mol) in the

hydrogen-loss BDEs of the heterocyclic compounds occur over this temperature range;

the most dramatic variation, seen with 2-methylpyrrole and 3-methylpyrrole, is still less

than 10 kcal/mol. Thus, the 298 K thermodynamic data can also be useful in terms of predicting higher-temperature chemistry. It is notable that although any quantitative changes are relatively small, the qualitative trends are not completely consistent. Most of the heteroaromatics see a slight increase in their BDE value proportional to temperature, but a few actually exhibit slightly lower BDEs at higher temperatures (most evident in the case of 2-ethylpyrazine). These variations are minor; overall, chemistry at 298 K provides a good reference for the reactivity of the alkylated compounds.

134

(a) (b) (b) (a)

Figure 2.7. Variation of bond dissociation enthalpy (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered methyl-substituted heteroaromatics and (b) six-membered methyl-substituted heteroaromatics. The atypical trends of 2- methylpyrrole and 3-methylpyrrole (x) are denoted by an arrow.

135

(a) (b)

Figure 2.8. Variation of bond dissociation enthalpy (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered ethyl-substituted heteroaromatics and (b) six-membered ethyl-substituted heteroaromatics. The atypical trend of 2-methylpyrazine (-) is denoted by an arrow.

136

The free energies of reaction for hydrogen-atom loss were also explored as a function of temperature (Figures 2.9 and 2.10); these quantities experienced a large temperature effect, due to the entropic term for these dissociative processes. At high temperatures

(2000 K), the free energies of reaction are roughly 60 kcal/mol more favorable than at

298 K, making these radicals ready participants in high-temperature combustion processes.

(a) (b)

Figure 2.9. Variation of free energy of reaction (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered methyl-substituted heteroaromatic rings and (b) six-membered methyl-substituted heteroaromatic rings.

137

(a) (b)

Figure 2.10. Variation of free energy of reaction (kcal/mol) with temperature (K) for hydrogen-atom loss in the (a) five-membered ethyl-substituted heteroaromatic rings and (b) six-membered ethyl-substituted heteroaromatic rings.

Moreover, comparative temperature profiles were generated to explore the relative energetics of hydrogen-atom loss and alkyl-group loss (Figures 2.11 and 2.12).

Representative cases are shown; a more complete set of information is included in the

Supporting Information. Both pathways see large entropic contributions at higher temperatures. In all cases, hydrogen-atom loss is initially the favored pathway, but at

2000 K, alkyl-group loss is favored slightly. At no temperature is one pathway overwhelmingly dominant over the other, and the energetics actually overlap at several points, so that the further combustion pathways of both sets of radicals will likely contribute in comparable capacity.

138

(a) (b)

Figure 2.11. Comparison of hydrogen-atom loss and methyl-group loss free energies with increasing temperature. Representative pathways shown for (a) 2-methylpyrrole, (b) 3-methylpyrrole, (c) 3-methylpyridazine, and (d) 4-methylpyridazine. Free energies for hydrogen-atom loss are denoted with open squares; free energies for methyl loss are denoted with solid triangles.

139

(a) (b)

Figure 2.12. Comparison of hydrogen-atom loss and ethyl-group loss free energies with increasing temperature. Representative pathways shown for (a) 2-ethylpyrrole, (b) 3- ethylpyrrole, (c) 3-ethylpyridazine, and (d) 4-ethylpyridazine. Free energies for hydrogen-atom loss are denoted with open squares; free energies for ethyl loss are denoted with solid triangles.

2.4.7.4 Approximations: Another set of calculations was run to determine what, if any,

error was introduced via using the harmonic oscillator approximation in finding the

enthalpic and entropic thermal corrections. As described previously, the lowest-energy

vibrations (i.e. the motions of the alkyl chain) were identified and treated as rotations, using a hindered rotor approximation rather than the harmonic oscillator. The enthalpies are essentially consistent between approximations (Table 2.6), while the free energies reflect a small change, generally less than 1 kcal/mol. Considering that this variation in

140

approximation would have the most impact on the entropy of these species, it seems logical that the free energies would see more of an effect than the enthalpies. However, neither quantity was greatly affected.

ΔH ΔH ΔG ΔG ΔH ΔH ΔG ΔG Methyl 298 298 298 298 Ethyl 298 298 298 298 (vib) (rotor) (vib) (rotor) (vib) (rotor) (vib) (rotor) Pyrrole 2 83.1 83.1 75.3 74.5 2 80.8 80.5 72.2 72.7 3 86.8 86.8 78.9 79.6 3 83.8 83.7 75.3 75.5 Furan 2 83.1 83.1 75.3 76.0 2 80.1 79.9 71.6 72.8 3 87.4 87.4 79.5 80.3 3 84.2 84.1 75.4 75.8 Thiophene 2 85.2 85.2 77.4 78.0 2 79.8 79.5 71.1 71.7 3 87.0 87.0 79.1 79.8 3 83.5 83.5 74.4 73.8 Oxazole 2 86.4 86.4 78.7 79.4 2 82.4 82.3 74.1 74.8 4 88.1 88.0 80.2 80.8 4 84.5 84.5 76.0 76.2 5 84.5 84.5 76.6 77.4 5 81.5 81.5 73.0 72.3 Pyridine 2 88.1 88.3 80.5 81.0 2 84.2 84.3 75.2 78.0 3 87.0 87.3 79.6 80.1 3 82.9 82.9 74.8 74.7 4 87.9 88.1 80.6 80.9 4 83.7 83.9 74.5 75.8 Pyridazine 3 88.9 89.0 81.3 81.9 3 84.7 85.4 77.6 75.9 4 87.6 87.9 80.6 80.7 4 83.7 83.6 75.1 75.2 Pyrimidine 2 89.5 89.7 82.4 82.6 2 84.2 84.5 76.1 76.4 4 89.3 89.5 81.9 82.4 4 83.9 84.0 75.7 76.2 5 87.5 87.8 80.7 80.7 5 84.3 84.3 74.9 76.0 Pyrazine 2 88.0 88.2 80.5 81.1 2 83.8 83.7 75.1 75.7 a Enthalpies and energies in kcal/mol, obtained at the B3LYP/6-311+G**//B3LYP/6- 31G* level of theory.

Table 2.6: Comparison of approximations (harmonic oscillator to hindered rotor), as applied to the thermodynamics of hydrogen-atom loss for methyl-substituted heteroaromatic rings.

141

2.5 Conclusions

Using the B3LYP level of theory, the bond dissociation enthalpies for hydrogen

loss and alkyl-group loss were compiled for the alkylated heteroaromatics. Using the

small 6-31G* basis set for geometry optimization, followed by single-point energies

using the larger 6-311+G** basis set, this efficient method was shown to give reliable

results, matching well with experimental values for C-H BDE values when known, and in

agreement with all of the qualitative BDE trends predicted by the CBS-QB3 method.

Overall, loss of hydrogen to form a benzylic-like radical was roughly 10 kcal/mol more favorable than loss of an alkyl group, regardless of ring size or heteroatom. BDE trends varied considerably with respect to ring size and bond type. For the hydrogen-loss reactions, the methyl-substituted azabenzenes saw higher BDEs than their hydrocarbon counterpart, toluene. However, the methyl-substituted five-membered heteroaromatic

rings displayed consistently lower BDEs than the azabenzenes and, moreover, exhibited a

trend where the 2-substituted compounds had lower BDEs than the 3-substituted

compounds, due to increased stabilization of the radical via increased proximity to the

heteroatom. In the hydrogen-atom fragmentation reactions of the ethyl derivatives, the

trends within each class of compounds (azabenzenes vs. heteroaromatic rings) were

duplicated, but an overall stabilization of the radicals of interest caused the BDEs of these

reactions to drop by ~4 kcal/mol. In terms of alkyl-group loss, the ortho-substituted

azabenzenes were more able to stabilize the in-plane sp2 radicals in these reactions, due

to the adjacent nitrogen atom, and had consistently lower BDEs than their counterparts.

The five-membered heteroaromatic rings could not exploit a similar relationship, as their

142

alkyl-loss reactions caused geometric perturbations to the ring, decreasing any aromatic contribution to resonance stability and thus increasing the BDEs for these compounds.

Spin densities were calculated for these heterocyclic radicals and correlated well with the BDE values; this was seen especially in the case of the five-membered heteroaromatics. Temperature effects were explored for the hydrogen-loss reactions and demonstrated that the reactions stayed constant in their endothermicity but became substantially less endoergic over the 298-2000 K range, due to entropic effects on the free energy. The free energy profiles of hydrogen-atom loss compared to alkyl-group loss showed that both pathways experienced similar temperature effects. Finally, the vibrational frequencies attributed to methyl and ethyl rotations were also explored for their effect on the thermodynamic predictions using the hindered rotor approximation, and it was seen that this treatment gave comparable results for the enthalpies and free energies of these reactions.

With respect to predicting the chemistry of the larger heterocyclic systems found in coal, our work suggests that both hydrogen-atom loss and alkyl-group loss reactions will contribute as initiation steps for the high-temperature combustion reactions of these rings. Longer alkyl chains and larger ring sizes will increase reactivity. The initial steps of radical formation are expected to become much more favorable at high temperatures.

This chapter represents the first in a series exploring the combustion pathways of the alkylated heteroaromatic rings. The B3LYP method has shown promise in elucidating these pathways, which have implications for exploring combustion pathways of coal compounds.

143

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149

CHAPTER 3

COMBUSTION PATHWAYS OF THE ALKYLATED HETEROAROMATICS: PEROXY RADICAL PATHWAYS OF THE ALKYLATED AZABENZENES

3.1 Introduction

The structure of coal is notoriously difficult to study with any degree of precision,

given its complex structure and the variation of that structure with geography.1 However,

an understanding of coal’s combustion processes is valuable, given the fact that this fossil

fuel accounts for a great deal of America’s electrical power,2 and has recently shown

promise for use in hydrogen fuel generation.3 A potential approach for examining the

chemistry of coal specimens involves the fact that aromatic hydrocarbons and

heteroaromatic rings are recurring components of these larger structures.4 Since it is

known what types of coal dominate in certain parts of the country, knowing the reactions available to each type of monocyclic unit can ultimately provide clues as to how the overall coal structure in a certain area might react, better predicting the dominant reactions and likely emissions of a given geographical specimen.

Small aromatic heterocyclic units (Figure 3.1) have been used as models for coal

chemistry in several pyrolytic studies; using shock tube studies, Mackie et al. observed

the thermal decompositions of pyridine,5 while Kiefer et al. examined the processes of

150 pyrazine, pyrimidine, and pyridine;6 commonly observed products of pyrolysis involved

ring-scission species such as HCN, HC≡C-C≡N, and acetylene.

N N N N 2 N 2 2

3 3 5 N N 4 4 4 Pyridine Pyridazine Pyrimidine Pyrazine

Figure 3.1. Heteroaromatic rings of interest. These six-membered heteroaromatic rings are commonly classified as the azabenzenes.

Substantially fewer oxidative studies have been completed. Tabares et al. studied the

oxidation of pyridine with O(3P) and noted a decrease in reactivity relative to benzene.7

Alfassi et al. have examined the formation and reactivity of pyridylperoxy radicals in solution.8 Additionally, Eisele’s work on pyridine and picoline ions in the troposphere

suggested that the low-temperature oxidation pathways of these species have implications

for atmospheric processes.9 This supposition was validated by Yeung and Elrod, who

performed chemical ionization mass spectrometric studies of the reactions of hydroxyl

(HO•) radical with pyridine, the picolines, the lutidines, and the ethylpyridines, and

postulated that these pyridinated compounds could indeed have substantial implications

on tropospheric ion content.10 These heteroaromatics have the potential to be oxidized at

151 11 the nitrogen atom and thus form NOx species, which can subsequently react to over-

produce tropospheric ozone and contribute to acid rain.12

Our group has examined several aspects of heteroaromatic combustion.

Barckholtz et al. explored the use of various methods and basis sets in calculating the

C−H bond dissociation enthalpies (BDEs) of a number of unsubstituted

heteroaromatics.13 It was determined that DFT methodology (B3LYP) afforded the most

useful balance of accuracy and computational cost, and this approach has been used in

much of our subsequent work on these compounds. Fadden et al. examined the oxidation

pathways of these species, noting that after addition of molecular oxygen at 298 K, five-

membered heteroaromatic rings were most likely to lose atomic oxygen,14 while the six-

membered heteroaromatics (azabenzenes) favored dissociation back to molecular oxygen

and the relevant aromatic radical.15 Intramolecular pathways competed with these reactions, regardless of ring size, and in some cases had implications for NOx formation.

As temperatures increased, the entropic benefit of dissociative pathways increased. For

the alkyl-substituted heteroaromatic rings, the chemistry of these compounds is likely

complicated via their dual nature: both alkyl and aromatic. Our previous work suggests

that the chemistry of the relevant peroxy radicals affords a logical starting point for

considering these effects.

Studies of the alkylated heteroaromatic rings and their oxidized derivatives are

limited in the literature despite the fact that these species actually provide the most

rational model for coal chemistry. Mackie et al. have postulated several pathways in the

thermolytic decomposition of the picolines,16 while Frerichs et al. examined the reaction

152 of the picolines with atomic oxygen.17 Therefore, it is also instructive to consider the

pathways of the equivalent alkylated aromatic hydrocarbon and oxidized aromatic

hydrocarbon species—in this case, toluene and benzylperoxy radical—as model species.

Several studies have been completed on the oxidation of toluene in general and formation

of benzylperoxy radical in particular. Emdee et al. proposed that toluene’s combustion is

most sensitive to its reaction with oxygen to form benzyl radical and hydroperoxyl

radical. Dagaut et al. proposed that toluene combustion proceeds mainly through

generation of the benzyl radical, which can thermally decompose to acetylene and

cyclopentadienyl or oxidatively decompose to phenyl and formyl radicals (via

benzaldehyde).18 Pitz et al. have generated comprehensive mechanisms for toluene combustion in varying settings, due to its widespread use as a fuel additive.19 Andino et

al. modeled the atmospheric photooxidation of toluene and substituted xylenes, noting

that several cyclized peroxy radical rearrangement products were energetically stable.20

Elmaimouni et al. studied the equilibrium between benzylperoxy radical and its

component parts (benzyl radical and O2), calculating the enthalpy of the peroxy radical

formation pathway to be –20.1 kcal/mol, and extrapolating the free energy to be −11.4

21 22 kcal/mol. Fenter et al. completed a kinetic study which proposed kf of (7.6 ± 2.4) x

-13 3 4 -1 10 exp[(190 ± 160)K/T] cm /molecule-s, Kp of (6.3 ± 0.2) x 10 atm , and an enthalpy

of reaction of –21.8 kcal/mol. Hoyermann and Seeba used a flow reactor coupled to

23 mass spectrometric detection to study the same equilibrium, determining kf = (4.44 ±

11 3 -1 1.3) x 10 cm / molecule-s and Kp = 57,200 bar .

153 Several plausible routes are available to this species, some dissociative and others

intramolecular (Figure 3.2). Benzylperoxy radical can lose atomic oxygen to form benzyloxy radical, dissociate back to molecular oxygen and benzyl radical; dissociate into phenyl radical and the cyclized side chain; cyclize at various positions within the

benzene ring (ipso, ortho, meta, and para); or undergo a hydrogen transfer to yield a

benzylic hydroperoxide radical. Initial calculations on these pathways were used to

generate hypothetical routes for the corresponding azabenzylperoxy species, which were

subjected to a more rigorous study. The experimental data available for benzylperoxy

radical also allowed us to corroborate our computational approach before moving on to

the more pertinent calculations of the azabenzenes.

154 CH2O +O(3P)

O + O A

B O O CH2OO

+O2 C

D H OO

G E F

O O H CHOOH O O

Figure 3.2. Likely pathways for the alkylated aromatic peroxy radicals, using benzylperoxy radical as a model compound.

The work outlined in this study modeled the oxidation pathways of the alkylated azabenzenes at 298 K, examining both the kinetic and thermodynamic aspects of these reactions. The picolinylperoxy radicals were studied in greatest detail; geometries and electron distributions were studied to elucidate the changes in reactivity resulting from the nitrogen atom’s presence in the ring. The general trends of temperature effects, increasing alkyl substitution, and varying approximations (harmonic oscillator vs. rotor)

155 were also examined. Additionally, the thermodynamics of the reactions of the

picolinylperoxy radicals were compared to those of the alkylated diazabenzylperoxy

radicals, to explore the effect of multiple nitrogen atoms on these compounds’ reactivity.

A subsequent study will examine similar pathways in several five-membered

heteroaromatic rings (furan, thiophene, pyrrole, and oxazole) that also have relevance to

coal chemistry; these smaller compounds will afford the additional benefit of being able

to observe the effects of varying and multiple heteroatoms, while comparing the results of

the two studies will elucidate any potential effects of ring size.

3.2 Computational Methods

All geometry optimizations, vibrational frequency calculations, and single-point

energy calculations were completed with Gaussian 9824 and 0325 at the Ohio

Supercomputer Center. The B3LYP/6-31G* hybrid density functional theory (DFT)26 level was used for all geometry optimizations and vibrational frequency calculations.

Single-point energies were calculated at the B3LYP/6-311+G** level, using six Cartesian d functions with the scf=tight option; it has been shown that there is a small basis set effect with more polar systems,27 so this larger basis set was selected to compensate for

that effect. Natural Population Analyses (NPA)28 were also obtained at the B3LYP/6-

311+G**//B3LYP/6-31G* level of theory. Additionally, certain geometries and energies

were also obtained using Complete Basis Set (CBS-QB3) methods,29 to validate the DFT

approach for these particular systems.

156 Vibrational frequencies were calculated for each stationary point to characterize

these structures as minima or transition states. The unscaled vibrational frequencies were

used to calculate the thermodynamic corrections to the enthalpy and free energy. Once

obtained, zero-point vibrational energy corrections were scaled by a factor of 0.9806.30

Transition states were connected to reactants and products by either using intrinsic reaction coordinate (IRC)31 searches or displacing the relevant geometries by ±

10% along the reaction coordinate characterized by the imaginary vibrational frequency,

then carefully optimizing (opt = calcfc) these resulting geometries to their corresponding

minima.

For the doublet radical species and many transition states, spin contamination

() was negligible (no greater than 0.80). The DFT methods employed in this work have demonstrated an ability to minimize spin contamination for the radicals of interest,

keeping the computed values near the expected value of 0.75. Spin densities were

obtained for the hydrogen-loss radicals using the natural population analysis (NPA)

method.32

Because flame processes are some of the reactions of interest for these

compounds, it is necessary to see how these species react at higher temperatures. The

enthalpies of both the parent compounds and the resultant radicals were calculated from

298 to 2000 K via the temperature-dependent term:33

157 =Δ trans + rot + vib )()()()( + RTTHTHTHTH

3 3 i / kThv −1 )( ++=Δ ∑ i evNhRTRTTH )1( +− RT 2 2 i

The summation takes place over all 3N−6 normal modes. For each compound, the scaled zero-point energy and enthalpy contribution were computed at various temperatures via the given equations and added to the B3LYP total energy, to obtain the bond dissociation enthalpies as a function of temperature. A similar approach was used with calculation of the entropic corrections, to determine the free energies of reaction over the same temperature range.34

To reduce potential errors in the thermodynamic values arising from treating all

vibrations according to the harmonic-oscillator rigid-rotor approximation, low-energy

torsions in the alkyl-substituted species were also treated as hindered rotors,35 and the resulting energetics were compared to those from the original calculations.

3.3 Results

Our first set of calculations examined the kinetics and thermodynamics of the pathways available to benzylperoxy radical, calibrating our computational approach against experimental findings by way of DFT and complete basis set calculations. The most likely pathways were delineated and selected for further exploration with the alkylated heteroaromatic rings.

The oxidation pathways of the azabenzenes— pyridine, pyrimidine, pyridazine, and pyrazine— were then subjected to a thorough analysis. This work began from where our earlier work36 ended: i.e. the most stable radical species were formed from H-atom

158 loss at the benzylic position of the compound. We explored the various conformations of

the peroxy radicals that could result from reaction of these heterocyclic radicals with

molecular oxygen, to determine the minimum-energy conformation, thus allowing

calculation of enthalpies and energies of oxidation. Once these peroxy radical geometries were obtained, the possible pathways available to these species were examined and their enthalpies and energies compiled. High-temperature pathways were also considered.

The nomenclature used throughout the remainder of the discussion will indicate

that all radicals are located on the terminal oxygen of the compound; that is, 2-

picolinylperoxy radical will be used as an abbreviation for 2-picolin-2’-ylperoxy (c-

• C5H4N-CH2OO ) radical; similarly, 2-ethylpyridinylperoxy radical will be used to refer to

• 2-ethylpyridin-2’-ylperoxy radical (c-C4H4N2-C(H)(CH3)OO ). Finally, unless otherwise

specified, the reactions will be discussed in the context of free energies of activation and

free energies of reaction at 298 K.

3.4 Discussion

3.4.1 Toluene as reference compound

As with the case of our previous work on the C−-H and C−alkyl bond dissociation enthalpies of the heteroaromatic rings, more information is available on the hydrocarbon analogue of these species, in this case benzylperoxy radical. These data provide a chance to calibrate our computational method against experimental results, even though directly relevant experimental studies are not yet available. Thus, the

159 oxidation pathways of benzyl radical and subsequent reactions of benzylperoxy radical

were explored via DFT and CBS-QB3 methods. As mentioned in the introduction, the

enthalpy of reaction for the oxidation of benzyl radical has been calculated to be –20.1

and –21.8 kcal/mol in two different studies;21,22 the free energy of reaction has also been

extrapolated to be –11.4 kcal/mol. The CBS calculations yielded results within 1

kcal/mol of experiment, predicting an enthalpy of oxidation of –22.7 kcal/mol, with a free

energy of oxidation of –12.2 kcal/mol. Moreover, both DFT and CBS methods predicted

comparable results for the possible benzylperoxy radical pathways (Table 3.1):

cyclization to form a five-membered ring was most favorable, followed by cyclization to form a four-membered ring, followed by an internal 1,3-hydrogen-atom transfer that ultimately yields benzaldehyde and hydroxyl radical.

160

B3LYP CBS-QB3 Experiment ΔΗ ο ΔG ο ΔΗ ο ΔG ο ΔΗ ο ΔG ο Dissociation to -16.0 -5.5 -22.7 -12.2 -20.1a -12.2 benzyl radical -21.8b + O2

B3LYP CBS-QB3 ΔΗ ο ΔG ο ΔΗ ο ΔG ο Path A 56.5 47.3 61.9 52.5 Path B 53.7 42.9 55.8 45.3 Path C 33.2 34.2 25.8 26.9 Path D 35.6 23.7 14.6 15.1 Path E NO CYCLIZATION Path F NO CYCLIZATION Path G -33.9 -35.4 -37.7

B3LYP CBS-QB3 ΔΗ ‡ ΔG‡ ΔΗ ‡ ΔG‡ Path C 35.7 37.2 30.1 31.7 Path D 33.5 35.6 29.7 31.8 Path G 37.9 38.9 38.4 39.2

Table 3.1. Comparison of DFT (B3LYP/6-311+G**//B3LYP/6-31G*) and CBS-QB3 results for key processes in the reactions possible for benzylperoxy radical. (See Figure 3.2 for the different pathways.)

DFT replicated the qualitative trends obtained by the CBS-QB3 calculations, which correspondingly replicated the quantitative values obtained by experiment. The DFT energies therefore provided an economic route to valid energetic conclusions and will be referenced in the course of this discussion.

At 298 K, the likeliest pathways included cyclization at the ortho position to form a five-membered ring, with a barrier of 35.6 kcal/mol (Pathway D); cyclization at the ipso

161 formation to form a four-membered ring, with a barrier of 37.2 kcal/mol (Pathway C);

and internal H-transfer, with a barrier of 38.9 kcal/mol (Pathway G). This last step was

particularly interesting. The internal hydrogen transfer facilitated by the sp3 C−H bonds of the benzylic position was expected to yield a benzylic hydroperoxide radical; however, after displacement of the relevant transition state and minimization to products, it was seen that this transition state connected the benzylperoxy radical directly to benzaldehyde and hydroxyl radical. The dissociative nature of the reaction and stability of the products formed led to a highly favorable free energy of reaction, which would be expected to become moreso with increasing temperature. An analogous reaction would not be possible for phenylperoxy radical and the related azabenzylperoxy radicals; it is the additional methylene unit of benzylperoxy radical that facilitates this unique path, generating a stable carbonyl species as well as the reactive hydroxyl radical (thereby contributing to the radical pool). Geometries for cyclization at the meta and para positions failed to optimize; this was unsurprising, with the amount of strain these species would incur given their starting aromatic geometries. Dissociative processes were endoergic at low temperatures, as expected.

At 298 K, the rearrangements available to the benzylperoxy radical dictate the

low-temperature combustion pathways, and the kinetic trends largely mimic the

thermodynamic trends. It was assumed, however, that the dissociative pathways would

become more likely at temperatures increased into the high-temperature combustion

range. Six pathways (dissociation to reactants, ipso cyclization, ortho cyclization, H-

162 transfer, oxygen loss, and dioxirane loss) were thus explored for each of the

picolinylperoxy radicals (Figure 3.3).

O N H OO O

3.3

3.4a

OO O

N N CH 2OO N N CH 2O +O2

3.4b 3.2 3.1

N CH OO H N CHO N HO O + + O 3.5

N CH 2O +O(3P) 3.7

3.6

Figure 3.3. Numbering scheme for the azabenzylperoxy radicals.

3.4.2 Methyl-substituted pyridines (Picolines)

As with benzylperoxy radical, the reactions of 2-picolinylperoxy radical were first studied via DFT methods, calibrating the most likely pathways against CBS-QB3 energies (Table 3.2). Overall, the B3LYP method predicts reaction energies that are actually 6-7 kcal/mol lower than those predicted by CBS-QB3. Most importantly, it was

163 again seen that DFT and CBS matched qualitative trends; thus, the introduction of a

heteroatom did not affect our computational approach.

B3LYP CBS-QB3 ΔΗ ΔG ΔΗ ΔG 3.2 → 3.1 16.3 6.5 22.7 13.2 TS(3.2-3.3) 37.1 39.4 31.0 33.4 3.2 → 3.3 34.2 35.7 26.1 27.9 TS(3.2-3.4a) 30.4 33.2 25.6 28.7 3.2 → 3.4a 20.6 23.2 13.2 16.0 TS(3.2-3.4b) 47.1 49.8 3.2 → 3.4b -5.8 -4.1 TS(3.2-3.5) 38.0 39.4 37.6 39.2 3.2 → 3.5 -24.7 -33.6 -23.7 -32.4 3.2 → 3.6 61.6 53.0 3.2 → 3.7 49.2 38.7

Table 3.2. Comparison of reaction pathways available to 2-picolinylperoxy radical at 298 K, via B3LYP/6-311+G**//B3LYP/6-31G*. All enthalpies and energies are relative to the peroxy radical (2); when preceded by TS, the relative data are the enthalpy and energies of activation. Where applicable, 4a refers to cyclization at carbon and 4b refers to ortho cyclization at nitrogen. For the most likely pathways, B3LYP results were calibrated against CBS-QB3 calculations.

The numbering scheme used in Figure 3.3 will be adopted over the course of the paper, as

each alkylated heterocyclic peroxy radical (3.2) is systematically examined: the routes of interest include dissociation back to reactants (3.1); cyclization at the ipso position (3.3);

cyclization at the ortho position, which could be either carbon (3.4a) or nitrogen (3.4b)37;

internal H-transfer and subsequent scission (3.5); loss of atomic oxygen (3.6); and loss of

dioxirane (3.7). Where relevant, transition states will be referred to as “TS” between the

164 two numbered species; i.e., the transition state for cyclization at the ipso position would

be TS(3.2-3.3).

Comparing the 2-picolinylperoxy radical pathways to those of benzylperoxy radical illuminated interesting trends. Overall, the same pathways were preferred for both 2-picolinylperoxy radical and benzylperoxy radical. Cyclization at the ortho position (3.2 → 3.4a) yielded a stable five-membered ring, while cyclization at the ipso position (3.2 → 3.3) yielded a four-membered ring; the strain present in the four-

membered ring disfavored ipso cyclization relative to ortho cyclization. Ortho

cyclization at nitrogen was also a plausible route to yield a stable nitrosyl radical, but this

occurred with a substantially higher barrier. The internal H-transfer yielded hydroxyl

radical and 2-picolinal, presumably via a benzylic-like radical; the barrier for this

pathway was roughly equivalent to that of ipso cyclization. Thus, ipso cyclization, ortho

cyclization (at carbon), and H-transfer followed by scission are the processes likely for 2-

picolylperoxy radical in low-temperature combustion (atmospheric) reactions.

In terms of comparative quantitative energies of the reactions, loss of dioxirane to

form the 2-pyridyl radical (3.2 → 3.7) was less endoergic than in the hydrocarbon

analogue; this makes sense in the context of our previous work in this area, which has

suggested that the nitrogen atom in 2-pyridinyl radical increases its resonance stability,

rendering it more stable than phenyl radical. Aside from this one exception, the

picolinylperoxy radical pathways were more endoergic than the corresponding benzylperoxy radical pathways; several aspects of the relevant structures were examined

to discern the cause of this effect.

165 As can be seen in Figure 3.4, the introduction of the nitrogen atom introduces some slight changes into the aromatic ring.

Cmeth O2

Cmeth C6 O1 N1 C6 O2 C1 C5 C2 O1

C2 C5 C C3 4 C4 C3

Benzylperoxy radical 2-Picolinylperoxy radical Change in bond length C6-C1 1.402 N1-C2 1.341 -0.061 C1-C2 1.400 C2-C3 1.399 -0.001 C2-C3 1.395 C3-C4 1.393 -0.002 C3-C4 1.396 C4-C5 1.395 -0.001 C4-C5 1.397 C5-C6 1.395 -0.002 C5-C6 1.394 C6-N1 1.338 -0.052 C1-Cmeth 1.502 C2-Cmeth 1.508 0.006 Cmeth-O1 1.476 Cmeth-O1 1.462 -0.014 O1-O2 1.320 O1-O2 1.322 0.002

Figure 3.4. Change in bond lengths with addition of nitrogen atom to the aromatic system. All bond lengths in angstroms and obtained from the B3LYP/6-31G* optimized structures.

Most notably, both carbon-nitrogen bonds are shortened by more than 0.5 angstroms, due to the increased electronegativity difference. Overall, however, the ring structures are highly similar. The difference in preferred dihedral orientation is apparent between the hydrocarbon and heteroaromatic ring; it seems possible that however,

166 rotation of the relevant dihedral angles occurs with small barrier heights (< 1 kcal/mol), such that this could not account for any substantive differences. In terms of the aromaticity lost in the course of the cyclization reactions, benzene has a resonance energy of 36 kcal/mol,38 while pyridine’s resonance energy is 34 kcal/mol.39 It seems that the cyclization steps, each of which involves loss of aromaticity, would thus be less favorable for benzylperoxy than for picolinylperoxy, contrary to the calculated energetics.

One possible answer to these energetic differences might be that the allylic system remaining in the cyclized hydrocarbon peroxy radicals more readily stabilizes the resultant radical than does that of the heterocyclic derivatives. The excess spin densities of a representative cyclization were examined for both benzylperoxy and 2- picolinylperoxy radicals (Figure 3.5). The resulting allylic system for both ortho- cyclized species involves atoms 2, 1, 6, 5, and 4, as numbered. It can be seen that the two cyclized derivatives experience virtually identical spin densities, with notable increases in spin density on the terminal and central atoms of the allylic system (2, 6, 4) and corresponding decreases on the other two atoms (1, 5). The only discernable difference between the two systems arises on atom 1, which is carbon in the benzylperoxy derivative and nitrogen in the picolinylperoxy derivative; the nitrogen experiences substantially less of a change (roughly half compared to carbon) in its excess spin density. It can be hypothesized that the presence of the nitrogen might slightly disrupt the allylic delocalization in the heterocyclic derivatives and thus account for the higher energies of reaction seen for the alkylated azabenzylperoxy radicals.

167

1 1 2 7 N 2 7 6 6 O 8 O 8 3 3 5 O 5 O 9 9 4 H 4 H

Position Benzylperoxy radical 2-Picolinylperoxy radical 1 -0.11 -0.06 2 0.23 0.22 3 0.09 0.10 4 0.21 0.20 5 -0.09 -0.09 6 0.26 0.25 7 -0.01 -0.01 8 -0.22 -0.21 9 -0.40 -0.40

Figure 3.5. Variation in excess spin density via cyclization at the ortho position, for benzylperoxy radical and 2-picolinylperoxy radical. Excess spin density (α−β) calculated via comparison between cyclized product and relevant peroxy radical, using NPA analyses (B3LYP/6-311+G**//B3LYP/6-31G*). Numbering scheme used for convenience of reference.

Another possible factor involves the negative inductive effect of the nitrogen’s presence in the aromatic ring. Taberes et al. noted a smaller rate constant for the reaction of pyridine with O(3P) as compared to benzene and O(3P), attributed to this phenomenon.

Although the referenced work discussed the aromatic rings as pure electrophiles, it is plausible that a related trend could be repeated in the radical pathways of these related compounds, hence the relative kinetic barriers of benzylperoxy radical and its nitrogen analogue.

168 The reaction enthalpies and energies are summarized for 3-picolinylperoxy radical and 4-picolinylperoxy radical (Table 3.3). The barrier to ortho cyclization was consistently lowest, roughly 2-4 kcal/mol less endoergic than the barrier to ipso cyclization, and 5−6 kcal/mol lower than the barrier to hydrogen transfer. 3-

Picolinylperoxy radical presented an interesting case in that both of its ortho cyclization pathways (3.2 → 3.4a and 3.2 → 3.4b) generated a new carbon-carbon bond; neither ortho cyclization occurred at nitrogen. Between these two options, cyclization adjacent to nitrogen was slightly more favorable than at the position para to nitrogen. 3-

Picolinylperoxy and 4-picolinylperoxy radicals did allow for a more careful delineation of the hydrogen-atom transfer pathway. The values reported in Table 3.3 reflect complete dissociation to products (for the benefit of comparison to previous data), but actual displacement of the transition state in these two cases resulted in a stable complex and a benzylic-like radical, respectively.

169

3-picolinylperoxy radical ΔΗ ΔG 3.2 → 3.1 15.6 5.6 TS(3.2-3.3) 36.2 38.2 3.2 → 3.3 33.5 34.8 TS(3.2-3.4a) 32.8 35.4 3.2 → 3.4a 21.3 23.8 TS(3.2-3.4b) 34.0 36.6 3.2 → 3.4b 24.4 26.8 TS(3.2-3.5) 38.6 39.8 3.2 → 3.5 -29.3 -38.3 3.2 → 3.6 56.3 49.3 3.2 → 3.7 53.8 43.2

4-picolinylperoxy radical ΔΗ ΔG 3.2 → 3.1 15.2 5.6 TS(3.2-3.3) 38.3 40.6 3.2 → 3.3 35.7 37.5 TS(3.2-3.4) 31.8 34.7 3.2 → 3.4 21.9 24.5 TS(3.2-3.5) 38.7 40.1 3.2 → 3.5 -28.7 -37.4 3.2 → 3.6 62.7 53.8 3.2 → 3.7 52.0 41.6

Table 3.3. Compiled enthalpies and energies of reaction (kcal/mol) for 3- and 4- picolinylperoxy radical (B3LYP/6-311+G**//B3LYP/6-31G*). Where applicable, 4a refers to cyclization at carbon and 4b refers to ortho cyclization at nitrogen. All energies and enthalpies relative to those of the relevant peroxy radical (2).

170 C O N O C C + C C

0.0 39.4 -33.6

C C

0.0 39.8 -34.3

C C

0.0 40.1 0.1

Figure 3.6. H-transfer pathways delineated for each of the three picolinylperoxy radicals. Free energies of reaction at 298 K calculated at the B3LYP/6- 311+G**//B3LYP/6-31G* level of theory.

Simultaneously looking at all three picolinylperoxy radicals (Figure 3.6) allows a better understanding of the overall reaction. As seen for 4-picolinylperoxy radical, the hydrogen-atom transfer yields a hydroperoxide-functionalized, benzylic-like radical, with a free energy of reaction of only 0.3 kcal/mol. This had been the expected product in all

171 three cases; however, the 4-substituted derivative was the only one to yield the actual

radical. For 3-picolinylperoxy radical, displacement of the transition state and minimization to products yielded a complex of 3-picolinal and hydroxyl radical, presumably stabilized by an apparent hydrogen bond between the carbonyl oxygen and the hydroxyl hydrogen; the free energy of reaction for this step was –34.3 kcal/mol, while the infinitely separated 3-picolinal and hydroxyl radical were at –38.3 kcal/mol relative to the initial peroxy radical. The 2-picolinylperoxy radical’s hydrogen-atom transfer was included as a frame of reference; displacement from to the transition state yielded separated products, with a free energy of –33.6 kcal/mol. This unusual reactivity is facilitated by the dual nature of the alkylated heterocyclic peroxy radical. The 1,3-H transfer is of interest given its ability to ultimately form a stable carbonyl species and reactive hydroxyl radical, and will be studied further.

Overall, the picolinylperoxy radicals all demonstrate the kinetic preferences of

ortho cyclization, ipso cyclization, and internal H-transfer over all potential pathways at

298 K. While NOx formation did not seem probable at 298 K due to the high barrier of

the cyclization at nitrogen, the relevant N−O radicals were thermodynamically stable and merited further attention at higher combustion temperatures.

3.4.3 Temperature effects for the picolinylperoxy radicals

As the temperature of combustion increases, dissociative pathways become vastly

more favorable due to entropic effects. These effects can be monitored by calculating the

thermal corrections to enthalpy and free energy at a variety of temperatures. Graphs are

172 provided for the case of 2-picolinylperoxy radical (Figures 3.7 and 3.8). In terms of

thermodynamics, raising the combustion temperature generally increased the enthalpy of

reaction slightly for all pathways considered. As expected, the free energies of reaction

changed dramatically, with the dissociative pathways becoming vastly more exoergic.

This was most evident in the case of atomic oxygen loss (3.2 → 3.6) and dioxirane loss

(3.2 → 3.7), as both these pathways were substantially endoergic at 298 K. The peroxy radical cyclizations generally saw a smaller decrease in free energy of reaction; ortho cyclization at carbon was still preferred over ipso cyclization at carbon at 2000 K.

Notably, both the processes of ortho cyclization at the nitrogen atom (3.2 → 3.4b) and of internal H-transfer followed by scission to hydroxyl and 2-picolinal (3.2 → 3.5) were exoergic at 298 K, and became substantially moreso with increasing temperature.

173

Figure 3.7. Variation in ΔHrxn with temperature for the pathways available to 2- picolinylperoxy radical. 3.2 → 3.3 denoted by open diamond; 3.2 → 3.4a denoted by solid square; 3.2 → 3.4b denoted by open triangle; 3.2 → 3.5 denoted by x; 3.2 → 3.6 denoted by dash; 3.2 → 3.7 denoted by solid diamond. All enthalpies calculated at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory.

174

Figure 3.8. Variation in ΔGrxn with temperature for the pathways available to 2- picolinylperoxy radical. 3.2 → 3.3 denoted by open diamond; 3.2 → 3.4a denoted by solid square; 3.2 → 3.4b denoted by open triangle; 3.2 → 3.5 denoted by x; 3.2 → 3.6 denoted by dash; 3.2 → 3.7 denoted by solid diamond. All energies calculated at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory.

The effects of temperature on barrier heights were also explored for 2-

picolinylperoxy radical (Figures 3.9 and 3.10). The lowest barriers at 298 K involve the peroxy radical processes: cyclizations (TS(3.2-3.3), TS(3.2-3.4a), and TS(3.2-3.4b)) and internal H-transfer (TS(3.2-3.5)). The activation barriers for these four routes were explored at temperatures up to 2000 K. While the activation enthalpies rose slightly over the given temperature range for all four routes, maintaining the relative preferences, the activation energies differed. While activation energies steadily decreased in all four

175 cases, the effect was substantially more pronounced for TS(3.2-3.5). This pathway

competed with TS(3.2-3.3) at 298 K for the second most favorable barrier (TS(3.2-3.4a)

being dominant); near 1250 K, TS(3.2-3.5) overtook all of the other pathways, due to its

greater entropic effects, and became the major high-temperature decomposition pathway.

The H-transfer pathway is unique in that it proceeds through a peroxy radical

rearrangement to yield two products; it exhibits characteristics of both low-temperature

and high-temperature oxidation reactions. Thus, it is not surprising that this reaction

competes across temperature ranges. Notably, TS(3.2-3.4b) continuously demonstrated a

relatively high activation barrier in both low and high temperatures. This is the pathway

that demonstrates the greatest implication for NOx formation; however, it seems as though this hazard would be circumvented at all but the highest combustion temperatures.

176

Figure 3.9. Change in ΔHactivation with increasing temperature, for 2-picolinylperoxy radical. Activation enthalpy for 3.2 → 3.3 denoted by open diamond; activation enthalpy for 3.2 → 3.4a denoted by solid square; activation enthalpy for 3.2 → 3.4b denoted by open triangle; activation enthalpy for 3.2 → 3.5 denoted by x. All enthalpies calculated at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory.

177

Figure 3.10. Change in ΔGactivation with increasing temperature, for 2-picolinylperoxy radical. Activation energy for 3.2 → 3.3 denoted by open diamond; activation enthalpy for 3.2 → 3.4a denoted by solid square; activation enthalpy for 3.2 → 3.4b denoted by open triangle; activation enthalpy for 3.2 → 3.5 denoted by x. All energies calculated at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory.

The enthalpies and energies for the pathways of the 3- and 4-substituted

picolinylperoxy radicals were compiled over varying temperatures (Tables 3.4 and 3.5).

Similar trends were seen for these derivatives; TS(3.2-3.4a) consistently demonstrated the lowest reaction barrier at 298 K, while the dissociative nature of TS(3.2-3.5) made its reaction barrier lowest at 2000 K. Each of these pathways is clearly only the first step in the combustion of these species; subsequent possible steps will be discussed.

178

3-picolinylperoxy radical 3.2 → 3.3 3.2 → 3.4a 3.2 → 3.4b 3.2 → 3.5 3.2 → 3.6 3.2 → 3.7 298 22.5 34.7 25.6 -27.9 57.9 52.4 500 23.7 36.1 26.8 -26.4 59.5 52.3 750 25.4 38.0 28.6 -25.1 61.2 51.5 1000 27.1 40.0 30.3 -24.0 62.9 48.7 1250 28.8 41.5 31.9 -23.0 64.4 49.8 1500 30.4 43.1 33.6 -22.1 65.8 48.9 1750 32.0 44.7 35.1 -21.3 67.2 47.9 2000 33.6 46.3 36.7 -20.5 68.6 47.0

4-picolinylperoxy radical 3.2 → 3.3 3.2 → 3.4 3.2 → 3.5 3.2 → 3.6 3.2 → 3.7 298 35.7 22.0 -28.5 62.6 52.1 500 35.9 22.0 -28.3 62.9 51.6 750 36.1 22.1 -28.5 63.1 50.9 1000 36.2 22.2 -29.0 63.1 50.1 1250 36.4 22.4 -29.6 63.1 49.2 1500 36.5 22.5 -30.3 62.9 48.3 1750 36.6 22.5 -30.9 62.9 47.3 2000 36.7 22.6 -31.7 62.7 46.4

Table 3.4. Variation in enthalpies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*) for 3- and 4-substituted picolinylperoxy radicals, with increasing temperature.

179 3-picolinylperoxy radical 3.2 → 3.3 3.2 → 3.4a 3.2 → 3.4b 3.2 → 3.5 3.2 → 3.6 3.2 → 3.7 298 32.6 21.5 24.5 -40.4 45.7 41.8 500 30.7 20.5 23.5 -49.3 37.1 35.0 750 27.6 18.5 21.1 -61.0 25.4 26.9 1000 23.9 16.0 18.8 -73.1 13.2 19 1250 19.8 13.0 15.7 -85.5 0.7 11.4 1500 15.3 9.7 12.3 -98.1 -12.2 3.9 1750 10.5 6.2 8.6 -110.8 -25.3 -3.8 2000 5.5 2.4 4.7 -123.7 -38.7 -10.6

4-picolinylperoxy radical 3.2 → 3.3 3.2 → 3.4 3.2 → 3.5 3.2 → 3.6 3.2 → 3.7 298 37.6 24.6 -37.2 53.9 41.8 500 38.8 26.3 -43.2 48.0 35.0 750 40.2 28.4 -50.6 40.4 26.9 1000 45.2 30.6 -57.9 32.9 19.1 1250 42.8 32.7 -65.0 25.4 11.4 1500 44.1 32.7 -72.0 17.8 3.9 1750 45.4 36.7 -78.9 10.3 -3.4 2000 46.6 38.7 -85.8 2.8 -10.6

Table 3.5. Variation in free energies of reaction (B3LYP/6-311+G**//B3LYP/6-31G*) for 3- and 4-substituted picolinylperoxy radicals, with increasing temperature.

3.4.4 Ethyl-substituted pyridines (thermodynamics):

The ethyl-substituted pyridinylperoxy radicals were also studied, to gauge the

effect of increasing alkyl substitution on these species’ reactivity (Table 3.6). Overall,

the free energies of both activation and reaction were comparable to those of the methyl- substituted picolines. The dissociative pathway 3.2 → 3.1 saw a larger ΔGo for the

methyl-substituted pyridinylperoxy radicals. This makes sense given the greater stability

that accompanies increasing substitution on an alkyl radical center; the ethyl radicals

180 would be more stable than their methyl counterparts, so dissociation to these more stable

species would be more favorable. The ipso cyclization pathway 3.2 → 3.3 demonstrated

a lower barrier height and a lower energy of reaction for the ethyl derivatives, as did the

H-atom transfer/scission pathway 3.2 → 3.5.

2-Substituted 3-Substituted 4-Substituted Methyl Ethyl Methyl Ethyl Methyl Ethyl 3.1 6.5 5.1 5.6 4.9 5.6 4.2 TS(3.2-3.3) 39.4 37.7 38.2 36.1 40.6 38.4 3.3 35.7 34.1 34.8 32.6 37.5 35.3 TS(3.2-3.4a) 33.2 34.7 35.4 34.2 34.7 33.0 3.4a 23.2 23.8 23.8 22.3 24.5 23.1 TS(3.2-3.4b) 49.8 48.9 36.6 37.2 34.7 33.0 3.4b -4.1 1.8 26.8 27.3 24.5 23.1 TS(3.2-3.5) 39.4 37.8 39.8 38.4 40.1 38.8 3.5 -33.6 -35.7 -38.3 -41.0 -37.4 -40.9 3.6 53.0 48.3 49.3 49.7 53.8 48.7 3.7 38.7 32.4 43.2 36.1 41.6 34.8

Table 3.6. Comparison of free energy profiles (kcal/mol) at 298 K for the picolinylperoxy (methylpyridinylperoxy) and ethylpyridinylperoxy radicals. Where applicable, 4a refers to cyclization at carbon and 4b refers to ortho cyclization at nitrogen. All energies relative to those of the relevant peroxy radical (2) and calculated at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory. For each pair of structures, the more favorable energetic barrier or energy of reaction is indicated by bold italics, to best illustrate the differences in reactivity caused by increasing the length of the alkyl chain.

These results were counterintuitive, since it would seem that the ethyl-substituted

compounds would experience more steric strain in the cyclization steps. The additional

radical stabilization afforded to the ethyl derivatives outweighs these steric effects;

moreover, given the planar nature of both the initial aromatic ring and the newly-formed

181 ring, the additional carbon of the methyl group does not come near the new bond, so the

actual steric strain sustained by the reaction is less than would be imagined.

Ortho cyclization afforded the most varied results. For the 2-substituted

derivatives, the ethyl-substituted pyridinylperoxy radical saw a higher barrier to

cyclization and higher energy of reaction, at carbon (TS(3.2-3.4a)) this might be attributed in part to the greater van der Waal’s forces present in the ethyl derivative, which could have destabilizing interactions with the nitrogen. Interestingly, 2- ethylpyridinylperoxy radical showed a slightly lower barrier to cyclization at nitrogen

(TS(3.2-3.4b)), even while 2-methylpyridinylperoxy radical had a substantially lower energy of reaction for this process. The 3-substituted derivatives likewise exhibited contradictory results. For cyclization at C-2, the ethyl derivative reacted more readily; for cyclization at C-4, the methyl derivative did. This would seem to support our earlier hypothesis that cyclization at C-4 incurs a degree of geometric strain for the 3-substituted derivatives that is not seen in the other ortho cyclization pathway. While in the 3- methylpyridinylperoxy radical, the difference in energy between the two cyclizations was roughly 1.2 kcal/mol, in the 3-ethylpyridinylperoxy radical, this difference was more than

twice as high (3.0 kcal/mol). The additional alkyl group present in the ethyl derivative

increases the strain in the less favorable TS(3.2-3.4b) transition state. Finally, for the 4-

substituted derivatives, 4-ethylpyridinylperoxy radical reacted more readily and formed a

more stable ortho cyclization derivative (the 3.4a and 3.4b pathways were equivalent in

each case due to symmetry) than did 4-methylpyridinylperoxy radical; both the distance

182 from nitrogen and the relative planarity of the newly-formed ring likely contributed to

these effects.

Loss of atomic oxygen (3.2 → 3.6) was approximately 5 kcal/mol more favorable for the 2- and 4-ethyl-substituted derivatives than their methyl counterparts, due to the increased alkyl stabilization of the ethyl oxyradical over the methyl oxyradical.

In the case of substitution at the 3-position, the methyl and ethyl derivatives saw nearly identical free energies of reaction. Our group has previously noted that the unusual reactivity of 3-substituted pyridinyl derivatives, 3-pyridinyloxy radical in particular, and it is plausible that the stability afforded to 3-methylpyridinyloxy radical stems from similar factors. Finally, loss of the side chain (3.2 → 3.7) to form the aromatic radical and cyclized dioxiranyl species was roughly 6 kcal/mol more favorable for the ethyl derivatives regardless of substitution, which must be attributed to the increased stability of methyl dioxirane over dioxirane, since the resulting aromatic radicals are identical.

It is worth reiterating that, in the most likely pathways at 298 K, the differences in energetics were generally less than 2 kcal/mol between the methyl and ethyl derivatives.

Moreover, the trends of the ethyl derivatives echo those of the methyl derivatives: ortho cyclization was the most favorable pathway, followed by ipso cyclization and hydrogen- atom transfer. Thus, the methyl derivatives provide a good qualitative guide for the overall reactions of alkylated heteroaromatic rings, even while the quantitative energies may vary slightly.

183 3.4.5 Diazabenzene trends

From the exhaustive study of the picolinylperoxy radicals, it is evident that of the

cyclization pathways available, two main cyclizations, at the positions ipso and ortho to

the alkyl substitution, will dominate the chemistry at 298 K. Moreover, an internal H-

transfer will compete with both of these cyclization possibilities at 298 K. In certain

cases, a less-kinetically-favorable ortho cyclization pathway yields a stable N−O radical that increases the thermodynamic benefits of this reaction. At higher temperatures, the

dissociative processes of oxyradical formation, aromatic radical formation will see an

entropic benefit that will increase their energetic favorability; the aforementioned H-

transfer ultimately leads to a carbonyl-functionalized aromatic radical and hydroxyl

radical, so is a factor in both low and high-temperature combustion.

The same six pathways (dissociation, ipso cyclization, ortho cyclization, atomic

oxygen loss, dioxirane loss, and internal H-transfer) were considered as the major

combustion pathways for the azabenzylperoxy radicals. The free energies at 298 K for

these pathways were compiled (Table 3.7). Comparing the thermodynamics of these

reactions to those of the picolinylperoxy radicals, it is evident that the second nitrogen

atom does not alter the qualitative trends of reaction; ortho cyclization at carbon still

demonstrates the lowest kinetic barrier, followed by ipso cyclization and hydrogen-atom

transfer. While these two-nitrogen species would seem to double the potential for NOx formation seen in the picolinylperoxy radicals, the barrier of such a process is still prohibitive.

184

Parent Diazabenzene Substitution 3.1 3.3 3.4a 3.4b 3.5 3.6 3.7 Pyridazine 3 6.0 36.5 22.2 -9.1 -32.4 50.5 39.5 4 4.1 35.1 24.7 24.0 -36.8 50.5 39.8 Pyrimidine 2 6.3 37.5 0.2a 0.2b -33.6 52.5 40.4 4 5.8 39.8 25.3 1.1 -31.5 50.9 38.4 5 8.2 33.9 26.2 26.2b -35.2 51.6 45.6 Pyrazine 2 4.4 33.3 21.3 -6.1 -34.1 50.4 37.5 a For 2-methylpyrimidinylperoxy radical, both 4a and 4b refer to ortho cyclization at nitrogen. bOrtho pathways equivalent via symmetry.

Table 3.7. Free energies of reaction at 298 K (kcal/mol) for reaction pathways available to the peroxy radicals of the diazabenzenes. Where applicable, 3.4a refers to cyclization at carbon and 3.4b refers to ortho cyclization at nitrogen. All reaction pathways relative to the peroxy radical (3.2) of the relevant parent compound.

Overall, the picolinylperoxy radicals provide excellent predictive models for the

diazabenzenes; moreover, these peroxy radicals also demonstrate fairly consistent

quantitative energetics. Kinetic barriers and temperature profiles for some reactions of

interest of the diazabenzenes are included in Supporting Information and compare well to the overall energetics of the picolinylperoxy radicals.

3.4.6 Approximations

Calculations were run to determine the validity of the harmonic oscillator

approximation in obtaining the thermal corrections to the enthalpy and entropy (Table

3.8). The lowest-energy vibrations (i.e., the motions of the side chain) were identified

and treated as rotations, using a hindered rotor approximation rather than the harmonic

oscillator. The free energies of reaction reflected small changes in most cases, but these

185 were generally less than 2 kcal/mol. Considering that this variation in approximation

would have the most impact on the entropy of these species, it seems logical that the free energies would see more of an effect than the enthalpies (Supporting Information).

However, these slight quantitative differences did not yield any difference in the relative favorability of the pathways available to the peroxy radicals.

Parent Azabenzene Substitution 3.1 3.3 3.4a 3.4b 3.5 3.6 3.7 Pyridine 2 7.6 36.8 24.3 -3.0 -32.5 53.5 39.9 3 7.1 36.3 25.3 28.3 -36.8 48.4 44.6 4 7.3 37.5 26.0 26.0a -36.0 55.2 43.1 Pyridazine 3 6.7 37.3 22.9 -8.4 -31.7 46.6 40.2 4 6.6 36.7 26.2 25.5 -35.2 48.0 41.3 Pyrimidine 2 7.5 38.7 1.4 1.4a -32.4 48.8 41.5 4 6.5 39.3 24.8 0.6 -32.0 52.6 38.0 5 5.6 35.3 27.6 27.6a -36.7 48.2 44.1 Pyrazine 2 5.2 34.1 22.2 -5.3 -33.2 52.1 38.3 aOrtho cyclization identical via symmetry.

Table 3.8. Free energies of reaction at 298 K (kcal/mol), using rotor approximation in place of harmonic oscillator approximation in calculating the thermal correction to the enthalpy and entropy. Energies calculated at the B3LYP/6-311+G**//B3LYP/6-31G* level of theory.

3.4.7 Subsequent steps

Clearly, the peroxy radical pathways delineated in this article are only the first of

many steps involved in the combustion of these complicated compounds. Overall, logical subsequent pathways can be delineated for the products of several of the peroxy radical pathways discussed, many of which lead into already-established combustion routes.

186 As shown (Figure 3.11), aromatic radicals can be generated either directly or gradually via several of the intermediates discussed above. Following hydrogen-atom transfer and scission (3.5), the resulting 2-picolinal can dissociate into 2-pyridinyl radical and formyl radical. The oxyradical (3.6) can lose its side chain to form 2-pyridinyl radical and formaldehyde; likewise, loss of dioxirane (3.7) directly generates 2-pyridinyl radical.

These aromatic radicals can either cleave the aromatic ring (at high temperatures) to form multiple smaller products or be oxidized at the incipient radical center; these pyrolytic processes are fairly prevalent in the literature, and the oxidative decomposition processes of the non-alkylated aromatic radicals have been thoroughly studied by our group.

Correspondingly, ipso cyclization (3.3) could be followed by re-opening of the four- membered ring to replace the original Cring−Cside_chain bond with a Cring−O bond, then losing formaldehyde to generate the non-alkylated oxyradical. This latter species has again been modeled via previous work in our group.14,15 While the overall decompositions of these species are quite complex, the reactions delineated herein can be viewed as a subset of the chemistry available to these compounds.

187 O N N N O OOCH2 O 3.3 +CH2O

N CHOOH N CHO N O + 3.5 H N CH2OO

+ HO

3.2

N CH2O N

+CH2O 3.6

+O(3P)

N O + O

3.7

Figure 3.11. Subsequent steps available to certain peroxy radical rearrangement products, which could build on extant combustion pathways known for the non-alkylated azabenzyl radicals and oxy radicals.

3.5 Conclusions

Coal combustion has enormous energetic implications, and yet this process is chemically difficult to understand, given the complexity and variation of coal structure.

188 One approach to simplifying this problem is to model the oxidation processes of smaller

aromatic hydrocarbons and heteroaromatic rings, then extrapolate from these smaller

compounds to better understand coal chemistry. In this work, we have delineated key

steps available to the oxidized derivatives of alkylated azabenzenes, mainly using free

energies (298 K) of activation and reaction obtained at the B3LYP/6-

311+G**//B3LYP/6-31G* level of theory.

Benzylperoxy radical was first explored to obtain a qualitative picture of the likely peroxy radical pathways for a species containing both alkyl and aromatic components. From these initial calculations, it was determined that cyclizations at the ipso and ortho positions, relative to side chain substitution, were most likely at 298 K.

Also competitive was an internal 1,3-H transfer that could occur via the side chain of the species, ultimately yielding benzaldehyde and hydroxyl radical. These three pathways were modeled, along with dissociation back to the benzylic-like radical and molecular oxygen, loss of atomic oxygen, and loss of dioxirane; these latter three processes were expected to contribute heavily at high temperatures.

The picolinylperoxy radicals (methylpyridinylperoxy radicals) were explored at

298 K. It was seen that their chemistry mimicked that of benzylperoxy radical: ortho

cyclization at carbon occurred with a barrier of around 30 kcal/mol; ipso cyclization

occurred with a barrier of around 35-40 kcal/mol; internal H-atom transfer occurred with

a barrier of roughly 40 kcal/mol. The additional functionality afforded by the nitrogen

atom allowed a cyclization resulting in a stable N−O radical, which has the potential for

NOx chemistry; however, this process had a substantially high barrier (~50 kcal/mol) and

189 was unlikely to be a factor at atmospheric temperatures. The energetics of the 2-

picolinylperoxy radical were closely compared to those of benzylperoxy radical, since the only difference between them was a nitrogen atom. It was seen that while the qualitative trends were replicated between benzylperoxy radical and its nitrogen analogue, 2- picolinylperoxy radical had slightly higher activation barriers and energies of reaction in nearly every case, which was attributed to the relative stabilization of the allylic systems in the cyclized derivatives of the two species. Additionally, CBS-QB3 calculations were performed on both benzylperoxy and 2-picolinylperoxy radical and demonstrated that the

DFT approach performed well in replicating the trends seen via the CBS method.

Temperature effects were explored; over the range 298 to 2000 K, the inherently

dissociative processes (atomic oxygen loss, molecular oxygen loss, dioxirane loss) saw a

large entropic benefit and became substantially exoergic. The rearrangement pathways

decreased somewhat in energy, as did the kinetic barriers to these processes. Notably, the

hydrogen-atom transfer pathway saw the most precipitous drop in its barrier and became

the dominant processes around 1250 K. This reaction was of considerable interest given

its relevance to both low-temperature and high-temperature combustion, as a

rearrangement pathway that culminates in dissociation to a stable aldehyde-

functionalized heteroaromatic compound and hydroxyl radical. Even at higher

temperatures, it was seen that the reaction resulting in N−O radical formation occurred

with a barrier substantially higher than that of other rearrangements; this process likely

only contributes minimally and at extremely high flame temperatures to NOx formation.

190 The effects of increasing alkyl substitution were explored. It was seen that the same rearrangement pathways were favored for the ethylpyridinylperoxy radicals as for their methyl counterparts. Generally, the energies of activation and reaction for the most likely pathways were comparable, within 2 kcal/mol of one another, which suggests that the methyl compounds can provide good models for the alkylated heteroaromatic rings in general. Small differences in reaction energetics were attributed to inductive effects of the nitrogen atom and to differing amounts of geometric strain introduced via cyclization, where applicable.

After the picolinylperoxy radicals had been thoroughly modeled, these results were compared to the energies of reaction for the relevant processes of the alkylated diazabenzenes (pyridazine, pyrimidine, and pyrazine). It was seen that the presence of a second nitrogen atom had little effect on either the identity or the energetics of the preferred pathways.

Finally, due to the presence of low-energy torsions in the alkylated peroxy side chain, the effect of changing from a harmonic oscillator approximation to a rotor approximation in the case of these lowest vibrations was explored for all the methylazabenzylperoxy radicals. It was seen that this change did slightly affect the thermal corrections to the enthalpy and entropy and was most evident in the free energies of reaction. However, these changes were small (< 2 kcal/mol) and did not affect the relative preferences of the pathways.

In summary, these findings suggest that the overall chemistry of the alkylated heterocyclic peroxy radicals is consistent regardless of alkyl substitution or number of

191 nitrogen atoms. The picolinylperoxy radicals provide excellent models for the chemistry exhibited by this larger class of species. Moreover, aromatic hydrocarbons can themselves predict several aspects of this chemistry, the exception being those processes involving oxidation or rearrangement at the nitrogen atom itself. Subsequent work in this area will explore comparable pathways for the five-membered heteroaromatic rings, in an attempt to discern the effects of both ring size and of different heteroatoms on the favorability of these reactions. It is hoped that these studies of models for coal chemistry will elucidate key combustion processes of this important energy source.

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