Electronic Spectroscopy of the Alkoxy Radicals

Home , Structural isomer

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate

School of The Ohio State University

Sandhya Gopalakrishnan, B.Sc., M.Sc.

*****

The Ohio State University

2003

Dissertation Committee: Approved by

Terry A. Miller, Adviser Heather C. Allen Adviser Bern Kohler Department of Chemistry Abstract

Alkoxy radicals were produced in a supersonic free-jet expansion and probed via laser induced ﬂuorescence spectroscopy. Over 20 alkoxy radicals (CnH2n+1O) containing from 3-12 carbon atoms were investigated at moderate (0.1 cm−1) resolution by prob- ing the B − X electronic transition to obtain vibrationally resolved spectra. The interpretation of these spectra in terms of serving as a diagnostic for detection and excited state vibrations and/or diﬀerent conformations is discussed.

The diagnostics for the alkoxy radicals was further extended by studies aimed at obtaining their molecular structure. A few bands in the vibrationally resolved spectra of the primary alkoxy radicals, 1-propoxy, 1-butoxy, and 1-pentoxy were studied under high (0.01 cm−1) resolution to resolve the rotational structure. A method for the detailed rotational analysis of these bands was developed which involved a comparison of the experimentally determined molecular constants with those obtained from quantum chemistry computations. The rotational constants of the ground and excited states as well as the spin-rotation constants in the ground state were obtained from these spectra. A rotational bar-coding technique was used to assign the vibronic bands based upon the principle that the rotational structure of a given vibronic band bar-codes for the species carrying the spectrum. The assigned bands can be used as unambiguous diagnostics of the radical species, its structural isomer, and

ii its conformation. The spectra also shed light on the dynamical properties of these radicals which will be important in ultimately understanding their photochemistry.

iii To My Parents Devanayaki & H. Gopalakrishnan

iv Acknowledgments

There have been several people who have been instrumental in making my experience as a graduate student rewarding and memorable. The list of all these people would be far too long, but there are some people I would like to mention here.

First, I would like to thank my advisor, Terry Miller, for his constant guidance and support, and giving me a training in science beyond my imagination. Next, I have to thank Chris to whom I owe a lot of what I know about the hi-res system.

Without his active encouragement, I would not have embarked upon the alkoxy saga

(which turned out to be pretty good in retrospect).

It was a wonderful experience to work with all the other members, past and present, of the Miller group. I would like to thank co-authors and members of the alkoxy gang - Gyuri, Lily, and Vadim. Thanks to Dmitry for introducing me to microwave spectroscopy before I started working on the alkoxies. I would like to thank fellow graduate students Sergey, Brent, Jinjun, and Ilias as well as Andy and

Patrick for some great times.

Outside the lab, Becky has been a wonderful friend and support from the begin- ning. I thank her for the coﬀee breaks without which I would not have ﬁnished my dissertation, and the delicious treats that brightened many days.

I thank my parents who constantly encouraged me and took great pride in my progress in this endeavor. Without their selﬂess acts, I would have never made it.

v I am also indebted to my sister and brother and their families for their constant support and help in every possible way. They made my transition into life in the

United States easy and eﬀortless. My in-laws have stood by me at all times. I thank them for their encouragement. Finally, I would like to thank my husband for being there at all times and bringing cheer when life in the lab was bleak.

vi Vita

1974 ...... Born,Secunderabad, India

1995 ...... B.Sc., Chemistry,Physics, Mathemat- ics, St. Francis’ College, Hyderabad, India 1997 ...... M.Sc.,Chemistry,UniversityofHyder- abad, Hyderabad, India 1997-1998 ...... Graduate Teaching Assistant, Depart- ment of Chemistry, The Ohio State University 1998-present ...... GraduateReasearchAssistant, Depart- ment of Chemistry, The Ohio State University

Publications

Sandhya Gopalakrishnan, Christopher C. Carter, Lily Zu, Vadim L. Stakhursky, Gy- orgy Tarczay, and Terry A. Miller, Rotationally resolved B − X spectra of both conformers of the 1-propoxy radical. J. Chem. Phys. 118(11) pp. 4954–4969 , 15 March 2003.

Christopher C. Carter, Sandhya Gopalakrishnan, Jeﬀrey R. Atwell and T. A. Miller, Laser excitation spectra of large alkoxy radicals containing 5-12 carbon atoms. J. Phys. Chem. 105(13) pp. 2925–2928, 5 April 2001.

Christopher C. Carter, Jeﬀrey R. Atwell, Sandhya Gopalakrishnan and T. A. Miller, Jet-cooled laser-induced ﬂuorescence spectroscopy of some alkoxy radicals. J. Phys. Chem. 104(40) pp. 9165–9170 , 24 July 2000.

Dmitry G. Melnik, Sandhya Gopalakrishnan, T. A. Miller, and F. C. DeLucia, The absorption spectroscopy of the lowest pseudorotational states of tetrahydrofuran. J. Chem. Phys., 118(8), 3589-3599, 22 February 2003.

vii Dmitry G. Melnik, Sandhya Gopalakrishnan, T. A. Miller, F. C. DeLucia, and Sergey Belov, Submillimeter wave vibration-rotation spectroscopy of Ar·CO and Ar·ND3. J. Chem. Phys., 114(14), 6100-6106, 8 April 2001

Fields of Study

Major Field: Chemistry

viii Table of Contents

ABSTRACT...... ii

DEDICATION...... iv

ACKNOWLEDGMENTS...... v

VITA...... vii

LISTOFFIGURES...... xi

LISTOFTABLES...... xix

CHAPTER PAGE

1 Introduction...... 1

2 Experimental...... 7

2.1Introduction...... 7 2.2AlkoxyRadicalProduction...... 7 2.3LIFexperimentalapparatus...... 11 2.3.1 Moderate resolution LIF apparatus ...... 11 2.3.2 High-resolutionLIFapparatus...... 13 2.3.3 Frequencycalibration...... 15

3 Theory...... 17

3.1Introduction...... 17 3.2Hamiltonian...... 19 3.2.1 Matrix Elements and Eﬀects of HRot and HSR ...... 22 3.3 Quantum Chemistry Computations and Predicted Molecular Param- eters...... 29 3.3.1 Introduction...... 29

ix 3.3.2 Method...... 30 3.3.3 ComputationalMethods...... 38

4 ModerateResolutionLIFSpectra...... 39

4.1Introduction...... 39 4.2Results...... 41 4.2.1 Propoxy...... 41 4.2.2 ButoxyIsomers...... 50 4.2.3 PentoxyIsomers...... 55 4.2.4 HigherAlkoxyRadicals...... 57

5 High-ResolutionSpectroscopyof1-Propoxy...... 66

5.1Introduction...... 66 5.2Results...... 66 5.2.1 Results...... 67 5.2.2 1-propoxy,TConformer...... 70 5.2.3 1-Propoxy,GConformer...... 83 5.2.4 Discussion...... 95

6 High-ResolutionSpectroscopyof1-Butoxy...... 101

6.1Introduction...... 101 6.1.1 Results...... 104 6.1.2 1-Butoxy Conformer T1T2 ...... 107 6.1.3 Conformer G1T2 -BandA...... 119 6.1.4 1-Butoxy Conformer T1G2 ...... 126 6.1.5 Discussion...... 132 6.1.6 ElectronicOrigins...... 134 6.1.7 ConformationalSelectivity...... 136

7 High-ResolutionSpectroscopyof1-Pentoxy...... 138

7.1Introduction...... 138 7.2Results...... 138 7.2.1 Discussion...... 157 7.2.2 ConformationalSelectivity...... 159

8 Conclusions...... 162

BIBLIOGRAPHY ...... 171

x List of Figures

FIGURE PAGE

1.1 Simpliﬁed scheme for “low-temperature” alkane oxidation...... 2

2.1Alkoxyradicalproductioninasupersonicjet...... 10

2.2Moderateresolutionexperimentalapparatus...... 12

2.3High-resolutionexperimentalapparatus...... 14

3.1Orbitalpictureoftheoxygenatom...... 18

3.2Bondingschemeinmethoxy...... 18

3.3Energyleveldiagramofmethoxyandethoxy...... 20

3.4Conformationsof1-propoxy...... 31

3.5 a) Values for 1-butoxy of the dihedral angles φ1 and φ2 (staggered) for which local minima occur. b) Structures of ﬁve unique conformers of 1-butoxy corresponding to the combination of angles φ1 and φ2 at their localminima...... 33

3.6 Structures of fourteen unique conformers of 1-pentoxy at their local minima. The corresponding Newman projections of are also shown. . 35

4.1 Structural isomers of propoxy and butoxy radicals...... 42

4.2LIFexcitationsurveyspectrumof1-propoxy...... 43

4.3LIFexcitationsurveyspectrumof2-propoxy...... 43

xi 4.4 Comparison of the LIF excitation spectra of 2-propoxy taken in A) supersonic jet, B) room temperature (by Balla et al.)...... 44

4.5 Low frequency region of the 2-propoxy spectrum...... 46

4.6 Moderately high-resolution spectra of bands A and B of 1-propoxy. The rotational contours of the two spectra are clearly diﬀerent. . . . . 48

4.7 Simulations of the rotational contours of bands A and B of 1-propoxy using the calculated rotational constants of the two conformers G and T respectively (see chapter 3) of 1-propoxy. The rotational temperature for both spectra was 3K. The ratios of the transition dipole moments are a:b:c=0:0:1 for band B and 1:1:2 for band A as obtained from our ab initio calculations on the B state...... 49

4.8 Survey jet-cooled LIF excitation spectra of the structural isomers of butoxy:, a) 1-butoxy, b) 2-butoxy, and c) t-butoxy...... 51

4.9 Rotational contours of bands A and B of 1-butoxy. The simulations shown were obtained by using the calculated rotational constants of conformers G1T2 and T1T2 respectively (see chapter 3) of 1-butoxy. The rotational temperature for both spectra was 3K. The ratios of the transition dipole moments are a:b:c=0:0:1 for band B and 2:1:3 for bandA...... 54

4.10Surveyscansofthefourisomersofpentoxy...... 56

4.11 Survey scan of the jet-cooled LIF excitation spectra of the primary (1-) alkoxy radicals, CnH2n+1O, for n=3-10. “Persistent” lines in the spectrum are marked A and B, see text for further details...... 58

4.12 Survey scan of the jet-cooled LIF excitation spectra of the secondary (2-) alkoxy radicals, CnH2n+1O, for n=3-10. “Persistent” lines in the spectrum are marked A and B, see text for further details. Essentially no LIF signals, except for propoxy, are observed to frequencies higher thanthoseshown...... 59

xii 4.13 a) Moderately high-resolution (≈0.1 cm−1) scans of the “origin” bands of the 2-alkoxy radicals. Some rotational structure is apparent even for the largest radical, b) Moderately high-resolution (≈0.1 cm−1)scans of band A of the 2-alkoxy radicals (see Fig. 4.12). The rotational structures of the origin band and band A for each radical are clearly diﬀerent, indicating the presence of two diﬀerent conformers...... 62

4.14 Frequencies of apparent origin bands of the observed alkoxy radicals plotted vs number of carbon atoms in the radical. The grouping of the radicals into families based on the nature of the isomer is clearly apparent...... 63

4.15 Moderately high-resolution (≈0.1 cm−1) scans of the “origin” bands of the 1-alkoxy radicals. Some rotational structure is apparent even for the largest radical and a red shift in the origin frequencies is discernable withincreasingsizeoftheradicals...... 64

4.16 Survey LIF spectra of some miscellaneous alkoxy radicals...... 65

5.1Overviewof1-propoxysurveyLIFspectrum...... 68

5.2 Rotationally resolved spectra of bands, marked A through E in spec- trumof1-propoxyshowninFig.5.1...... 69

5.3 Conformers of 1-propoxy; a) Conformer G, b) Conformer T...... 70

5.4 a) High-resolution spectrum of 1-propoxy band A, b) Simulation of rotational structure of the B˜ − X˜ transition using the calculated rotational constants of the G conformer, c) Simulation of rotational structure of the B˜ − X˜ transition using the calculated rotational constants of the T conformer, d) High-resolution spectrum of 1-propoxy band B. For both simulations, for the simulation the relative weights of the transition dipole moment components are obtained from the ab initio calculations on the B˜ excited state and the rotational temperature is takentobe1.1K...... 71

5.5 a) Simulation of band B using calculated ground and excited state rotational constants of 1-propoxy T conformer, at 1.1 K with a pure c-type transition moment (demanded by symmetry for a A-A transition). The assignments are made using a prolate asymmetric top notation, b)ExperimentalspectrumofbandB...... 73

xiii 5.6 Illustration of splitting of the |K|=1 transitions. The splitting of the R1 transition is determined uniquely by the constant (a0 + a/2). The splitting of the two pairs of asymmetric doublets of the R2 and R3 transitions is also eﬀected by this constant (although not uniquely). a) Experimental spectrum, b) simulation of B−X transition of conformer T using calculated rotational constants with no spin-rotation coupling, c) simulation after adding the calculated value of one combination, (a0 + a/2), spin-rotation constants, of d) simulation after ﬁtting three linear combinations of the rotational constants in the excited state, and (a0 + a/2)...... 78

5.7 Illustration of splitting of the R3(K =0) transition upon adding the spin-rotation constant (a0 − a). a) Experimental spectrum of band B, b) Simulation with reﬁned constants after adding (a0 + a/2), c) Simulation after adding the calculated value of (a0-a) and ﬁtting all B+C linear combinations of rotational constants in the excited state, 2 , B−C 2 ,and(a0 + a); d) Addition of calculated values of the spin- rotationconstantsb,anddtosimulationc)...... 80

5.8 Simulation of band B using the experimentally determined rotational and spin-rotation constants from the ﬁt of band B. a) Experimental spectrum of band B, b) Simulation. The rotational temperature is 1.1 K and the ratio of the squares of the dipole moment is a:b:c=0:0:1 as demanded by the Cs symmetry of this conformer...... 84

5.9 a) Experimental spectrum of 1-propoxy band A, b) Simulation using calculated rotational constants of 1-propoxy G conformer without spin- rotation coupling, c) Simulation using calculated rotational and spin- rotation constants of 1-propoxy G conformer. The ratios of the square of transition dipole moments are a:b:c=1:1.1:4 (obtained from ab initio calculations on the excited state). The rotational temperature is 1.1 K. 86

5.10 Effect of spin rotation on transitions involving |K| >0. a) Red end of experimental spectrum, b) Simulation of band A using calculated rotational constants of both states but with no spin-rotation coupling, c) Addition of the calculated value of one spin-rotation constant, (a0 + a), d) Simulation after refining one linear combination of the rotational constants in the excited state. The discrepancy between the frequencies in d and a is due to the fact that all the molecular constants have not beenfit...... 87

xiv 5.11 The spectrum of band A may be assigned by systematically ﬁtting one constant at a time and successively “improving” the simulation (see text for details). a) Experimental spectrum of band A of 1-propoxy; b) Simulation of B˜ − X˜ transition of G conformer using calculated rotational constants and zero spin-rotation coupling; c) Simulation using calculated values of all rotational and spin-rotation constants and B+C ﬁtting 2 after making the assignments shown (using solid lines) in Fig. 5.10. The additional assignments shown using solid lines, can nowbemade...... 89

5.12 a) Experimental spectrum of band A of 1-propoxy; b) Simulation of X˜ − B˜ transition of G conformer with ﬁt rotational constants in both states and calculated spin-rotation constants; c) Simulation after making several more assignments (not shown) and ﬁtting all rotational and spin-rotationconstants(seetextfordetails)...... 90

5.13 a) Comparison of the experimental spectrum of band A to its simulation using the ﬁt molecular parameters of Table 5.4. The rotational temperature is 1.3 K, b) Simulation of rotationally hot spectrum. The rotational spectrum is 3 K. The ratio of the components of the transition dipole along the inertial axes is a:b:c=2:1:3 as taken to best reproducetheobservedspectralintensities...... 91

5.14 Blow-up of a 1 cm−1 region of the rotationally hot spectrum. a) Ex- perimental, b) Simulation at 3 K after ﬁtting cold spectrum...... 93

6.1 1-butoxy survey LIF spectrum ...... 102

6.2 Rotationally resolved spectra of bands A through E in 1-butoxy. . . . 103

6.3 The ﬁve unique conformers of 1-butoxy ...... 105

6.4 Simulations of the B −X transitions of the ﬁve conformers of 1-butoxy using calculated rotation and spin-rotation constants. The rotational temperature is 1.5 K and the ratios of the square of the electric dipole moment a:b:c were taken from the B state calculations and are respectively 17:1:8, 0:0:1, 1:14:13, 1.5:1:2.3, and 1:0:1.5 for conformers G1T2 , T1T2 ,T1G2 ,G1G2 ,andG1G2 ...... 108

xv 6.5 Comparison of the experimental spectrum of band A of 1-butoxy with the simulations of the B − X transitions of the ﬁve conformers of 1- butoxy using calculated and rotation and spin-rotation constants. . . 109

6.6 Comparison of the experimental spectrum of band B of 1-butoxy with the simulations of the B − X transitions of the ﬁve conformers of 1- butoxy using calculated and rotation and spin-rotation constants. . . 110

6.7 Comparison of the experimental spectrum of band C of 1-butoxy with the simulations of the B − X transitions of the ﬁve conformers of 1- butoxy using calculated and rotation and spin-rotation constants. . . 111

6.8 a) Low frequency end of the experimental spectrum of band B, b) Simulation of the B˜ − X˜ transition of T1T2 conformer of 1-butoxy (relative intensity of dipole components, µα,a:b:c=0:0:1), c) Addition of calculated value of one spin-rotation constant (a0 + a/2) that splits transitions with |K|=1, d) Simulation after fitting two linear combinations of the rotational constants, e) Simulation after fitting five linear combinations of the rotational constants and the spin-rotation constant (a0 + a/2)...... 114

6.9 a) Portion of experimental spectrum of band B of 1-butoxy, b) Simu- lation of the B˜ − X˜ transition of T1T2 conformer showing the |K | = 1 ↔ K = 0 R branch transitions using a rigid-rotor Hamiltonian with no spin-rotation, c) simulation upon adding the calculated value of the spin-rotation constant a0 − a; the splitting of the R2 and R3 transitions is noticeable, d) Simulation after adding the calculated value of the spin-rotation constant d.TheR4 transition (marked with an asterisk) which was more split before adding this constant looks more like the experimental transition due to the addition of this oﬀ-diagonal constant. Thus these two spin-rotation constants can be determined fromthisportionofthespectrum...... 115

6.10 Comparison of experimental sepctrum and simulation based upon ﬁt constants (Table 6.2) for band B and conformer T1T2 of 1-butoxy. a) Experimental spectrum of band B, b) Simulation using ﬁt constants. The ratio of the square of the transition electric dipole moment a:b:c=0:0:1 and the rotational temperature is 1.15 K...... 117

xvi 6.11 Spin-rotation in 1-butoxy conformer G1T2 : a) Simulation using calculated rotational constants without spin-rotation, b) splitting of transitions upon adding the calculated values of all six spin-rotation constants, c) ﬁt of one linear combination of the rotational constants in theexcitedstate,d)Experimentalspectrum...... 121

6.12 Spin-rotation coupling in conformer G1T2 of 1-butoxy: a) expanded view of experimental spectrum of band A showing two Q-branches (in boxes), b) simulation using refined (fit) rotational constants as demonstrated in Fig. 6.11, c) Simulation obtained after fitting all three linear combinations of the rotational constants in the ground state, d) simulation after fitting all six linear combinations of rotational constants in the ground and excited states, e) Simulation after fitting the spin-rotation constants (a0 + a/2), (a0 − a)andb, f) Simulation after fitting six linear combinations of the rotational constants and five spin-rotationconstants(seetextfordetails)...... 123

6.13 Comparison of the experimental spectrum with the simulation based upon ﬁt constants (Table 6.4) for band A and conformer G1T2 fo 1- butoxy. The ratio of the square of the transition electric dipole moment a:b:c is 10:2:9 (the calculated values are 17:1:8) and the rotational temperatureis1.2K...... 124

6.14 a) Experimental spectrum of band C, b) Simulation of B − X transition of conformer T1G2 of 1-butoxy using only calculated rotational constants, c) Simulation with spin-rotation turned on using the calculated values of the spin-rotation constants, d) Simulation after fitting one linear combination of the rotational constants in the excited state, e) Simulation after fitting all three linear combination of the rotational constants in the excited state, f) Simulation after fitting all six linear combinations of the rotational constants in the ground and excited states, g) Simulation after fitting all six rotational constants and the spin-rotation constant (a0 + a/2), h) Simulation after fitting all six rotational constants and four spin-rotation constants...... 129

6.15 Comparison of experimental sepctrum and simulation based upon ﬁt constants (Table 6.5) for band C and conformer T1G2 of 1-butoxy. The ratio of the squares of the transition electric dipole moments a:b:c=3:7:7 (the calculated values are 1:14:13) and the rotational temperature is 1.0K...... 130

xvii 7.11-pentoxysurveyLIFspectrum...... 140

7.2 Rotationally resolved spectra of bands A, G, C, F, J, and K of 1-pentoxy141

7.3 Rotationally resolved spectra of bands B, I, a,E,H,andDof1-pentoxy142

7.4 Structures of fourteen unique conformers of 1-pentoxy at their local minima. The corresponding Newman projections of are also shown. . 143

7.5 Simulations of the B−X transition using the calculated rotational and spin-rotation constants of ﬁve conformers of 1-pentoxy. The similarity intheoverallrotationalproﬁlesisevident...... 145

7.6 Comparison of experimental spectra with simulations based upon ﬁt constants (Table 7.3) for band A and conformer G1T2T3 of 1-pentoxy, band a and conformer G1T2G3 , and band E and conformer T1G2T3. The ratio of the square of the electric dipole moments a:b:c are respectively 3:1:2, 1:4:6, and 1:8:10 for bands A, a, and E (the calculated values are respectively 2:1:4, 1:8:12, and 1:10:13). The rotational temperatures are 1.5, 1.3, and 1.3 K respectively for bands A, a, and E. . 149

7.7 Comparison of experimental spectra with simulations based upon ﬁt constants (Table 7.3) band B and conformer T1T2G3, and band C and conformer T1T2T3. The ratio of the square of the electric dipole moments a:b:c are respectively 1:2:4 and 0:0:1 for bands B and C (the calculated values are respectively 1:6:2 and 0:0:1). The rotational tem- peratureis1.3Kforbothbands...... 150

7.8 Comparison of experimental spectrm of band D with simulations using the calculated rotational and spin-rotation condtants and ratio of the square of the electric dipole moment a:b:c of 4 “cyclic” conformers of 1-pentoxy having similar rotational constants in both the ground and excited states (Tables 7.1 and 7.2). The poor S/N ratio of band D and the large number of possible conformer candidates prevented a deﬁnite assignment for this band from being made...... 151

xviii List of Tables

TABLE PAGE

3.1Symmetrydesignationofrotorlevels...... 26

4.1 Some low frequency (below the C-O stretch) vibrations observed in the spectrumof2-propoxy...... 46

4.2 Origin and C-O stretch frequencies for various alkoxy radicals . . . . 52

5.1 Calculated ground and excited state constants of the diﬀerent conform- ersof1-propoxy...... 74

5.2 Molecular constants of T conformer of 1-propoxy. The constants reported for the ground state are the standard deviation weighted average of the constants obtained in the ﬁt of the three individual bands B, D, and E. The excited state constants are those corresponding to the vibrationless band in the B˜ state...... 81

5.3 Results of the independent ﬁts of bands B, D, and E of 1-propoxy. T00 −1 −1 −1 (cm )=29218.54(1), T0D (cm )=T00+238.26(1), T0E (cm )=T00+676.32(1) 82

5.4 Molecular constants of G conformer of 1-propoxy. The ground state constants are the stantard deviation weighted average of the constants obtained from independent ﬁts of bands A and C. The excited state constants are those corresponding to the vibrationless level of the B˜ stateobtainedfromtheﬁtofbandA...... 92

5.5 Results of the independent ﬁts of bands A and C of 1-propoxy. The spin-rotation constants c and e could not be determined from the ﬁt ofbandC...... 94

5.6 Spin-rotation constants of T and G conformers of 1-propoxy . . . . . 100

xix 6.1 Calculated ground and excited state constants, and relative energies of the diﬀerent conformers of 1-butoxy. The relative energies were calcualted with zero point energy correction...... 106

6.2 Experimentally determined molecular constants of conformer T1T2 of 1-butoxy. The calculated constants are those predicted from the quantum chemistry calculations. Experimental ground state constants were obtained by averaging over all the vibrational bands (D and F) observed while the excited state constants are those for the vibrationless level obtained from ﬁtting the origin band B...... 116

6.3 Results of the independent ﬁts of bands B, D, and F of 1-butoxy. T00 −1 −1 −1 (cm )=29095.28(1), T0D(cm )=T00+168.55(1), T0F (cm )=T00+670.91(1).118

6.4 Molecular constants of conformer G1T2 from the ﬁt of band A of 1- butoxy...... 125

6.5 Molecular constants of conformer T1G2 of 1-butoxy. The ground state constants are the standard deviation weighted average of the constants obtained from the ﬁts of bands C and E while the excited state constants are those corresponding to the vibrationless level obtained from ﬁttingtheoriginbandC...... 128

6.6 Results of the independent ﬁts of bands C and E. The spin-rotation −1 constants d and c could not be determined from the ﬁts. T00(cm )=29163.73(1) −1 and T0E(cm )=T00+199.83(1)...... 131

6.7 Vibrational assignments of the bands of 1-butoxy. νCO is the C-O stretch and νCCO is the backbone C-C-O deformation...... 132

6.8 Spin-rotation constants of conformers G1T2 ,T1T2 ,andT1G2 of 1- butoxy...... 136

7.1 Calculated ground and excited state rotational constants in GHz of the diﬀerent conformers of 1-pentoxy as obtained at the B3LYP/6-31+G* leveloftheory...... 144

7.2 Predicted ground-state electron spin-molecular rotation constants (in GHz)ofthe14conformersof1-pentoxy...... 144

xx 7.3 Experimentally determined rotational and spin-rotation constants (in GHz) from ﬁve sets of rotational bands of 1-pentoxy. The ground state constants correspond to an average of the values from all bands, weight inversely by the standard deviation, σ. The excited state constants correspond to the vibrationless level obtained from the ﬁts of the origin bands A, C, B, a, and E respectively. The calculated constants of the assigned conformers (whose calculated values most closely match the experimentalones)aregiveninbrackets...... 152

7.4 Results of the independent ﬁts of bands A and G of 1-pentoxy. The spin-rotation constants e could not be determined from the ﬁt of band G and was frozen at the calculated value given in Table 7.3 for con- 0 −1 0 −1 former G1T2T3 .T0(cm ) = 28643.38(1), TG(cm ) = 29277.65(1) . 153

7.5 Results of the independent ﬁts of bands C, F, and J of 1-pentoxy. The 0 −1 ﬁts of all three bands were done by freezing ˜cc at 0.00. T0(cm )=29012.82(1), 0 −1 0 −1 TF (cm )=29140.80(1), TJ (cm )=29683.47(1) ...... 154

7.6 Fits of bands B and I of 1-pentoxy. The spin-rotation constants c could not be determined from the ﬁt of band B, while the spin-rotation constants c and e could not be determined from the ﬁt of band I. These constants were frozen at the calculated values given in Table 7.3 for 0 −1 0 −1 conformer G1T2G3 .T0(cm )=28986.98(1), TI (cm )=29653.41(1) 155

7.7 Fits of bands E and H of 1-pentoxy. The spin-rotation constants c could not be determined from the ﬁt of band B, while the spin-rotation constants b, d, c and e could not be determined from the ﬁts of bands E and H and were frozen at the calculated values given in Table 7.3 0 −1 0 for conformer T1G2T3 .T0(cm ) = 29121.57(1), TH = 29232.21(1). 156

7.8 Vibrational assignments of the bands of 1-pentoxy. νC−O is the C-O stretch and νC−C−O is the backbone C-C-O deformetion...... 158

xxi CHAPTER 1

Introduction

The oxidation of hydrocarbons is among the most important, and the most complex, of chemical processes. It is critical to the combustion of fossil fuels, from which the majority of energy for anthropogenic use is derived. It is also of great importance for the degradation of organic molecules injected into our atmosphere. Free radicals are key components in this oxidation chemistry and the simplest oxygen-containing organic radicals are alkoxy (RO) and peroxy (RO2), the former species being the focus of this thesis.

The chemistry of the alkoxy radicals has been fairly well investigated.1–3 The low-temperature chemistry of propane and larger alkanes is shown in Fig. 1.11 at temperatures between about 500 and 1000 K.

1 Q = -CH2-CH2-CH2

Figure 1.1: Simpliﬁed scheme for “low-temperature” alkane oxidation.

2 In addition to the branching reaction shown in Fig. 1.1 that leads to the formation of alkoxy radicals, the peroxy radicals formed in low temperature alkane oxidation

(Fig. 1.1) can react and decompose to produce alkoxy radicals:

RO2 · +RO2·→ROOR + O2 → 2RO · (1.1)

ROOH → RO · + · OH (1.2)

(1.3)

It is also well known that alkoxy radicals play a key role in atmospheric chemistry and are formed in the degradation of volatile organic compounds as shown in the scheme below:2

OH + RH → H2O + R (1.4)

R + O2 → RO2 (1.5)

RO2 + NO → RO + NO2 (1.6)

The reactions of alkoxy radicals in the atmosphere are very important and hence of great interest. The most important reactions are decomposition, reaction with O2 and isomerization.2

The reactions of the alkoxy radicals have predominantly been studied via laser induced ﬂuorescence spectroscopy. The spectroscopic characterization of these radicals is thus a prerequisite for kinetics work. However the spectroscopy of all but the smallest alkoxy radicals is relatively unknown and this has proved to be a stumbling block in studying the kinetics of larger alkoxy radicals.

3 The spectroscopy of the smallest alkoxy radicals is well studied, with detailed

4–9 10–13 spectral analyses having been reported for CH3O and C2H5O, with less de-

14, 15 tailed work on isopropoxy, 2-C3H7O. For many years, the spectra of other (larger) alkoxy radicals were unknown. While the smaller alkoxy radicals have the strongly

ﬂuorescent B − X transition in the near ultra violet, conventional wisdom appears to have been that the quantum yield for this transition in the larger radicals would rapidly decrease as non-radiative processes become dominant. Even if some ﬂuores- cence would be observed, it was expected that the resulting spectra would be very complex and congested and unlikely to yield much useful information.

This situation began to change recently with reports of the laser induced ﬂuores- cence (LIF) spectrum of 2- and t-butoxy16 and 3- and t-pentoxy17 at near ambient temperatures by Wang et al. However they reported the failure to observe structured

LIF spectra from 10 other butoxy, pentoxy, and hexoxy structural isomers. Further- more, the four reported LIF spectra did little to dissuade the notion that the spectra of the larger alkoxy radicals would be congested and complex. Their spectra stimu- lated us to try to obtain simpler, jet-cooled LIF spectra of these species. Such spectra can give us valuable information on the photophysical and dynamical properties of these radicals.

The alkoxy radicals are rich in structural and conformational isomerism. High- resolution spectroscopy oﬀers the opportunity to characterize molecular systems in great detail. We can, for example, get information on the structure of the carrier of the spectra and the nature of chemical bonding in the molecule.

4 The rotational structure serves as a ﬁngerprint for the molecule bearing the spectrum and can thus be used as a diagnostic. Furthermore, the database comprising the results of the analyses of alkoxy radical spectra will serve as a benchmark to test ab initio methods.

Given both the fundamental and practical importance of the alkoxy radicals, we undertook the task of developing laser diagnostics to characterize these species. More than 20 large alkoxy radicals were investigated via laser induced ﬂuorescence spectroscopy in a supersonic free jet under moderate resolution to obtain vibrationally resolved spectra. Of these, the primary alkoxy radicals were investigated further under higher resolution to obtain rotationally resolved spectra of a few selected vibronic bands. Detailed analyses of the spectra of the primary alkoxy radicals were carried out to yield important information on their structure and photophysics.

The work described in this thesis has been organized into eight chapters. In this chapter, the importance of alkoxy radicals and the motivation for this study was described. The next chapter describes the experimental apparatus used to obtain the spectra in detail. The particular techniques used to produce the alkoxy radicals and the importance of supersonic jet expansions is also discussed.

Chapter 3 gives a detailed description of the theoretical model used to analyze the rotationally resolved spectra of the primary alkoxy radicals. A description of the spin- rotation interaction which plays an important role in the alkoxy radicals is given. The

Hamiltonian and its matrix elements are described as well as the rotational transition intensities and selection rules. A description of ab initio methods used to calculate rotational constants, relative energies etc. to aid in the analysis as well as a model developed to predict the spin-rotation constants is given.

5 The survey LIF spectra of several alkoxy radicals obtained in the supersonic jet using the moderate resolution experimental apparatus is presented in Chapter 4.

These spectra are pre-requisites for obtaining high-resolution rotationally resolved spectra of these radicals.

In the following two chapters, the rotational analysis of the high-resolution spectra of 1-propoxy and 1-butoxy is described to illustrate the approach used to analyze the spectra. A detailed description of how individual lines were assigned is given.

The results of the rovibronic analysis is presented followed by a discussion of the implications of these results on the spectroscopy and dynamics of these radicals.

In Chapter 7, the results of the rotational analyses of the high-resolution spectra of

1-pentoxy carried out using the approach used to analyze the spectra of 1-propoxy and

1-butoxy is presented, followed by a discussion of the implications of these results on the spectroscopy of this radical. This is followed by the ﬁnal chapter which describes the conclusions drawn from this study of the alkoxy radicals.

6 CHAPTER 2

Experimental

2.1 Introduction

The alkoxy radicals were studied under moderate and high resolution in a supersonic- free jet. Since the ultimate goal was to obtain rotationally resolved spectra of these species to obtain their molecular structure, it is critical to have the simplest possible spectra to enable detailed rotational analysis. Supersonic jet expansions produce translationally and rotationally cold molecules (temperatures of a few degrees Kelvin are easily achieved).18–21 They thus have the dual advantage of providing an ideal environment to study free radicals, and also yield simple (uncongested) rotational spectra because only a few, lowest-lying rotational quantum states will be populated at these temperatures.

2.2 Alkoxy Radical Production

A number of methods have been used to produce radicals. Some of the common techniques include ﬂash photolysis, laser photolysis, pyrolysis, and electric discharge.

A pulsed excimer laser is capable of large peak photon flux and thus offers an effecient means of producing radicals which was the chosen technique to produce the alkoxy radicals. In order to produce the radicals, one first needs a precursor molecule which will yield the radical of interest when photolyzed. The precursor molecule should

7 possess some important properties. Firstly, it should be stable and have a vapor pressure of a few torr under conditions easily achieved in the laboratory. Secondly, eﬀecient photolysis of the precursor must occur at typical excimer laser frequencies

(193 nm ArF, 248 nm KrF, 351 nm XeF, or 308 nm XeCl). A precursor for the alkoxy radicals that meets the above criteria is the alkyl nitrite (RONO). Methyl and ethyl nitrite are gases at room temperature and have been the standard precursors for methoxy8, 9 and ethoxy10–13 respectively. A well known method to synthesize the alkyl nitrites involves the dropwise addition of concentrated sulfuric acid to a saturated solution of sodium nitrite and the corresponding alcohol.22 This method was found to work well in synthesizing the alkyl nitrite precursors used to produce all the alkoxy radicals investigated in this study. Alkyl nitrites containing 3 or more carbon atoms are all liquids and have appreciable vapor pressure at room temperature. They were held in a stainless steel reservoir at a constant temperature so that the vapor pressure was 5-10 Torr. A carrier gas (usually Helium in these experiments) at a high backing pressure (200 psi typically) was ﬂowed through the reservoir containing the precursor.

This gas mixture was then expanded into a vacuum chamber evacuated to ≈ 10−3 Torr through a circular oriﬁce of diameter 0.25 mm. This nozzle was driven by a pulsed valve (General Valve) to produce gas pulses for an adjustable duration (typically 700

µs) at a repetition rate of 20 Hz.

All the alkoxy radicals were produced by XeF (351 nm) photolysis of the corresponding alkyl nitrite precursor. The excimer laser beam entered the vacuum chamber through an arm with a quartz window at Brewster’s angle and was focussed to around

1mm just on top of the oriﬁce. This is shown in Fig. 2.1.

8 A series of baﬄes were placed in the arm to minimize scattered light inside the chamber. The power required to achieve eﬀecient photolysis of the alkyl nitrite was typically 50 mJ per pulse.

9 To Pump

Vacuum Chamber

Brewster window Jet expansion Probe laser

Pulsed Photolysis laser valve 10

Precursor + carrier gas

Figure 2.1: Alkoxy radical production in a supersonic jet. 2.3 LIF experimental apparatus

Once the alkoxy radicals are produced in the supersonic expansion, they can be in- terrogated downstream using a suitable laser. All the alkoxy radicals studied in this thesis were investigated in two steps. The ﬁrst was to obtain vibronically resolved, survey LIF spectra of these radicals using a moderate resolution experimental apparatus. The second step was to use our high-resolution experimental apparatus to obtain rotationally resolved LIF spectra of a few vibronic bands of interest.

2.3.1 Moderate resolution LIF apparatus

In the moderate resolution apparatus (shown in Fig. 2.3.1), a XeCl (Lambda Physik

EMG 103) pumped dye laser (Questek PDL3) with a linewidth of 0.1 cm−1was used to pump the B˜ − X˜ transition of the alkoxy radicals ≈ 1cm (30 nozzle diameters) downstream from the oriﬁce. The maximum power achieved from the XeCl excimer laser is 180 mJ per pulse and has a pulse duration of 9 ns. A number of blue dyes were used to generate the UV radiation including PTP, DMQ, BBQ, BPBD, PBBO,

Exalites 376, and 351. The total fluorescence was collected from the supersonic jet using a 1 inch f/1 lens and imaged onto a photomultipiler tube (EMI QB9659). The resulting signal was preamplified and sent to a boxcar (Stanford Research) for averaging. The resulting signal was amplified and sent to the computer that stepped the dye laser. All the resulting spectra were calibrated using the lines from an iron/neon lamp. The error in determining the absolute frequency was ± 2cm−1.

11 Vacuum chamber 12

Figure 2.2: Moderate resolution experimental apparatus. 2.3.2 High-resolution LIF apparatus

The high-resolution apparatus is shown in Fig. 2.3.2. It consists of an Ar+ Ion (20 W,

Coherent Innova Sabre) laser pumping a continuous wave (CW) ring laser (Coherent

899-29) which could be a dye or Ti:Sa crystal depending on the wavelength needed.

The linewidth of the ring laser is typically ≈ 1 MHz, and the maximum output power is typically 200-300 mW for the dye and 1 W for the Ti:Sa. This beam was used as a seed for a pulse amplifier system (Lambda Physik FL 2003). The pulse-amplifier is a three stage system pumped by the same XeCl (308 nm) excimer laser that was used to pump the Questek PDL3 dye laser in the moderate resolution set-up. The dye in the pulse-amplifier was chosen for best output power at the desired frequency range and is typically ≈ 4-5 mJ per pulse. The resulting pulse (9 ns duration) of visible radiation has a linewidth of ≈ 75-100 MHz. This beam is telescoped into a KDP crystal (Quanta Ray) to frequency double into the UV region required to pump the

B˜ − X˜ transition in the alkoxy radicals.

The fluorescence was collected in the same manner as described in the moderate resolution experiments with one modification. An optical slit whose width could be adjusted, was placed in front of the PMT so that only the fluorescence from the central portion of the jet is detected (as shown in Fig. 2.1, the jet expansion is conical and hence there are molecules with velocity components along the axis of the PMT). This reduces the Doppler width of the signal due to off axis velocity components. The slit width was generally set to 200 µm. The resulting signal is preamplified, averaged and sent to the computer that steps the ring laser.

13 VACUUM CHAMBER PMT Doubling Crystal 5-10 mJ 120 MHz

ArF, KrF, XeF Pulse Amplifier Photolysis Excimer Laser Laser 0.5mJ (XeCl) PD

I 2/Te 14 2

PD CW ring Ar+ Laser 20W Dye Laser/Ti:Sa Computer

External etalon

Figure 2.3: High-resolution experimental apparatus. 2.3.3 Frequency calibration

The program, Autoscan, that controls the ring laser scans the laser 10 GHz at a time.

However, each vibronic band of the alkoxy radicals can be 4-5 cm−1wide. Thus in order to obtain the whole band, it is necessary to overlap 12-15 such scans. Therefore, it is extremely critical to have proper frequency calibration of the spectra so that the individual scans can be overlapped properly. This is achieved as follows. Before the

CW beam from the ring laser entered the pulse-amplifier, part of the beam was picked off using a pellicle beam-splitter (to minimize power loss), square-wave modulated using a chopper operating at 200 Hz, and sent into an external low-finnesse etalon and an iodine cell. The external etalon has a free spectral range (FSR) of ≈274 MHz. The signal from the etalon was detected by a photodiode and sent into a lock-in amplifier

(Stanford Research) for relative frequency calibration. This was then recorded by the computer. The iodine cell was used for absolute frequency calibration. It consisted of an evacuated cell containing a crystal of iodine and then sealed. The tube needed to be heated to ≈ 400-5000 C to get reasonable absorption in certain frequency regions.

The absorption signal was detected by a second photodiode, sent to another lock-in ampliﬁer, and sent to the computer. In addition to the above, data was also recorded from an internal etalon located in a wave-meter on the ring laser. The data was thus acquired simultaneously from four channels for each scan; 1) the experimental LIF signal, 2) the internal etalon from the wave-meter on the ring laser, 3) fringes from the external etalon, and 4) the absorption signal from the iodine crystal. The individual scans were then overlapped electronically using the external etalon to correct for any non-linearities. The iodine absorption signals were used for absolute frequency

15 calibration. The resulting single file was used to analyze each band. Multiple scans were taken of each band to check for any errors. The actual spectral line frequencies were measured using a Graphical User Interface (GUI) program SpecView developed in our lab by Vadim Stakhursky.23 This program was written in C++ and runs under a Windows environment. All data files comprising the rotationally resolved spectra analyzed in this thesis are attached in Appendix 2. A brief description on how to use these files to determine the line positions is also given in Appendix 2.

16 CHAPTER 3

Theory

3.1 Introduction

In order to get an understanding of the spectroscopy of alkoxy radicals, it is useful to

examine the bonding pattern in these species. The electronic conﬁguration of oxygen

is 1s2,2s2,2p4 and the ground state is 3P. The orbital picture is shown in Fig. 3.1.

In the ﬁgure, the px and py electrons are unpaired although there is no preference in

direction for the lone pair of electrons which are perpendicular to the plane of the

paper.

In methoxy, an sp3 hybridized orbital on the carbon atom forms a sigma bond

with one of the orbitals on the oxygen containing an unpaired electron as shown in

2 Fig. 3.2 and the ground state is doubly degenerate ( E) because of the C3v point

group symmetry.

The electronic transition A − X involves the excitation of a σpelectroninthe

C-O bond to ﬁll the orbital containing the unpaired electron. This transition is in

the UV at 31644 cm−1 in methoxy . When a hydrogen atom is replaced by a methyl group to yield ethoxy, the ground state degeneracy is broken and the orbital angular momentum is quenched. Recent photodetachment experiments24 on the negative ion

of ethoxy have shown the X − A separation to be ≈350 cm−1 (±10 cm−1). This is

17 y

x O z

Figure 3.1: Orbital picture of the oxygen atom.

H y H x O C z H

Figure 3.2: Bonding scheme in methoxy.

18 consistent with high level calculations that we have performed on ethoxy. Fig. 3.3

shows the energy level diagram for methoxy and ethoxy for the ﬁrst few electronic

states. The B − X transition of ethoxy lies in the UV at 29000 cm−1and the rota-

2 tionally resolved spectra of the origin band and 90 band of this transition have been

obtained and analyzed.13 Ethoxy may be considered a prototype for all the other primary alkoxy radicals.

3.2 Hamiltonian

All the alkoxy radicals (except methoxy, t-butoxy, and in principle some conformers of

CR3O) are asymmetric tops and hence the rotational structure of their high-resolution

spectra may be modeled by an asymmetric top Hamiltonian. Because of the very low

temperature in the jet only the lowest few rotational states are populated. Therefore

centrifugal terms in the rotational Hamiltonian HRot are usually negligible. However

molecules containing one unpaired electron (but with the orbital angular momentum

quenched) exhibit spin-rotation interaction which is basically the interaction of the

weak magnetic ﬁeld generated by the rotation of the molecule with the electron spin

magnetic moment. Therefore it is necessary to add spin-rotation coupling, HSR,to

model the ﬁne structure of the bands. Thus the Hamiltonian may be written:

H = HRot + HSR (3.1)

Denoting the rotational angular momentum by N and the spin angular momentum

25, 26 by S we may expand both HRot and HSR:

2 2 2 HRot = ANa + BNb + CNc (3.2) 1 HSR = αβ(NαSβ + SβNα) (3.3) 2 α,β

19 2 A′ A1

~31600 cm-1 ~29200 cm-1

′ A 350 cm-1 2 E A″ ~ ~ ~ 2 2 2 ′ 2 ″ Methoxy A A1 X E transition Ethoxy B A X A transition

Figure 3.3: Energy level diagram of methoxy and ethoxy.

20 where A, B,andC are the conventional rotational constants, and αβ are the com-

ponents of the spin-rotation tensor in the inertial axis system.

26–28 It is well-known that there are two contributions to the αβ parameters. The

ﬁrst is direct coupling of the electron spin to the magnetic ﬁeld caused by the rota-

tion of the molecule. This is usually considered negligible compared to the second

order contribution generated by the interaction of the spin-orbit coupling and Coriolis

interaction, i.e.,

i|ξLˆα|jj|XβLˆβ|i + c.c. αβ ≈−2 (3.4) i − j i=j E E

where ξ is an electronic operator which can be taken to be the spin-orbit constant

of the molecule, L is the electronic orbital angular momentum with component α,

Xβ is the rotational constant for the β inertial axis, and i and j are the interacting electronic states.

The matrix elements of the total Hamiltonian (Eqs. 3.2-3.3) can be set up in a basis set |JNKSMJ . J is the total angular momentum and is formed via coupling

J=N+S (3.5)

where |NKMK is the symmetric top eigenfunction. Here K is the projection of N

on the molecular symmetry axis and MJ and MK are respectively the projections of

J and N on the laboratory ﬁxed z-axis. The primary alkoxy radicals are near prolate

symmetric tops and so this is a convenient basis set.

21 3.2.1 Matrix Elements and Eﬀects of HRot and HSR The Rotational Hamiltonian

25 The matrix elements of HRot in a prolate symmetric top basis are well-known and

the non-vanishing ones can be summarized as follows:

1 1 2 JNKSMJ |HRot|JNKSMJ = (B + C)N(N +1)+[A − (B + C)]K (3.6) 2 2

1 1/2 JNKSMJ |HRot|JNK ± 2SMJ = (B − C)[(N ∓ K)(N ± K +1)] × 4 [(N ∓ K +1)(N ± K +2)]1/2 (3.7)

As is discussed elsewhere,29 we have made extensive ab initio calculations of the

rotational constants, Xα(= A, B, C) and also the spin-rotation constants αβ. Gener-

ally, but not always, the rotational constants Xα are 5-10 larger than the αβ.Thus

we expect the general appearance of the spectra, but certainly not the details, to be

explained by the eigenvalues of HRot.

The Spin-Rotation Hamiltonian

The spin-rotation Hamiltonian (Eq. (3.3)) may be recast in irreducible tensor nota-

tion:30, 31 2 1 k k k k HSR = [T () · T (N,S)+T (N,S) · T ()] (3.8) 2 k=0

where T k(N,S) is the tensor operator obtained by coupling the two ﬁrst-rank tensors

T 1(N)andT 1(S) as follows: k p 1 1 1 11 k Tp (N,S)=(−1) (2k +1)2 Tp (N)Tp (S) (3.9) 1 2 p1 p2 − p p1,p2

T k() is the spin-rotation tensor (k=0,1,2) whose elements are given below:

22 √ 0 T0 ()=(−1/ 3)(aa + bb + cc) (3.10) √ 1 T0 ()=(−1/ 2)i(bc − cb) (3.11)

1 T±1()=(1/2)[(ba − ab) ± i(ca − ac)] (3.12) √ 2 T0 ()=(1/ 6)(2aa − bb − cc) (3.13)

2 T±1()=∓(1/2)[(ba + ab) ± i(ca + ac)] (3.14)

2 T±2()=(1/2)[(bb − cc) ± i(bc + cb)] (3.15)

In general, all nine components can be non-zero. Brown and Sears26 applied a series of unitary transformations on the standard spin-rotation Hamiltonian (Eq. (3.3)) to obtain a reduced Hamiltonian. The reduced spin-rotation Hamiltonian has the same eigenvalues as the Hamiltonian in Eq. (3.3), but diﬀerent parameters (which are less in number, 6 for C1 symmetry, 4 for Cs, 3 for Oh, etc.) have to be determined. One can choose the transformations so that the antisymmetric parts of the spin-rotation

1 tensor vanish, which correspond to the Tp elements. Thus we can rewrite HSR as 1 k k k k HSR = [T (˜ε)T (N,S)+T (N,S)T (˜ε)] (3.16) 2 k=0,2 with √ √ 0 −1 T0 (˜ε)= 3 (˜εaa +˜εbb +˜εcc)= 3a0 (3.17)

√ √ 2 1 − − − T0 (˜ε)= 6 (2˜εaa ε˜bb ε˜cc)= 6a (3.18)

2 1 T (˜ε)=∓ [(˜εba +˜εab) ± i (˜εca +˜εac)] = ± (d ± ie) (3.19) ±1 2

23 2 1 T (˜ε)= [(˜εbb − ε˜cc) ± i (˜εbc +˜εcb)] = (b ∓ ic) (3.20) ±2 2

32, 33 The parameters a0, a, b, c, d, and e were introduced by Raynes and because of

their convenience in notation are used in our spectral analysis.

The matrix elements of HSR in the |JNKSMJ basis can be adapted from Bowater

et al.30 as

1/2 JN K SMJ |HSR|JNKSMJ = (2k +1) k=0,2 [S(S + 1)(2S +1)]1/2[(2N + 1)(2N +1)]1/2(−1)J+S+N NSJ 1 k 1/2 11k × (−1) [(N(N + 1)(2N +1)] + SN 1 N NN 2 1/2 11k N −K N kN k [(N (N + 1)(2N +1)] (−1) T (˜) NN N −K qK q q (3.21)

where {} and () denote 6-j and 3-j symbols respectively. This expression yields iden-

tical matrix elements to those explicitly derived by Raynes (in terms of a0, a,etc.)

except that all elements with N = N + 1 have the opposite sign owing to a diﬀerent choice of phase factors.

Characterization of the H matrix

As mentioned previously, we use as a basis for the H matrix the case (b) like prolate symmetric top functions |JNKSMJ . The total angular momentum J (nuclear spin

eﬀects are certainly negligible in our spectra) is obviously a good quantum number

and the matrix is blocked by J.

24 ± 1 For each J there are two values of N(= J 2 ) and for each N,(2N +1)values 1 − 1 of K. This leads to matrices of order [2(J + 2 )+1]+2(J 2 )+1]=(4J + 2) for

each J.

31 If HSR is omitted, then the matrix can be further blocked according to the irre-

ducible representations of the D2 symmetry group with respect to whose operations

HRot is invariant. Functions transforming according to irreducible representations of

D2 can be constructed as

1 s |JNKSMJ s = √ [|JNKSMJ +(−1) |JN − KSMJ ] (3.22) 2

Here s=0 or 1 for K =0. For K =0,s mayonlybe0.

While the actual eigenfunctions of H are not precisely of this form, “approximate”

values (valid in the limit that HSR vanishes) of N and s can be assigned to each

level by the following procedure. A search was made for the largest coeﬃcient of

the eigenfunction in the linear combination of the basis functions |JNKMJ S.The

assignment for N is determined by the value of N associated with this coeﬃcient.

The coeﬃcient of the basis set function |JN −KMJ S is then examined to determine

the value of s required by Eq. (3.22), based upon the relative sign of its coeﬃcient

compared to that of |JNKMJ S.

For the purpose of carrying out a rotational analysis, the “approximate” symme-

try species of the eigenfunctions of each of the four sub-blocks is determined based on

the N, K,ands quantum numbers. These “assignments” facilitate identifying eigen-

functions involved in particular transitions and corresponding approximately good

selection rules. The symmetry species of the asymmetric top wavefunctions are sum-

marized in Table 3.1. This approach is valid only if the perturbation of the rigid-rotor

25 spectrum by spin-rotation is small enough to enable one to assign a reasonably “good”

N and K (and hence s) quantum number to any given state.

Secular Symmetry Designation Determinant K s Neven Nodd + E Even 0 A Bz − E Even 1 Bz A + O Odd 0 Bx By − O Odd 1 By Bx

Table 3.1: Symmetry designation of rotor levels

A ﬁnal issue deals with the diagonalization of H to obtain its eignevalues and vec- tors. If one consults Eqs. (3.19- 3.21) it is clear that while the Hamiltonian matrix is Hermitian, it is also complex. The eigenvalues remain real since it is a Hermitian matrix; however the standard computer diagonalization programs, are written for real symmetric matrices only. In a similar fashion, while the transition probabili- ties remain real, the eigenfunctions become complex and so can possibly complicate their calculation. We describe in Appendix I our procedures for dealing with this complication.

26 Transition Line Strengths

The line strengths of the transitions were calculated according to the procedure used in the analysis of the high-resolution spectra of ethoxy.13 The eigenfunctions of an asymmetric rotor with spin-rotation may be written as

We may use tensor algebra to derive the line strength, S, of the transition between these two states:25

S(τ J ; τ J )=| (−1)N +S+J +1[(2J + 1)(2J +1)]1/2 × N N N J S 1/2 2 S (τ N ; τ N )| (3.24) J N 1 where

1/2 1/2 N −1−K S¯ (τ N ; τ N )=(2N +1) aτ K aτ K (−1) (2N +1)× K K q N 1 N 1 T (µ) (3.25) K q −K q

27 1 In equation 3.25, Tq (µ) is a spherical tensor component of the transition dipole

moment. S¯(τ N ; τ N ) is the line strength of the transition between two asymmetric

rotor states whose wavefunctions are given as:

|τ N M = aτ K |N K M K |τ N M = aτ K |N K M (3.26) K

Some rigorous and some approximate selection rules apply beyond the numerical

results. Equation 3.25 demands that only terms satisfying K −K = q can contribute

to the sum. Equation 3.24 implies the following selection rules on J and N:∆J =

0, ±1, and ∆N =0, ±1.

We can also use the “bad” quantum number s, (see Table 3.1). Recognizing that µa,µb, and µc, the components of the transition dipole along the inertial axes, transform respectively as Bz, Bx,andBy, we can use Table 3.1 to derive a set of

selection rules in terms of the labels E± and O±. The selection rule for a type transitions is:

O± ↔ O±, E± ↔ E± for ∆N = ±1

O± ↔ O∓, E± ↔ E∓ for ∆N = ±0

for b type transitions:

E± ↔ O∓ for ∆N = ±1

E± ↔ O± for ∆N =0

and for c type transitions:

E± ↔ O± for ∆N = ±1

E± ↔ O∓ for ∆N =0

28 For the simulations, the relative intensities of the spectral lines were calculated

as the product of the line strength factor and of the Boltzmann factor ((2J +

−(E −E0)/kT 1)e J )whereE0 is the lowest rotational energy level, and EJ is the ground-

state rotational energy involved in the transition. These simulations (and eventually

ﬁts) were performed using the graphical interface program,23, 34 SpecView.

3.3 Quantum Chemistry Computations and Predicted Molec- ular Parameters

3.3.1 Introduction

The simplest alkoxy radicals, methoxy and ethoxy, have a unique structural isomer.

However, larger alkoxy radicals can have multiple structural isomers which in turn can

exist in diﬀerent conformations. The number of structural isomers increases rapidly

with the number of carbon atoms as does the number of conformations for a particular

structural isomer. Structural isomers like 1- and 2-propoxy have distinctly diﬀerent

energies and large barriers separating their local minima on the global potential energy

surface. These barriers are of the order of the sum of a C-C and C-H bond energy

or ≈ 180 kcal/mol. Such high barriers make it likely that in our experiments, which photolyze a speciﬁc structural isomer of the precursor, propyl nitrite, we observe only the corresponding alkoxy structural isomer.

On the other hand a specific alkoxy structural isomer, e.g., 1-propoxy, has different conformations that have quite similar energies, within ≈ 3kcal/molofeachother, with comparable barriers separating their minima. Thus sufficient energy is available in the photolysis to populate all, or most all, possible conformers of a given structural isomer, although even this small energy difference in conformers is sufficient so that

29 at equilibrium only one conformer should exist at jet temperatures. The number of structural isomers increases rapidly with the number of carbon atoms and so do the number of conformations for a particular structural isomer. At room temperature numerous conformers should be populated and may easily interconvert to one another.

Using the standard value of 3 kcal/Mol for the barrier to torsion about a C-C bond, we have calculated the RRKM rate constant for this interconversion to be >109 s−1 at room temperature. However at jet temperatures the rate constant for the interconversion should be << 1s−1. It therefore may be possible in the jet expansion to “freeze out” molecules in conformations which are separated by large barriers compared to kT and would be populated in thermal equilibrium.

3.3.2 Method Determining the number of conformers

For propoxy it is possible to determine the number of conformers by inspection.

However, it will be useful to employ a somewhat more systematic procedure so that we can extend it to the larger alkoxy radicals. In 1-propoxy there is one pair of three- bond sets, i.e., C2-C1-O and C3-C2-C1, that can form a dihedral angle (φ1). If we consider the conformer shown in Fig. 3.4A, which has Cs symmetry, as a reference structure then we can rotate about the C1-C2 bond to other values of the angle φ1.

Assuming that there are only interactions between substituents on adjacent carbon atoms, only the three completely staggered positions shown in Fig. 3.4 should be

minima. These conformers are designated G1,T1,andG1 respectively, for gauche clockwise, trans (or anti), and gauche counterclockwise for the C1-C2 torsion.

30 O O O CH H H CH H H 3 3

H H H H H H H H CH3 A B C 0 0 T 180 G1 -60 ′ 0 1 G1 60

Figure 3.4: Conformations of 1-propoxy

Conformers G1 and G1 are indistinguishable and should give identical spectra.

Thus there are two conformer spectra possible for 1-propoxy, which we will henceforth denote simply as T and G.

In 1-butoxy, there are two pairs of three-bond sets, i.e., C2-C1-O with C1-C2-C3 and C1-C2-C3 with C2-C3-C4 that can form two dihedral angles, φ1 and φ2, illustrated in the Newan diagrams of Fig. 3.5a. If we consider the ﬁrst structure shown in Fig.

3.5a which has Cs symmetry as a reference structure, then rotation about the C1-C2 bond changes the value of the angle φ1 with three values expected to correspond to staggered minima, as shown in the ﬁrst row of Fig. 3.5a. The three structures

are designated T1,G1,andG1 respectively for trans, gauche clockwise, and gauche

31 counterclockwise for the C1-C2 torsion. We can also rotate about the C2-C3 bond to obtain diﬀerent values of the angle φ2 with again three staggered minima expected, as shown in the second row of Fig. 3.5a. These are analogously designated T2,G2,

and G2 for the C2-C3 torsion. Since the values of φ1 and φ2 can be independent, they can be combined to form a total of nine conformers, but not all of them are unique. The conformer corresponding to T1T2 has Cs symmetry and is unique. Of the remaining 8 conformers 4 are unique and the others their mirror images (indicated

in parentheses), i.e., T1G2 (T1G2), G1T2 (G1T2), G1G2 (G1G2), and G1G2 (G1G2).

The unique conformers are pictured in Fig. 3.5b.

32 O O O a) C H H C H H H 2 5 H 2 5 φ 1 ( 1) H H H H H H C H H 2 5 H

0 0

T1 180 G1 60 ′ 0

G1 -60

CH H H H H H H 3 H

2 ( 2) H H H CH H 3 CH 3 CH O CH2O 2 CH2O

0 ′ 0 G 1200 T2 180 G2 -120 2

O H H

O CH H H H 3 H H H O CH3 H H

C2H5 H

H H CH3 H H H H H H C H H C2H5 2 5 CH2O H CH2O CH2O

G T T G

1 2 T1T2 1 2

H H

H H H O H O C H C2H5 H H 2 5

H CH CH H H 3 H H H 3 H CH2O H CH2O ′ G1G2 G1 G2

Figure 3.5: a) Values for 1-butoxy of the dihedral angles φ1 and φ2 (staggered) for which local minima occur. b) Structures of ﬁve unique conformers of 1-butoxy corresponding to the combination of angles φ1 and φ2 at their local minima.

33 By induction one can arrive at the following empirical formula to determine the

number of distinguishable conformations (N ) for the primary alkoxy radicals:

3n−2 − 1 N = + 1 (3.27) 2

where n is the number of carbon atoms. To rationalize, Eq. 3.27, we note that there

are n − 2 possible dihedral angles that can be combined. These angles have minima

at three possible values. Thus the total number of possible conformations is 3n−2.

Of these, half of the conformers (other than the Cs one) are mirror images and thus

indistinguishable. Thus the total number of distinguishable conformers is given by

Eq. 3.27.

We can carry out the same exercise for 1-pentoxy where there are 3 torsional an-

gles, and hence 33 = 27 possible conformers of which only fourteen are distinguishable in accordance with Eq. 3.27. These are given below:

T1T2T3,G1T2T3 (G1T2T3), T1T2G3 (T1T2G3), G1T2G3 (G1T2G3), T1G2T3 (T1G2T3),

G1T2G3 (G1T2G3), G1G2T3 (G1G2T3), T1G2G3 (T1G2G3), G1G2G3 (G1G2G3), G1G2T3

(G1G2T3), G1G2G3 (G1G2G3), T1G2G3 (T1G2G3), G1G2G3 (G1G2G3), G1G2G3 (G1G2G3).

The fourteen unique conformers of 1-pentoxy are pictured in Fig. 3.6.

34 T1T2T3

G1T2T3 T1T2G3

H C H H

2 5 H CH

H O 3

H H

CH H O H C H H H 3 2 5 H H H

C3H7 H C2H5 H O

H H H H H

H H H

HHH H H H H C H CH O H C H O 3 7 2 C2H4O H CH2O 2 4 C H CH3 C H O 3 7 CH2O 2 4 ' T1G2T3 G1T2G 3

G1T2G3

H H

C H H O CH H C H H 3 2 5 H O 2 5 H H

O H H C H

C3H7 H H 3 7 H H

H H

H H HH H C H H CH3 H 2 5 HH H CH O H C H C2H4O CH3 C H O 2 C H O 3 7 CH2O H 2 4 2 4 CH2O ' ' ' T1G2G 3 G1G 2G3 G1G 2T3

H H HH

O H

H H H H H H C H CH H O H O H

3 7 H 3 H C H H

H H 3 7 H

H H

H HH H C H H HC2H5 HH H 2 5 H CH C2H5 CH C3H7 CH2O 3 C2H4O 3 C2H4O CH2O C2H4O H CH2O '

G1G2T3 G1G2G 3 T1G2G3

H H HH

H H H H H H O H

O CH3 O H H H

C H C3H7 H H

H 3 7 H H

H H

H HCH H CH H H C H HH 2 5 H HC2H5 3 2 5 CH3 C H O C H H CH2O 2 4 3 7 H CH2O C2H4O H CH2O C2H4O

G1G2G3 G 1G2G3

H H H

H O

H H

O H H H C3H7 H

C3H7 H H

HH H HH HCH CH C H 2 5 H 3 2 5 CH C H O H CH O 3 2 4 H CH2O C2H4O 2

Figure 3.6: Structures of fourteen unique conformers of 1-pentoxy at their local minima. The corresponding Newman projections of are also shown.

35 Determination of relative energies and rotational constants

So far the discussion on conformers has been qualitative. We now need to determine their structure and relative energies so that we may have an initial guess for the rotational constants to start fitting the experimentally obtained spectra and get estimates for the barriers between the different conformers. Programs have been written that can search for conformations based upon an empirical force field to tackle the problem of finding the conformations of large molecules. These may be used to determine the structure and relative energies of the different conformers. The method used to explore the conformational diversity of the alkoxy radicals was the Systematic

Pseudo-Monte Carlo method (SPMC) which is available in the MacroModel package.

This method uses the AMBER* force field. The empirical force field for the corresponding fluoro alkane was used to generate the initial set of conformations since the parameters for alkoxy radicals are not available. This model ignores interactions other than those between substituents on adjacent carbon atoms. While searching for conformations, all those that are 5 kcal/mol (which is the approximate barrier between the eclipsed and staggered positions on adjacent carbon atoms) above a previously found conformer are ignored.

The following procedure was employed:

1) The structure of the ﬂuoroalkane was minimized in MacroModel.

2) The above structure was used as a starting structure in the SPMC search.

3) A search with 30000 steps was performed on each structure. The resulting conformers were compared with each other for possible duplication.

36 4) The conformers were then converted to Gaussian input ﬁles for the appro-

priate alkoxy radical to ultimately obtain the equilibrium rotational constants and

frequencies.

Spin-Rotation Constants

A semi-empirical approach was used to calculate the X state spin-rotation constants.

A full spectroscopic analysis of the B−X transition of the ethoxy radical is available13

and the experimentally determined spin-rotation constants of this radical were used as

a reference to predict the spin-rotation constants of the higher homologues based upon

the following principle. The spin-rotation tensor depends upon several properties

viz., the expectation values of the electronic angular momentum operator Lˆ,the spin-orbit coupling, and the energy separation of the interacting states. If there is a “privileged” coordinate system wherein these properties do not change, one can predict the spin-rotation tensor of any alkoxy radical in the homologuous series as follows. The experimental spin-rotation tensor of a given alkoxy, e.g., ethoxy, is rotated to this privileged coordinate system using a unitary transformation. This new tensor is now transferable to the inertial coordinate system of the target alkoxy radical via another unitary transformation. The question now is if such a privileged reference coordinate system exists.

The coordinate system defined by an axis along the C-O bond, the second axis perpendicular to the first and in the plane of the C-C-O atoms, and the third one perpendicular to the first two is a good choice29 for the privileged system because the

unpaired electron and the electron density diﬀerence between the X and A states is

primarily localized on the oxygen atom. Thus the elements of the spin-rotation tensor

37 for the primary alkoxy radicals may be predicted using the experimentally determined spin-rotation constants of the ethoxy radical as a reference. In the particular case of the electronic transition in alkoxy radicals, further simpliﬁcations can be made. First, the energy separation of the B state from any other state is large; consequently, the spin-rotation interaction in the excited state can be neglected because the splitting induced by it will not be resolved in our experiment. Second, the spin-rotation splitting in the ground state is mainly due to the interaction of the quasi-degenerate X and A states; the contributions from the other states can safely be neglected.

3.3.3 Computational Methods

Rotational constants were determined by analytic geometry optimization at the B3LYP/6-

31+G* and the CIS/6-31+G* levels for the X and B states respectively. The calculations were performed using the Gaussian 98 package.35 It has been suggested by

Bryal et al. and Tozer et al that the B3LYP method is an excellent compromise between accuracy and computational cost based upon the compraison of computational results with experimental results.

When a higher level of accuracy was desired, the G2, G2MP2, and CBS-QB3 methods were employed for the ground states. The A state of conformers with Cs symmetry may be calculated at the same level as the X state by just switching the occupancy of the two p-orbitals on the oxygen atom.

38 CHAPTER 4

Moderate Resolution LIF Spectra

4.1 Introduction

The LIF spectra of the alkoxy radicals can be very useful as a diagnostic to detect them. The importance of these radicals in the atmosphere and combustion processes is well known as described in chapter 1. From a fundamental standpoint, the spectroscopy of these radicals will yield important information on their structure and dynamics. For a long time only the smallest alkoxy radicals, methoxy, ethoxy, and isopropoxy were investigated. Methoxy has been studied extensively in the past by a variety of techniques like LIF, dispersed ﬂuorescence, photodetachment of the negative ion, and microwave spectroscopy.4–9, 24

Ethoxy has also been well studied; there exist moderate resolution LIF excitation spectra10–12 and rotationally resolved high-resolution spectra of two vibronic bands.13

More recently, photodetachment experiments on its negative ion were performed.24

Isopropoxy has received somewhat lesser attention. Moderate resolution LIF spectra have been obtained14, 15 and Foster et al. have reported a partially resolved spectrum of the B − X transition in the jet.36 This radical has also been investigated by photodetachment spectroscopy of its negative ion.24

These three smallest alkoxy radicals have been investigated both at ambient as well as jet-cold conditions and for the most part, vibrational and rotational analysis

39 for their spectra are available. These studies established that there is a low-lying A state in these radicals, derived from the upper component of the degenerate X2E

state of methoxy (see chapter 3). The B state of the radicals was found to ﬂuoresce

with the B − X excitation lying in the ultraviolet.

It was believed for a long time that the next higher alkoxy radical, butoxy (and

other higher alkoxy radicals), would not ﬂuoresce. According to conventional wis-

dom, ﬂuorescence from the B state was expected to be quenched because of the large

number of vibrational modes in this molecule which would cause non-radiative pro-

cesses like isomerization, fragmentation, or intramolecular vibrational redistribution

(IVR) to dominate. Such behaviour is typical for non-radical molecular species of

this size and larger. Thus the spectroscopy of the larger alkoxy radicals was virtually

unknown for a long time. Recently, there has been a renewed interest in the alkoxy

radicals. The kinetics of the t-butoxy radical has been reported in two works.37, 38

Wang and co-workers have reported LIF at ambient temperatures from two isomers of

butoxy (t-butoxy and 2-butoxy)16 and two isomers of the pentoxy radical (t-pentoxy

and 3-pentoxy).17 In their work, LIF studies were attempted on 14 alkoxy isomers

containing from 4 to 6 carbon atoms. Only the two butoxy and pentoxy isomers

mentioned above were reported to give distinct, structured LIF spectra; the other 10

radicals were characterized as (1) giving weak signals (3 radicals), (2) diﬀuse spec-

tra and/or signals only from formaldehyde (4 radicals), or (3) no signal (3 radicals).

The implication of these results is that these larger radicals do not have signiﬁcant

quantum yields for ﬂuorescence from the B state.

The work described in this thesis was undertaken based upon the renewed interest

in the larger alkoxy radicals. As part of the preliminary investigation, several alkoxy

40 radicals were studied in a supersonic jet in a systematic manner using the moderate

resolution LIF apparatus to obtain survey excitation spectra. The results of this

investigation will be presented below.

4.2 Results

As mentioned in Chapter 3, alkoxy radicals containing more than two carbon atoms

can have structural isomers. The diﬀerent structural isomers of propoxy and butoxy

are shown in Fig. 4.1. These radicals were the ﬁrst ones to be investigated.

4.2.1 Propoxy

Figs. 4.2 and 4.3 show the jet-cooled LIF excitation spectra of the B − X transition in the two isomers of propoxy, 1-propoxy and 2-propoxy respectively.

The spectra exhibit sharp and strong peaks which indicates that the quantum yield for ﬂuorescence is large for both isomers. It is clear from Fig. 4.4 that the jet-cold spectrum of 2-propoxy shows sharper, more structured LIF than the one obtained at room temperature by Balla et al.39 The jet-cold spectrum facilitates vibrational

analysis of this spectum as opposed to the room temperature one in which the bands

are broadened out.

It is very interesting that while there is a clear progression in the 2-propoxy

spectrum (Fig. 4.3) in what is likely the C-O stretch which is expected to carry

most of the oscillator strength, such a progression is conspicuous by its absence in

the 1-propoxy spectrum. The weakness of the last few members of the progression

in 2-propoxy is expected to be due to reduced quantum yields due to non-radiative

processes.

41 1-Propoxy 2-Propoxy

1-Butoxy 2-Butoxy t-Butoxy

Figure 4.1: Structural isomers of propoxy and butoxy radicals.

42 B

28400 28600 28800 29000 29200 29400 29600 29800 30000 30200 Frequency (cm-1)

Figure 4.2: LIF excitation survey spectrum of 1-propoxy.

vC-O= 012 3 4 5 67

27000 27500 28000 28500 29000 29500 30000 30500 31000 Frequency (cm-1)

Figure 4.3: LIF excitation survey spectrum of 2-propoxy.

43 A)

C-Ov = 012 3 4 5 6 7

27000 27500 28000 28500 29000 29500 30000 30500 31000 Frequency (cm -1 )

44 B)

Figure 4.4: Comparison of the LIF excitation spectra of 2-propoxy taken in A) supersonic jet, B) room temperature (by Balla et al.) We may speculate on the assignments of the vibronic bands. The B−X transition in the alkoxy radicals involves the excitation of an electron from an σp orbital on the oxygen atom with C-O bonding character to the half-ﬁlled p-orbital (the HOMO).

Therefore any vibration involving the C-O bond stretch can be expected to be very active. In general, vibrations involving signiﬁcant displacement of the oxygen atom are expected have the biggest oscillator strength because of the large transition electric dipole moment which will be induced by these vibrations subject of course to favorable

Franck-Condon factors. Other vibrations would be expected to be much weaker. In the 2-propoxy spectrum, the strongest features form the C-O stretch progression. The experimentally observed frequency of the fundamental for this vibration is in good agreement with ab initio calculations and is given in Table 4.1. Some other tentative assignments based on ab initio calculations for low frequency bands, i.e., below the

C-O stretch frequency shown in Fig. 4.5, are also indicated.

45 vC-O vC-O

vC-C

1 4 2 5 3

27000 27200 27400 27600 27800 28000 28200 28400 Frequency (cm-1)

Figure 4.5: Low frequency region of the 2-propoxy spectrum.

Band Experimental Assignment Calculated Frequency (cm−1) Frequency 1 344 out-of-phase methyl torsion 217 2 357 in-phase methyl torsion 257 3 378 C-C-C bend 338 4 449 Asym. C-C-O bend 429 5 466 Sym. C-C-O bend 446 574 C-O stretch 675

Table 4.1: Some low frequency (below the C-O stretch) vibrations observed in the spectrum of 2-propoxy.

46 In the case of 1-propoxy, there are two unique conformers as has already been discussed in Chapter 3. In order to determine the rotational contour, spectra of two strong bands labeled A and B in Fig. 4.2 were taken with the maximum resolution of the laser (0.1 cm−1). The rotational contours of these bands are clearly different as can be seen in Fig. 4.6. The difference in the rotational contours of these two bands are likely due to the fact that the carriers are the two different conformers of

1-propoxy. Furthermore, the rotational contours of these two bands can be simulated using the calculated rotational constants of the ground and excited states of the two conformers. These constants were calculated according to the recipe described in chapter 3. The simulations are shown in Fig. 4.7.

Since it is likely that the spectral features in Fig. 4.2 may be attributed to both conformers of 1-propoxy, a vibrational analysis of this spectrum will not be reliable when the error bars associated with ab initio predictions of the origin and vibrational frequencies of the B states of both conformers are taken into account. For example, our ab initio calculations indicate that the C-O stretch of the lowest energy conformer of 1-propoxy is at around 750 cm−1(our level of calculations on the B state are not very accurate). The calculated constants of this conformer reproduces the rotational contour of the “origin” band A rather well as shown in Fig. 4.7. However the strongest band in the C-O stretch region for this conformer is band B which has a very diﬀerent rotational contour (see Fig. 4.7). The average geometry of a molecule does not change by more than a fraction of a percent from the equilibrium geometry upon vibrational excitation. Thus the rotational structure of vibrationally excited bands are expected to be essentially identical to that of the electronic origin.

47 Band B

29120 29122 29124 29126 29128 29130 29132

Band A

28538 28540 28542 28544 28546 28548 28550 Frequency (cm-1)

Figure 4.6: Moderately high-resolution spectra of bands A and B of 1-propoxy. The rotational contours of the two spectra are clearly diﬀerent.

48 Band B

b) Sim.

a) Expt.

29120 29122 29124 29126 29128 29130 29132

Band A

b) Sim.

a) Expt.

28538 28540 28542 28544 28546 28548 28550 Frequency (cm-1)

Figure 4.7: Simulations of the rotational contours of bands A and B of 1-propoxy using the calculated rotational constants of the two conformers G and T respectively (see chapter 3) of 1-propoxy. The rotational temperature for both spectra was 3K. The ratios of the transition dipole moments are a:b:c=0:0:1 for band B and 1:1:2 for band A as obtained from our ab initio calculations on the B state.

49 The larger alkoxy radicals will have a variety of conformers and thus their jet-

cooled vibrational spectra can be expected to be quite complicated. The ultimate

test for the correct conformational assignment is rotational spectroscopy. By detailed

rotational analysis of the diﬀerent bands, one may hope to distinguish between con-

formers based upon diﬀerent rotational structure. The rotational structure can be

used as a bar code to identify the spectral bands carried by a speciﬁc conformer. Ab

initio calculations may then be used to help assign the vibronic bands associated

with each conformer.

4.2.2 Butoxy Isomers

As mentioned before, the butoxy radical has three structural isomers. The jet-cooled

LIF excitation spectra of all the isomers were obtained and are shown in Fig. 4.8.

It is interesting to note that while LIF was observed by Wang et al.from2-andt- butoxy at near ambient temperature, they reported only diﬀuse and/or formaldehyde

ﬂuorescence from 1-butoxy. Under jet-cooled conditions however, sharp, structured

LIF spectra are observed for all three isomers.

Another interesting feature of these LIF spectra is that a long progression in the

C-O stretch is observed only in t-butoxy while the spectra of the other two isomers span a relatively much shorter range, with at most one quantum excitation being observable. A similar progression is observed in 2-propoxy as shown in Fig. 4.3 as well as in ethoxy40 and methoxy.4 The C-O stretch frequency of t-butoxy is given in

Table 4.2 along with those of the other smaller alkoxy radicals.

50 c)

v C-O = 0 1 2 3 4 5 6 7

26000 27000 28000 29000 30000 b) 51 26800 27000 27200 27400 27600 27800 28000 28200

B a) A

28600 28800 29000 29200 29400 29600 29800 30000 Frequency (cm -1 )

Figure 4.8: Survey jet-cooled LIF excitation spectra of the structural isomers of butoxy:, a) 1-butoxy, b) 2-butoxy, and c) t-butoxy. species origin ωe ωexe methoxya 31614 677.2 4.6 ethoxy 29210b 609c 3.0c 2-propoxy 27171 574.4 5.2 1-propoxyd 28634 - - 2-butoxy 26757 559e - t-butoxy 25861 546 3.1 1-butoxy 28649 - -

Table 4.2: Origin and C-O stretch frequencies for various alkoxy radicals a From Foster et al., ref 36 and Powers et al., ref 6. b From Tan et al., ref 13. c From Zhu et al., ref 40. d For comments on the C-O stretch frequency, see text. e Frequency for the νC−O=0-1 separation.

Another interesting feature of the t-butoxy spectrum is the fact that the signal/noise ratio is much worse that those for the 1- and 2-butoxy spectra. However, the density of spectral lines in the former is much higher than in the latter. Further- more, some of the spectral lines appear on top of broad humps as can be seen in the

26500-27500 cm−1region.

The 2-butoxy spectrum shown in Fig. 4.8b seems to be dominated by one excitation of the C-O stretch whose frequency is given in Table 4.2. However, it should be noted that 2-butoxy has three unique conformers and thus it is possible that some of the bands in its survey spectrum may be attributed to the diﬀerent conformers.

The survey spectrum of 1-butoxy shown in Fig. 4.8a appears to be very similar to that of 2-butoxy in that the spectrum is dominated by a strong band (B) that is apparently the C-O stretch. However this band is at an anomalously low frequency of 444 cm−1rather than a frequency of around 560-580 cm−1. However there are three other relatively strong lines at 512, 612, and 710 cm−1that cannot be discounted as

52 likely candidates for the C-O stretch. Fig. 4.9 shows the rotational contours of two strong bands in the LIF spectrum of 1-butoxy, namely, the “origin” band A, and band

B. Clearly, the rotational contours of these bands are diﬀerent which again implies the existance of multiple conformers of this isomer as in the case of 1-propoxy. As described in chapter 3, the rotational constants of all the conformers of 1-butoxy were calculated and it was found that the rotational contours of bands A and B could be simulated quite well by using the calculated constants and transition dipole moments of the two lowest energy conformers G1T2 and T1T2 respectively as shown in Fig.

4.9. Thus band B may be ruled out as being the C-O stretch. Once again high- resolution rotationally resolved spectroscopy of the various bands should help in not only identifying diﬀerent conformers but also aid in the vibronic analysis.

53 B

Sim.

Expt.

29084 29086 29088 29090 29092 29094 29096 29098 29100 29102

Sim.

Expt.

28550 28552 28554 28556 28558 28560 28562 28564 28566 28568 Frequency (cm-1)

Figure 4.9: Rotational contours of bands A and B of 1-butoxy. The simulations shown were obtained by using the calculated rotational constants of conformers G1T2 and T1T2 respectively (see chapter 3) of 1-butoxy. The rotational temperature for both spectra was 3K. The ratios of the transition dipole moments are a:b:c=0:0:1 for band B and 2:1:3 for band A.

54 4.2.3 Pentoxy Isomers

The survey LIF spectra of four of the ﬁve structural isomers of pentoxy, namely, 1-,

2-, 3-, and t-pentoxy are shown in Fig. 4.10. As in the case of the propoxy and butoxy isomers, the spectra are sharp and structured. There are two interesting points about these spectra; ﬁrstly, while only 3- and t-pentoxy were found to exhibit structured

LIF spectra near room temperature,17 all four isomers exhibit structured LIF in the jet. Secondly, the spectra of all observed isomers of pentoxy span less than 1300 cm−1 with at most one quantum C-O stretch excitation being observable which is similar to the behavior of the isomers of propoxy and butoxy which have a C-C-C linkage i.e., 1-propoxy, and 1- and 2- butoxy. The signiﬁcance of this will be discussed later.

The isomer neo-pentoxy was not observed because we were unable to synthesize the precursor (neo-pentyl nitrite) by the standard procedures mentioned in chapter

2 as revealed by FTIR absorption spectra.

55 t-Pentoxy

25400 25600 25800 26000 26200 26400 26600 26800 27000

3-Pentoxy

26400 26600 26800 27000 27200 27400 27600 27800

2-Pentoxy

26600 26800 27000 27200 27400 27600 27800

1-Pentoxy

28600 28800 29000 29200 29400 29600 29800 30000 Frequency (cm-1)

Figure 4.10: Survey scans of the four isomers of pentoxy.

56 4.2.4 Higher Alkoxy Radicals

Based upon the success in observing sharp, strong LIF spectra for all the isomers of

propoxy and butoxy, and four of the ﬁve isomers of pentoxy, a systematic search for

LIF from several larger alkoxy radicals was made for the primary (1-) and secondary

(2-) alkoxy radicals with the number of carbon atoms (n) ranging from 6-10. The

spectral results of this survey are shown in Figs. 4.11 and 4.12 respectively, along

with the spectra of the corresponding propoxy, butoxy, and pentoxy radicals.

The spectra shown in Figs. 4.11 and 4.12 exhibit some interesting features. Firstly,

the spectra are all sharp with well characterized vibrational structure. The S/N ratio

decreases somewhat as n increases but not dramatically so and may be attributed mainly to the reduction of the vapor pressure for the larger molecular weight precursors.

Secondly, the vibrational structure seems to get simpler as the number of carbon atoms increases. It is possible that this may simply be attributed to the poorer S/N ratio for the larger alkoxy radicals, so that only the strongest bands appear above the noise. Two such bands are persistent in the primary as well as the secondary alkoxy radicals and are labeled as bands A and B in Figs. 4.11 and 4.12.

It has already been established in the case of 1-propoxy and 1-butoxy that multiple conformers were observed. In order to investigate the presence of multiple conformers of the secondary (2-) alkoxy radicals, moderately high-resolution spectra (0.1 cm−1)

of the “origin” band and band A in the spectra shown in Fig. 4.12 were taken to

obtain the rotational contours. These spectra are shown in Figs. 4.13a and b respec-

tively. Clearly, the rotational contours of these two bands are diﬀerent indicating that

57 1-Propoxy

1-Butoxy

1-Pentoxy

1-Hexoxy

1-Heptoxy

1-Octoxy

1-Nonoxy

A B 1-Decoxy

28600 28800 29000 29200 29400 29600 29800 30000 Frequency (cm-1 )

Figure 4.11: Survey scan of the jet-cooled LIF excitation spectra of the primary (1-) alkoxy radicals, CnH2n+1O, for n=3-10. “Persistent” lines in the spectrum are marked A and B, see text for further details.

58 2-propoxy

2-butoxy

2-pentoxy

2-hexoxy

2-heptoxy

2-octoxy

B A 2-nonoxy

2-decoxy

26700 26900 27100 27300 27500 27700 27900

Figure 4.12: Survey scan of the jet-cooled LIF excitation spectra of the secondary (2-) alkoxy radicals, CnH2n+1O, for n=3-10. “Persistent” lines in the spectrum are marked A and B, see text for further details. Essentially no LIF signals, except for propoxy, are observed to frequencies higher than those shown.

59 multiple conformers of the 2-alkoxy radicals as well exist in the jet. As the number

of carbon atoms increases, the number of possible conformers will increase. Thus it

is possible that some of the bands in the spectra shown in Figs. 4.11 and 4.12 may

be attributed to a variety of conformers of the particular radical.

Fig. 4.14 shows a plot of the origin frequency vs the number of carbon atoms

of all observed alkoxy radicals from methoxy (n=1) to dodecoxy (n=12). Fig. 4.14 shows that as the number of carbon atoms increases, the frequency shifts to the red.

However it quickly reaches a limiting value. However, higher resolution scans over the origin bands of the primary and secondary alkoxy radicals do indicate a small, but continuing red shift with increasing n as can be seen in Figs. 4.13a and 4.15.

The observation of the red shifting of the alkoxy origin with increased branching of

the hydrocarbon chain can be rationalized in terms of the inductive eﬀect of the alkyl

groups. It is well known that alkyl groups can donate electron density to a positively

polarized center in the molecule. Since the B − X transition involves the excitation

of a σp electron to ﬁll the half-ﬁlled p-orbital localized on the oxygen atom, the C-O

bond can be considered to be polarized in the B state, with the carbon atom attaining

a fractional positive charge. Thus the B state of the alkoxy radicals will be stabilized

more than the X state by the inductive eﬀect. Furthermore, it is well known that

the magnitude of the inductive eﬀect varies with the alkyl group as follows:

Methyl

Thus the red-shifting of the origins of the alkoxy radicals with increasing branching in the hydrocarbon chain mirrors the increasing inductive eﬀect with increasing branching in the alkyl groups, which results in the stabilization of the B state more than the X state in the corresponding alkoxy radical. However, the origin frequencies

60 for a particular family of structural isomers, like the 1-alkoxy radicals for example, asymtotically reach a limiting value, starting at 1-propoxy. This indicates that the inductive eﬀect also reaches a plateau, which is reasonable because this eﬀect is expected to be less important over more than two sigma bonds.

Fluorescence studies on various “miscellaneous” alkoxy radicals were also attempted and the results are shown in Fig. 4.16. Essentially, every alkoxy radical that was investigated, showed good quantum yield for ﬂuorescence from the B state.

The alkoxy radicals were studied under high-resolution to answer the questions posed by the survey spectra i.e., to determine the presence of multiple conformers, and subsequently, the vibronic assignments based upon rotational bar-coding for the different conformers. The results of these studies for the primary alkoxy radicals will be described in the following chapters.

61 a) 2-pentoxy

2-hexoxy

2-heptoxy

2-octoxy

2-nonoxy

2-Decoxy

26745 26750 26755 26760 26765 26770 Frequency (cm-1 ) b)

2-pentoxy

26886 26889 26940 26945 26950 26955 26960 26965 2-hexoxy

26888 26900 26905 26910 26915 26920 26925

2-heptoxy

2-hexoxy

2-nonoxy

2-Decoxy

26885 26890 26895 26900 26905 26910 Frequency (cm-1) Figure 4.13: a) Moderately high-resolution (≈0.1 cm−1) scans of the “origin” bands of the 2-alkoxy radicals. Some rotational structure is apparent even for the largest radical, b) Moderately high-resolution (≈0.1 cm−1) scans of band A of the 2-alkoxy radicals (see Fig. 4.12). The rotational structures of the origin band and band A for each radical are clearly diﬀerent, indicating the presence of two diﬀerent conformers.

62 32000

31000 1- 2- 3- 30000 t- ) -1 29000

28000

Frequency (cm Frequency 27000

26000

25000 0 1 2 3 4 5 6 7 8 9 10 11 12

No. of carbon atoms

Figure 4.14: Frequencies of apparent origin bands of the observed alkoxy radicals plotted vs number of carbon atoms in the radical. The grouping of the radicals into families based on the nature of the isomer is clearly apparent.

63 1-Pentoxy

1-Hexoxy

1-Heptoxy

1-Octoxy

1-Nonoxy

1-Decoxy

1-dodecoxy

28625 28630 28635 28640 28645 28650 Frequency

Figure 4.15: Moderately high-resolution (≈0.1 cm−1) scans of the “origin” bands of the 1-alkoxy radicals. Some rotational structure is apparent even for the largest radical and a red shift in the origin frequencies is discernable with increasing size of the radicals.

64 3-octoxy

26000 26200 26400 26600 26800 27000 27200

4-methyl-3-heptoxy

25800 26000 26200 26400 26600 26800 27000

2,4-dimethyl-3-pentoxy

25800 26000 26200 26400 26600

4-heptoxy

25600 25800 26000 26200 26400 26600 26800 27000 27200

2,3-dimethyl-2-butoxy

27000 27200 27400 27600 27800 28000

3-hexoxy

26000 26200 26400 26600 26800 27000 27200 Frequency (cm-1)

Figure 4.16: Survey LIF spectra of some miscellaneous alkoxy radicals.

65 CHAPTER 5

High-Resolution Spectroscopy of 1-Propoxy

5.1 Introduction

It clear from Chapter 4 that the LIF survey spectra of the alkoxy radicals studied are quite complex because of the likelihood that some of the spectral features of a particular structural isomer are carried by diﬀerent conformers. Thus the task of assigning the spectral features involves identifying it’s conformational identity.

Rotational spectroscopy is a powerful tool that may be used to unravel the structural identity of the carrier of a spectrum. Rotationally resolved spectra of the B − X electronic transition of the the primary alkoxy radicals 1-propoxy through 1-pentoxy were obtained in a supersonic jet. In this chapter, the method used to analyze the rotationally resolved spectra will be discussed, with full details described for the smallest investigated radical, 1-propoxy.

5.2 Results

Our approach, as well as the complexity of the problem for 1-propoxy, is best illustrated by reference to Figs. 5.1 and 5.2. Fig. 5.1 shows, a typical moderate resolution, survey LIF excitation spectrum of 1-propoxy. The ﬁve strongest bands, labelled A through E in Fig. 5.1, were studied in high resolution and their rotationally resolved spectra are shown in Fig. 5.2. As Fig. 5.2 shows, these spectra can immediately be

66 divided into two groups based upon similarity of rotational structure, with bands A and C in one group and B, D, and E in the other. The rotational structure of these two sets is clearly very different. As we will subsequently demonstrate we attribute this spectral difference to the fact that they arise from two different conformers of

1-propoxy. The lowest frequency band in each group is likely the origin of the given conformer. The other, higher-frequency bands of each group most likely terminate in excited vibrational levels of the B state of that particular conformer.

5.2.1 Results

As already described in Chapter 3, there are two distinct conformers for 1-propoxy shown in Figs. 5.3a) and b). The gauche (G) conformer has C1 point group symmetry while the trans conformer (T) has Cs symmetry. As Figs. 5.1 and 5.2 demonstrate, the spectral bands of 1-propoxy have two distinct rotational structures. The subtle variations within each set of rotational structures may well be attributed to the fact that the bands terminate on different vibrational levels of the B state. However the differences in rotational structure between the two classes of bands is far too great to attribute to different vibrational states.

We suspected that the two sets of bands exhibiting distinctly diﬀerent rotational structure corresponded to the T and G conformers of 1-propoxy. To help conﬁrm this hypothesis, and generally aid the rotational analysis, as described in Chapter 3, we

29 have carried out aseriesofab initio calculations on the alkoxy radicals, CnH2n+1O for n =3− 6. The rotational constants from these calculations for both the G and T conformers of 1-propoxy are given in Table 5.1.

67 B

D 68 A C E

28400 28600 28800 29000 29200 29400 29600 29800 30000 30200 Frequency (cm-1)

Figure 5.1: Overview of 1-propoxy survey LIF spectrum E

29893 29894 29895 29896 29897 29898

29455 29456 29457 29458 29459 29460

29217 29218 29219 29220 29221 29222

29228 29229 29230 29231 29232

28632 28633 28634 28635 28636 28637

Frequency (cm-1)

Figure 5.2: Rotationally resolved spectra of bands, marked A through E in spectrum of 1-propoxy shown in Fig. 5.1.

69 a) b)

Figure 5.3: Conformers of 1-propoxy; a) Conformer G, b) Conformer T.

The B − X transitions of the G and T conformers were simulated using only the rigid rotor asymmetric top Hamiltonian, HRot. These results are shown respectively

in Figs. 5.4b and c. The experimental resolution (200 MHz) is more than suﬃcient

to resolve this rotational structure as can be seen in the experimental spectra shown

in Figs. 5.4a and d. It is evident from Fig. 5.4 that the overall rotational structure of

bands A and B are reasonably well reproduced by the simulations b and c respectively.

Thus we conclude that the conformational assignment for band A (and C) is the G

conformer, and that for band B (as well as D and E) is the T conformer.

5.2.2 1-propoxy, T Conformer Rotational Structure

Because of the Cs symmetry of the T conformer and the resulting somewhat simpler

structure of its spectral bands, we present their analysis ﬁrst. Since the structure and

therefore the analysis of the B, D, and E bands diﬀer only in the slightest degree we

describe extensively only our analysis of the lowest frequency B band, presumed the

origin.

70 Expt. d

Sim. c

29217 29218 29219 29220 29221

b Sim. 71 a Expt.

28632 28633 28634 28635 28636 28637 Frequency (cm-1)

Figure 5.4: a) High-resolution spectrum of 1-propoxy band A, b) Simulation of rotational structure of the B˜−X˜ transition using the calculated rotational constants of the G conformer, c) Simulation of rotational structure of the B˜ −X˜ transition using the calculated rotational constants of the T conformer, d) High-resolution spectrum of 1-propoxy band B. For both simulations, for the simulation the relative weights of the transition dipole moment components are obtained from the ab initio calculations on the B˜ excited state and the rotational temperature is taken to be 1.1K. Fig. 5.5a shows the simulation of band B using the calculated ground and excited state rotational constants of the T conformer. Since Table 5.1 shows that the T conformer of 1-propoxy is a near prolate symmetric top, it is useful to use symmetric top notation to label the assignments shown in the predicted spectrum, as shown in Fig. 5.5a. The assignments correlate quite well with the experimental features although there are some details in the three Q-branches and the red and blue wings of the experimental spectrum which are obviously missing in the simulation. It is clear, for example, that there are easily distinguishable P, Q and R branches in both

Fig. 5.5a and 5.5b. In a rigid symmetric top, the spacing between the transitions

B+C B+C within a P- or R- branch is entirely determined by the constants 2 and 2 .

Thus these two constants can be easily determined from the experimental spectrum.

72 b)

|K'|=1 ↔ K"=0 Q-branch (|K'|=1 ↔ K"=0)

Q-branch (|K'|=1 ↔ |K"|=2)

K'=0 ↔ |K"|=1 Q-branch R1 (K'=0 ↔ |K'|=1) R0 ↔

73 |K'|=2 |K"|=1

↔ R2 P1 K'=0 |K"|=1 R |K'|=1 ↔ K"=0 1 R3 P2 R 2 R3 P3 R R R 1 4 2 a) P R3 P3 2 R P4 P5 P4 R5 4

29216 29217 29218 29219 29220 29221 29222 Frequency (cm-1)

Figure 5.5: a) Simulation of band B using calculated ground and excited state rotational constants of 1-propoxy T conformer, at 1.1 K with a pure c-type transition moment (demanded by symmetry for a A-A transition). The assignments are made using a prolate asymmetric top notation, b) Experimental spectrum of band B. Rot. Const.(GHz) G conformer T conformer A 15.46 27.87 B 5.10 3.89 C 4.35 3.64 ˜aa -1.60 -8.66 ˜bb -1.11 -0.15 ˜ cc -0.13 -0.0 |˜ ab| = |˜ ba| 1.53 1.73 |˜ ac| = |˜ ca| 0.55 0.0 |˜ bc| = |˜ cb| 0.37 0.0 A 14.10 26.72 B 5.23 3.86 C 4.36 3.60

Table 5.1: Calculated ground and excited state constants of the diﬀerent conformers of 1-propoxy.

It can be seen in Fig. 5.5a that the R-branch transitions involving |K| =1↔

|K | = 2 are doubled from R2 onwards. This is the asymmetry splitting of the ground

state rotational levels which is not seen for the K =0↔|K| = 1 transitions.

In the latter case, there is obviously no K-doubling in the B state and one of the transitions to the |K| = 1 doublet is forbidden by the symmetry properties of this

B−C conformer. Thus we can determine the constant 2 because it uniquely determines

the observed splitting.

In the excited state, there is no asymmtery splitting observed for the |K| =1↔

K = 0 transitions again due to symmetry considerations. However the eﬀect of

B−C 2 is to shift the transition frequencies. The magnitude of this shift increases

with increasing N . (The same phenomenon is observed for the K =0↔|K| =1

B−C transitions for which only one asymmetry component is observed). Thus 2 can

be determined independently as well.

74 We are now left with two constants, A and A to determine. These constants aﬀect the positions of the three Q-branches with diﬀerent |K|↔|K| quantum numbers and can hence be independently determined. We can therefore expect to obtain with reasonably high precision all six rotational constants from the spectrum.

Spin-Rotation Structure

As can be seen in Fig. 5.5, the overall rotational structure of band B is fairly well reproduced by the simulation using the calculated rotational constants alone. However, in order to ﬁt this spectrum in detail and derive structural information therefrom, we need to analyze the ﬁne-structure due to spin-rotation interaction as well, which as noted earlier is expected to arise solely from X state splittings.

As was mentioned before, the number of determinable, independent spin-rotation

41 constants reduces from six to four for the Cs symmetry T conformer of 1-propoxy.

Furthermore, the Hamiltonian matrix will be real because the spin-rotation constants that introduce the imaginary terms vanish for molecules with Cs symmetry.

As with the rotational constants, it is useful to qualitatively understand the ef- fects of the various spin-rotation parameters on the spectrum. This is important for assignment purposes and to verify the sensitivity of the experimental results to a given parameter. An examination of the diagonal matrix elements of the spin- rotation Hamiltonian in the X state shows that there are certain linear combinations of the diagonal components of the spin-rotation tensor that aﬀect certain transitions in unique ways.32

75 The splitting between the lower and upper spin-rotation components of the near

prolate top states |J = NKSMJ s is given in the symmetric top limit by the expres-

sion: 1 3K2 F2(J = N + S, N, K) − F1(J = N − S, N, K)= N + a0 + a − 1 2 N(N +1) (5.1) where a and a0 have been previously deﬁned in terms of the spin-rotation tensorial

components, ˜αβ. From Eq. (5.1) it is clear that for transitions involving K =0, the

splitting between the two components is (N+1/2)(a0 − a). This simple expression

should be a good approximation to the experimental splitting since this conformer

is a near prolate symmetric top and the eﬀects on the X state eigenvalues of the

spin-rotation terms oﬀ-diagonal in K are much smaller. For transitions involving

|K| > 0, the splitting is a more complicated function of N.

In the special case of |K|=1 and N =1, the splitting is again approximated by

a simple expression for its diagonal matrix elements, (3/2)(a0 + a/2). Therefore this

set of transitions taken together will uniquely determine a and a0.

This leaves two constants, b and d, to be determined. The constant b couples states

with ∆K = ±2, i.e., the same states that are mixed by the rotational asymmetry B−C H terms proportional to 2 in Rot, and therefore should be well determined. The

constant d appears only in the matrix elements with ∆N =0, ±1, and ∆K = ±1, so

that this constant will not be as well determined as the other spin-rotation constants.

We can make one further simpliﬁcation in the case of T conformer of 1-propoxy.

In this conformer, the molecular plane is perpendicular to the orbital which “carries”

the unpaired electron and which lies along the c inertial axis. Referring to Eq. (3.4)

which deﬁnes the αβ we expect by far the major contribution to the sum to arise

76 from the low-lying A2A state. However if we only include matrix elements between

2 2 the X A and A A states in Eq. (3.4), we note that cc = 0 by symmetry. As shown by Brown and Sears ˜cc = cc in Cs symmetry. Thus the following relationship is approximately valid:

1 −1 b = (˜bb − ˜cc) ≈ a − a0 = (˜cc +˜bb) (5.2) 2 2

With this understanding of how the spin-rotation tensor aﬀects the spectrum, the

ﬁne-structure may be assigned and analyzed in a systematic manner. We start with transitions involving |K|=1 since they can be identiﬁed unambiguously because they are well separated from other lines. The R branch region of the |K| =1↔|K| =2 transition is expanded in Fig. 5.6.

Trace 5.6b shows a simulation of the region without spin-rotation interaction, and reveals that the asymmetry splitting is resolved in the R2 and R3 lines but not R1.

However the |K|=1, N =1 transition will be split by the spin-rotation interaction by the amount (3/2)(a0 + a/2). It can be seen in the experimental trace (Fig. 5.6a)

that the transition R1(|K | =2↔|K | = 1) indeed appears to be split by around

7 GHz. This is in reasonably good agreement with the value of 6.5 GHz predicted from the calculated constants. So the next logical step was to add the calculated value for the spin-rotation constant (a0 + a/2) to generate a new simulation. The result is shown in Fig. 5.6c. The simulation reproduces the experimental spectrum reasonably well at this stage. We made the other assignments shown in Fig. 5.6 by adding the calculated value of just this one spin-rotation constant. These assignments are indicated by solid lines which trace the splitting of the asymmetry doublets of the R2 and R3 transitions due to spin-rotation. More assignments can easily be made

77 a)

R (|K'|=2 ↔ |K"|=1) 1 ↔ R3(|K'|=2 |K"|=1)

b) 78

↔ R2(|K"|=1 |K'|=2)

29220.8 29221.0 29221.2 29221.4 29221.6 29221.8 29222.0 Frequency (cm-1)

Figure 5.6: Illustration of splitting of the |K |=1 transitions. The splitting of the R1 transition is determined uniquely by the constant (a0 +a/2). The splitting of the two pairs of asymmetric doublets of the R2 and R3 transitions is also eﬀected by this constant (although not uniquely). a) Experimental spectrum, b) simulation of B − X transition of conformer T using calculated rotational constants with no spin-rotation coupling, c) simulation after adding the calculated value of one combination, (a0 + a/2), spin-rotation constants, of d) simulation after ﬁtting three linear combinations of the rotational constants in the excited state, and (a0 + a/2). in other parts of the spectrum so that all three linear combinations of the rotational

constants in the excited state in addition to (a0 +a/2) can be ﬁt to yield the improved

simulation shown in Fig. 5.6d. However we still expect discrepancies since only one

linear combination (a0 + a/2) of spin-rotation parameter has yet been determined.

To extend the analysis, we focus our attention on the K=0 transitions which 1 − should be split by the amount (N + 2 )(a0 a). The eﬀect of adding this interaction

is best seen on the transition R3(K =0) shown in Fig. 5.7c. We can see from this

ﬁgure that addition of the calculated value (0.1 GHz) of (a0 −a) causes the R3(K =0)

transition to split by an amount similar to what is observed experimentally. This

spin-rotation constant also aﬀects the K=0 Q-branch and can hence be uniquely

determined.

As previously noted for T 1-propoxy, the constant b has nearly the same value as

(a − a0). Including the calculated values of b along with the value of the oﬀ-diagonal parameter d results in the much improved simulation shown in Fig. 5.7d.

At this stage the correlation between the simulation and the experimental spectrum is so good that most of the remaining lines throughout the spectrum can be assigned. This enables a ﬁt of all the molecular constants.

We may use the same method to analyze the vibrationally excited bands of conformer T, namely bands D and E, which were fit independently. The ground state constants obtained from the fits of bands B, D, and E were all found to be within two standard deviations. Thus the X˜ state vibrational level is the same for all three bands and assigned to be the vibrationless level. The molecular constants for this level were determined by simply averaging the constants obtained from each of the three independent fits, inversely weighted by their corresponding standard deviation.

79 a)

* d)

R (|K'|=1↔ K"=0) 3 c) 80

29219.0 29219.5 29220.0 29220.5 29221.0 29221.5 29222.0 Frequency (cm-1)

Figure 5.7: Illustration of splitting of the R3(K =0) transition upon adding the spin-rotation constant (a0 − a). a) Experimental spectrum of band B, b) Simulation with refined constants after adding (a0 + a/2), c) Simulation after adding the calculated value of (a0-a) and fitting all linear combinations of rotational constants in the excited state, B+C B−C 2 , 2 ,and(a0 + a); d) Addition of calculated values of the spin-rotation constants b, and d to simulation c). The resulting constants for the vibrationless levels of the X and B state (derived from the individual fits of the B band) are given in Table 5.2. The molecular state constants derived from the individual fits bands B, D and E are given in Table 5.3. The simulation of band B obtained from the fit rotational and spin-rotational constants is shown in Fig. 5.8.

Const. (GHz) Fita Calc. A 27.46(3) 27.87 B 3.955(4) 3.89 C 3.702(2) 3.64 a0 − a 0.12(1) 0.08 a0 + a/2 4.43(3) 4.37 b -0.09(3) -0.08 d 0.81(4) 1.73 A 26.08(2) 26.72 B 3.865(5) 3.86 C 3.582(3) 3.60 −1 T00(cm ) 29218.54(1) -

Table 5.2: Molecular constants of T conformer of 1-propoxy. The constants reported for the ground state are the standard deviation weighted average of the constants obtained in the ﬁt of the three individual bands B, D, and E. The excited state constants are those corresponding to the vibrationless band in the B˜ state.

81 Const. (GHz) Band B Band D Band E 79 transitions assigned 79 transitions assigned 107 transitions assigned σ=127 MHz σ=173 MHz σ=56 MHz A 27.46(4) 27.52(4) 27.53(1) B 3.950(7) 3.98(1) 3.948(7) C 3.695(4) 3.710(7) 3.693(1) a0 − a 0.12(2) 0.11(2) 0.105(5) a0 + a/2 4.40(3) 4.44(4) 4.41(1) 82 b -0.12(2) -0.08(3) -0.07(4) d 0.86(6) 0.76(8) 0.88(2) A 26.084(9) 26.68(1) 25.880(4) B 3.865(5) 3.886(5) 3.829(2) C 3.582(3) 3.619(5) 3.561(1)

−1 Table 5.3: Results of the independent fits of bands B, D, and E of 1-propoxy. T00 (cm )=29218.54(1), T0D −1 −1 (cm )=T00+238.26(1), T0E (cm )=T00+676.32(1) Table 5.2 shows that all the rotational constants are determined quite well. Fur- thermore, not only were the diagonal components of the spin-rotation tensor determined well, but also the off-diagonal component. This may seem surprising considering that the effect of the off-diagonal component on the spectrum should be much smaller especially for the case of a near prolate symmetric top (since this constant mixes states with ∆K = ±1). The small error bar on this constant may be rationalized as follows. Firstly, transitions forbidden in the symmetric top case may become allowed because of the off-diagonal term in the spin-rotation Hamiltonian that mixes states with ∆N = ±1. Thus transitions with ∆N = ±2 become allowed. Secondly, the effect of this constant on the spectrum increases with increasing N . Therefore this spin-rotation constant (d) can actually be determined rather well.

5.2.3 1-Propoxy, G Conformer

While both the T and G conformers of 1-propoxy are asymmetric tops with comparable spin-rotation interaction, the spectrum of the G conformer appears more complicated because it has only C1 symmetry compared to the Cs symmetry of the

T conformer. This lowering of symmetry has several ramiﬁcations. There are now 3 non-zero components of the transition dipole rather than one. The asymmetry splittings in the rotational spectrum will have contributions from both the X and B states for the G conformer. The number of independent spin-rotation constants increases from 4 to 6. Finally,ε ˜cc can no longer be expected to be approximately zero.

Nonetheless it is possible to analyze the spectrum of the G conformer in part because the analysis of the spectral bands of the T conformer which has been detailed

83 a) 84

876510 876540 876570 876600 876630 876660 Frequency (GHz)

Figure 5.8: Simulation of band B using the experimentally determined rotational and spin-rotation constants from the ﬁt of band B. a) Experimental spectrum of band B, b) Simulation. The rotational temperature is 1.1 K and the ratio of the squares of the dipole moment is a:b:c=0:0:1 as demanded by the Cs symmetry of this conformer. in section 5.2.2, has shown us that the ab initio predictions of the molecular parameters should be quite reliable. Again we sketch our approach to the assignment and analysis of a single band, A, to illustrate its sensitivity to the values of the molecular constants and the likelihood of mis-assignments. Despite the additional complexity of the spectrum of the G conformer, we can produce a simulation of band A, using only the information from the quantum chemistry calculation. Fig. 5.9 illustrates that the overall correlation between the experimental and predicted spectra is still rather good. However Fig. 5.9 also illustrates the problem of not being able to easily identify rotational transitions and spin-rotation splittings due to the increased spectral congestion. To begin the assignment process we alleviate this problem by going to the relatively uncongested spectral region shown in Fig. 5.10 which illustrates the eﬀect of spin-rotation interaction on the high N , |K| >0, transitions in the red end of a

hot (Trot=3 K) spectrum. Fig. 5.10b is the simulation of this region of band A using just the calculated rotational constants with the spin-rotation constants set to zero.

Clearly, some transitions involving |K| > 0 appear to be split into doublets which

can be simulated by adding the calculated value of a combination of spin-rotation

constants, (a0 + a/2) (see Fig. 5.10c). Using the assignments shown (indicated by

the solid lines) one linear combination of the rotational constants in the ground state

B+C ( 2 ) can be ﬁt and the resulting simulation is shown in Fig. 5.10d.

Since we now have a handful of rather unambiguous assignments, we may now

make use of the predicted spin-rotation constants to help make more assignments.

This is illustrated in Figs. 5.11-5.12. Fig. 5.11c traces the splitting due to spin-

rotation, of the R1(|K | =1↔|K | = 2) transition in addition to those already

assigned in Fig. 5.10. The two rigid asymmetric rotor transitions shown in Fig. 5.11b

85 b)

a) 86

28632 28633 28634 28635 28636 28637 Frequency (cm-1)

Figure 5.9: a) Experimental spectrum of 1-propoxy band A, b) Simulation using calculated rotational constants of 1-propoxy G conformer without spin-rotation coupling, c) Simulation using calculated rotational and spin-rotation constants of 1-propoxy G conformer. The ratios of the square of transition dipole moments are a:b:c=1:1.1:4 (obtained from ab initio calculations on the excited state). The rotational temperature is 1.1 K. ↔↔ P4 (||K'|=3 |K"|=4) a

P (|K'|=3 ↔ |K"|=4) 6 ↔ P4 (|K'|=2 |K"|=3) b ↔ P (|K'|=2 ↔ |K"|=3) P5 (||K'|=3 K"|=4) 5

d 87

28629.0 28629.5 28630.0 28630.5 28631.0 28631.5 28632.0 28632.5 Frequency (cm-1)

Figure 5.10: Effect of spin rotation on transitions involving |K| >0. a) Red end of experimental spectrum, b) Simulation of band A using calculated rotational constants of both states but with no spin-rotation coupling, c) Addition of the calculated value of one spin-rotation constant, (a0 + a), d) Simulation after refining one linear combination of the rotational constants in the excited state. The discrepancy between the frequencies in d and a is due to the fact that all the molecular constants have not been fit. are asymmetry doublets which should be split by identical amounts (3/2(a0 + a/2)).

The calculated splitting (1.91 GHz) agrees well with experimental splittings (1.84 and

1.67 GHz) of these two transitions.

As the number of likely assignments increases, we can ﬁt additional constants.

Next we ﬁt two linear combinations of ground state rotational constants, namely,

B+C B−C 2 and 2 . Using this improved simulation, we can make additional assignments, and ﬁt all three ground state rotational constants. One more iteration of this process allows us to ﬁt all 6 rotational constants of the X and B states with the resulting simulation shown in Fig. 5.12b.

To this point only calculated spin-rotation constants have been used, but we are now in a position to determine ﬁt values from the assigned lines. Since the spin-

rotation constants that are diagonal in N and |K | (i.e., a0 and a) will have the

biggest effect on the spectrum, these were fit first. This enabled more definitive

assignments to be made. Since the G conformer is more asymmetric than the T

conformer, the spin-rotation constant b can be well determined and was ﬁt next.

We are then left with constants c, d,ande to be determined. These oﬀ-diagonal

spin-rotation constants have the least eﬀect on the spectrum and hence most line

assignments could be made before fitting them. In the final fit of the cold spectrum, all

the rotational and spin-rotation constants were determined. The resulting simulation

using ﬁt rotational and spin-rotation constants is shown in Fig. 5.12c, with the

corresponding complete simulation in Fig. 5.13a.

As an additional test to verify that the ﬁt obtained is unique, the spectrum was

simulated at 3 K (nearly three times warmer than the cold spectrum). Fig 5.13b shows

the comparison of this spectrum with an experimentally obtained “hot” spectrum.

88 a)

↔ P1 (|K'|=1 K"=0) ↔ R1(|K'|=2 |K"|=1)

28632.5 28633.0 28633.5 28634.0 28634.5 Frequency (cm-1)

Figure 5.11: The spectrum of band A may be assigned by systematically ﬁtting one constant at a time and successively “improving” the simulation (see text for details). a) Experimental spectrum of band A of 1-propoxy; b) Simulation of B˜ −X˜ transition of G conformer using calculated rotational constants and zero spin-rotation coupling; c) Simulation using calculated values of all rotational and spin-rotation constants and B+C ﬁtting 2 after making the assignments shown (using solid lines) in Fig. 5.10. The additional assignments shown using solid lines, can now be made.

89 a)

↔ P1 (|K'|=1 K"=0) ↔ R1(|K'|=2 |K"|=1) b)

28632.5 28633.0 28633.5 28634.0 28634.5 Frequency (cm-1)

Figure 5.12: a) Experimental spectrum of band A of 1-propoxy; b) Simulation of X˜ − B˜ transition of G conformer with ﬁt rotational constants in both states and calculated spin-rotation constants; c) Simulation after making several more assignments (not shown) and ﬁtting all rotational and spin-rotation constants (see text for details).

90 a)

Expt.

T=1.3 K

Sim.

28632 28633 28634 28635 28636 28637

Expt. 91

T=3 K

Sim.

28630 28632 28634 28636 28638 Frequency (cm -1)

Figure 5.13: a) Comparison of the experimental spectrum of band A to its simulation using the ﬁt molecular parameters of Table 5.4. The rotational temperature is 1.3 K, b) Simulation of rotationally hot spectrum. The rotational spectrum is 3 K. The ratio of the components of the transition dipole along the inertial axes is a:b:c=2:1:3 as taken to best reproduce the observed spectral intensities. Const. (GHz) Fita Calc. A 15.430(6) 15.46 B 5.211(3) 5.10 C 4.433(2) 4.35 a0 − a 0.628(6) 0.62 a0 + a/2 1.111(6) 1.11 b -0.45(1) -0.49 d 1.24(5) 1.53 c 0.36(5) 0.37 e 0.4(1) 0.55 A 13.574(2) 14.10 B 5.360(1) 5.23 C 4.401(1) 4.36 −1 T00(cm ) 28634.21(1) -

Table 5.4: Molecular constants of G conformer of 1-propoxy. The ground state constants are the stantard deviation weighted average of the constants obtained from independent ﬁts of bands A and C. The excited state constants are those corresponding to the vibrationless level of the B˜ state obtained from the ﬁt of band A.

Fig. 5.14 shows a 1 cm−1 slice of the comparison of the experimental and simulated

hot spectra and it can be seen that they agree very well.

The excited vibrational band C was ﬁt in a similar manner. The S/N ratio for

this band is signiﬁcantly worse than that of band A which prevented the spin-rotation

constants c and e from being determined from band C. The X˜ state molecular con-

stants obtained from the ﬁts of bands A and C were all found to be within 2 standard

deviations. Thus the weighted average of these constants are taken for the vibration-

less level of the X state. The molecular constants of the G conformer of 1-propoxy

are collected in Table 5.4, along with those for the vibrationless level of the B˜ state

obtained from the ﬁt of the origin band (A). The results of the individual ﬁts of bands

A and C are given in Table 5.5

92 T = 3K

a) Expt.

b) Fit 93

28634.0 28634.1 28634.2 28634.3 28634.4 28634.5 28634.6 28634.7 28634.8 28634.9 28635.0 Frequency (cm-1)

Figure 5.14: Blow-up of a 1 cm−1 region of the rotationally hot spectrum. a) Experimental, b) Simulation at 3 K after ﬁtting cold spectrum. Const. (GHz) Band A Band C 223 transitions assigned 119 transitions assigned σ=60 MHz σ=73 MHz A 15.438(2) 15.42(1) B 5.207(1) 5.217(5) C 4.432(1) 4.434(2) a0 − a 0.621(3) 0.63(1) a0 + a/2 1.110(4) 1.09(2) b -0.45(1) -0.44(2) d 1.15(4) 1.34(9) c 0.36(5) - e 0.4(1) - A 13.571(1) 13.635(6) B 5.361(1) 5.322(3) C 4.401(1) 4.404(1) −1 −1 T00 (cm ) 28634.21(1) T0C (cm )=T00+595.31(1)

Table 5.5: Results of the independent ﬁts of bands A and C of 1-propoxy. The spin-rotation constants c and e could not be determined from the ﬁt of band C.

94 5.2.4 Discussion Vibrational Assignments

It is useful to note from Table 5.1 that the calculated rotational constants of the T

and G conformers of 1-propoxy diﬀer by the order of 40%. However Tables 5.2 and 5.4

indicate agreement between the calculated and observed X state rotational constants

to within 3%. The same trend is clearly evident in the spin-rotation constants; how-

ever, the reliability of the prediction is much lower, as expected. It is therefore quite

clear that the rotational and ﬁne structure of a given vibrational band unambiguously

“bar-codes” for the conformer carrying that band. Thus it can be considered to be

ﬁrmly established that bands A and C correspond to the G conformer and bands B,

D, and E to the T conformer of 1-propoxy.

Let us ﬁrst consider the vibrational structure of the simpler spectrum of the G

conformer. It is reasonable to assume that band A corresponds to the origin of the

B −X electronic transition of this conformer. In all the smaller alkoxies,4, 5, 7, 8, 40, 42 by

far the dominant feature of the spectrum is a strong progression in the C-O stretch,

peaking at v 4, due to the large increase in the C-O bond in the B state of 1-

propoxy. One would again expect such a progression in 1-propoxy. In our previous low

resolution spectrum42 of 1-propoxy we assigned the ﬁrst member of that progression to

the B band (582 cm−1 higher), but our rotational “bar coding” now clearly indicates it is the C band, which appears as a shoulder on the high frequency side of the B band, that belongs to the G conformer. Therefore we assign the C band at 596 cm−1

above the A band as likely corresponding predominantly to the excitation of the C-O

−14,6 −140 stretch. This value is quite consistent with ω0 of 665 cm and 603 cm for

the C-O stretch in CH3OandC2H5O.

95 For the T conformer we have three lines, the lowest one (B) we assume to be the origin. That then places the band E at 676 cm−1 as the only one in the C-O stretch region. This frequency seems relatively high compared to 596 cm−1 in the

G conformer but ab initio calculations,29 while not particularly accurate for the B state, indicate that the C-O stretch frequency should be signiﬁcantly higher in the

T conformer compared to G. The remaining strong line, D, at 238 cm−1 above B presumably corresponds to a low frequency deformation of the C-C-C-O backbone.

There are a few weak lines in the region between A-E, but nothing strong enough to rotationally resolve and assign deﬁnitely. We have also scanned 1500 cm−1 above line E and found no additional observable lines. Thus we conclude that for both of the T and G conformers the LIF spectrum abruptly terminates at 700 cm−1 above its origin with only one quantum of C-O stretch being observed. This is in remarkable contrast to the previously reported4, 42 spectra of methoxy, ethoxy, and 2-propoxy. In each of these cases, the excitation spectra contained at least 5 quanta of C-O stretch

−1 excitation and extend for 3000 cm above the origin. The LIF spectrum of CH3O is known to be terminated by predissociation from repulsive states asymtotically approaching the X state R·+O dissociation limit. Using the observed B−X excitation frequency and calculations29 of the X˜ R·+O dissociation limit places the B state vibrationless level ≈ 3800 cm−1 and 3200 cm−1 above the R·+O dissociation limit for

G and T 1-propoxy respectively. Since the X state dissociation limit establishes a lower limit for the onset of predissociation in the B state, predissociation cannot be the explanation for the observed cut-oﬀ in ﬂuorescence below 700 cm−1 in 1-propoxy.

Rather we suspect that the B state of 1-propoxy undergoes rapid (compared to radiation) internal conversion to the X state when excess energy is deposited

96 in its vibrational modes. 1-propoxy has low frequency torsional modes due to the existence of a C-C-C linkage which is lacking in the molecules methoxy, ethoxy, and 2- propoxy, that show the longer progressions. Such C-C-C linkages have been shown to dramatically accelerate intramolecular vibrational redistribution (IVR) in comparable hydrocarbon systems.43–45 These studies have shown that there is eﬀecient coupling of excited C-H stretch modes with bath states in molecules with low frequency torsional modes via vibration-rotation mixing which leads to a dramatic increase in the density of states.

97 In the case of the alkoxy radicals, we suspect that there might be eﬀecient coupling

between the excited C-O stretch modes and the dense manifold of vibrational states

in the ground potential energy surface at these energies. Further experiments are

certainly necessary to deduce the mechanism of non-radiative decay in these species.

Electronic Origins

The simple picture of the B − X electronic transition in all the alkoxy radicals is that an electron jumps from a pσ C-O bonding orbital to pair with the unpaired electron localized in a nonbonding pπ O orbital in the X state. This transition weakens signiﬁcantly the C-O bond.

If we use the origin (29210 cm−1) of ethoxy as a reference, then the origins of T

and G 1-propoxy are shifted by +9 cm−1 and −576 cm−1. The implication would be that adding an additional CH2 to ethoxy shifts the X and B states almost exactly equally so long as Cs symmetry is maintained. However by rotating the O out of plane

in the G conformer the B state is lower by nearly 600 cm−1 more than the X state.

Our computations29 for the X state place the G conformer about 10 cm−1 below the

T conformer (B states calculations of these energy diﬀerences are not reliable). This

implies that the B state of G 1-propoxy is stabilized by ≈ 600 cm−1 compared to the

T conformer. Our ab initio calculations indicate that the B state of G 1-propoxy is

stabilized by 340 cm−1 relative to the B state of T 1-propoxy. This stabilization can

be rationalized in terms of non-classical C-H...O hydrogen bonding which is possible

in G but not in T 1-propoxy. This interaction is more important in the B state than

the X state because of the increase in the volume of the p-orbital on the oxygen atom

upon electronic excitation. Such non-classical hydrogen bonds have been detected

98 recently in complex biological systems.46–48 This interaction is more important in the

B state than the X state because of the increase in the volume and double occupancy

of the p-orbital on the oxygen atom upon electronic excitation.

Rotation and Spin-rotation Constants

As noted earlier there is good (3%) agreement between calculated and experimental rotational constants in both the B and X states. As with CH3OandC2H5Othe

rotational constants are consistent with the expected relatively dramatic change of

the C-O bonding in the X and B states. For simplicity one can assume that the only geometric changes between the two states are changes in C-O bond length and

C-C-O angle. Then one deduces from the observed rotational constants C-O bond length increases of 0.17 A˚ and 0.18 A˚ and C-C-O angle decreases of 5.50 and 80 for

the T and G conformers respectively.

The values for spin-rotation tensor components ˜αβ are given in Table 5.6. At ﬁrst

glance the values are rather discordant. However as Tables 5.2 and 5.4 show, they are

qualitatively consistent with our predictions. The basis of these predictions assumes

a model in which the nature of the orbital of the “unpaired spin,” largely localized

on the O atom, does not change signiﬁcantly from ethoxy to either conformer of 1-

propoxy. It would seem that at least in a qualitative sense this model is validated by

the present observation.

99 Conformer T Conformer G

Constant Fit Calc. Fit Calc.. ˜ aa -8.72(3) -8.66 -1.58(1) -1.60 ˜ bb -0.22(2) -0.15 -1.07(2) -1.11 ˜ cc -0.03(3) -0.0 -0.18(1) -0.13 |˜ ab| = |˜ ba| 0.81(4) 1.73 1.24(5) 1.53 |˜ bc| = |˜ cb| 0.0 0.0 0.36(5) 0.37 |˜ ac| = |˜ ca| 0.00 0.00 0.4(1) 0.55

Table 5.6: Spin-rotation constants of T and G conformers of 1-propoxy

100 CHAPTER 6

High-Resolution Spectroscopy of 1-Butoxy

6.1 Introduction

In the previous chapter, the vibronic assignments of the LIF bands observed in the moderate resolution spectrum of the 1-propoxy radical and also the results of the analysis of their rotational structure was described. In this chapter, the spectroscopy of the next alkoxy radical in the homologous series, namely 1-butoxy will be discussed along similar lines. The survey LIF spectrum of 1-butoxy is shown in Fig. 6.1. The bands labled A through F in Fig. 6.1 were studied under high resolution to resolve their rotational structure. The rotationally resolved spectra of 1-butoxy are shown in

Fig. 6.2.

Three unique sets of bands can immediately be distingushed based upon big differences in rotational structure with band A in one group, bands B, D, and F in the second, and bands C and E in the third. It is likely that the three sets of bands of 1-butoxy shown in Fig. 6.2 are due to diﬀerent conformers of this radical based upon a similar observation in the case of 1-propoxy. The number of conformations available for molecules belonging to a homologous series increases dramatically as the number of skeletal atoms (carbon atoms in the case of the alkoxy radicals) increases. Thus we expect the spectroscopy of 1-butoxy to be more complicated than

101 B

D A 102 E F

28400 28600 28800 29000 29200 29400 29600 29800 30000 Frequency (cm-1)

Figure 6.1: 1-butoxy survey LIF spectrum E

29362.0 29363.0 29364.0 29365.0 29366.0

29162.0 29163.0 29164.0 29165.0 29166.0

29765.0 29766.0 29767.0 29768.0 29769.0

29263.0 29264.0 29265.0 29266.0

29094.0 29095.0 29096.0 29097.0 29098.0

28648.0 28649.0 28650.0 28651.0 28652.0 Frequency (cm-1)

Figure 6.2: Rotationally resolved spectra of bands A through E in 1-butoxy.

103 that of 1-propoxy as indeed Fig. 6.2 demonstrates. The lowest frequency band in each

group is considered to be the apparent origin of the particular conformer. The other

higher frequency bands in each group are most likely vibrationally excited bands of

the particular conformer. The remainder of this chapter will detail the rotational

analyses of the spectra shown in Fig. 6.2. These analyses will result in a detailed

set of molecular constants (rotational and spin-rotational) for the states and species

involved. This data will also serve to conﬁrm the presence of multiple conformers

of the radicals and the corresponding vibronic assignment of these bands using the

“rotational barcoding” technique.

6.1.1 Results

As described in Chapter 3, there are ﬁve unique conformers of 1-butoxy pictured

in Fig. 6.3. The calculated molecular constants and realtive energies of the ﬁve

conformers are given in Table 6.1.

The B − X transitions of all five conformers were simulated and the results are shown in Fig. 6.4. It is evident from Fig. 6.4 that the rotational structure of all the five conformers can be distinguished from each other. The experimental spectra can be compared with these simulations to find the best match for the initial guess for the fit. Fig. 6.5 shows the comparison of the experimental spectrum of band A with the five simulations. The simulation using the calculated constants of conformer

G1T2 appears to be the best candidate for the spectrum.

104 O O O a) C H H C H H H 2 5 H 2 5 φ 1 ( 1) H H H H H H C H H 2 5 H

0 0

T1 180 G1 60 ′ 0

G1 -60

CH H H H H H H 3 H

2 ( 2) H H H CH H 3 CH 3 CH O CH2O 2 CH2O

0 ′ 0 G 1200 T2 180 G2 -120 2

O H H

O CH H H H 3 H H H O CH3 H H

C2H5 H

H H CH3 H H H H H H C H H C2H5 2 5 CH2O H CH2O CH2O

G T T G

1 2 T1T2 1 2

H H

H H H O H O C H C2H5 H H 2 5

H CH CH H H 3 H H H 3 H CH2O H CH2O ′ G1G2 G1 G2

Figure 6.3: The ﬁve unique conformers of 1-butoxy

105 Rot. Const.(GHz) G1T2 T1T2 T1G2 G1G2 G1G2 A 13.53 20.12 12.40 8.90 7.57 B 2.34 2.00 2.41 2.89 3.65 C 2.19 1.90 2.21 2.69 2.75 ˜ aa -1.13 -5.47 -3.99 -0.75 -0.08 ˜ bb -0.54 -0.15 -0.00 -0.29 -1.18 ˜ cc -0.08 -0.00 -0.06 -0.45 -0.05 |˜ ab|=|˜ ba| 1.10 1.60 0.00 0.53 0.30 |˜ ac|=|˜ ca| 0.43 0.0 0.68 0.68 0.07 |˜ bc|=|˜ cb| 0.20 0.0 0.00 0.36 0.23 A 12.33 18.56 12.73 8.18 7.51 B 2.42 2.02 2.35 3.02 3.46 C 2.19 1.90 2.21 2.69 2.75 Relative Energies (cm−1) 0.0 7 424 344 423

Table 6.1: Calculated ground and excited state constants, and relative energies of the diﬀerent conformers of 1-butoxy. The relative energies were calcualted with zero point energy correction.

106 The rotational constants of conformer T1T2 are unique and hence there is little doubt that the conformational assignment for band B (as well as bands D and F) is conformer T1T2 as is evident from Fig. 6.6. Finally it is clear from Fig. 6.7 that the best candidate for band C (and E) is conformer T1G2 .

The full rotational analysis of the bands A through F was carried out in a similar manner as in the case of 1-propoxy to conﬁrm the above conformational assignments and obtain structural information.

6.1.2 1-Butoxy Conformer T1T2 Rotational Structure

It is clear from Fig. 6.6 that the most likely conformational assignment for band B of 1-butoxy is conformer T1T2 which has Cs symmetry. The spectrum of band B is quite simple; pure c-type transitions are observed and clear P, Q, and R branches can be distinguished. This band is analogous in terms of rotational structure, to band B of 1-propoxy whose carrier was shown to be an analogous Cs trans conformer in the previous chapter. It was demonstrated in the analysis of the LIF spectra of 1-propoxy that all six rotational constants can be determined in principle from the spectra. As suggested by Table 6.1, all conformers of 1-butoxy are near prolate symmetric tops.

Thus it is reasonable that line assignments and approximate selection rules for the rotational transitions were made assuming symmetric top quantum numbers.

Spin-Rotation

In order to ﬁt the spectrum and obtain structural information therefrom, one has to consider the eﬀect of spin rotation on the spectrum. A detailed analysis of this has been presented in the analysis of the spectral bands of 1-propoxy. Since conformer 2

107 ' e) Conformer G1 G2

d) Conformer G1G2

c) Conformer T1G2

b) Conformer T1T2

a) Conformer G1T2

-2.0 -1.3 -0.7 0.0 0.7 1.3 2.0 Relative Frequency (cm-1)

Figure 6.4: Simulations of the B − X transitions of the ﬁve conformers of 1-butoxy using calculated rotation and spin-rotation constants. The rotational temperature is 1.5 K and the ratios of the square of the electric dipole moment a:b:c were taken from the B state calculations and are respectively 17:1:8, 0:0:1, 1:14:13, 1.5:1:2.3, and 1:0:1.5 for conformers G1T2 ,T1T2 ,T1G2 ,G1G2 ,andG1G2 .

108 ' Conformer G1 G2

Conformer G1G2

Conformer T1G2

Expt. spectrum of band A

Conformer T1T2

Conformer G1T2

Figure 6.5: Comparison of the experimental spectrum of band A of 1-butoxy with the simulations of the B − X transitions of the ﬁve conformers of 1-butoxy using calculated and rotation and spin-rotation constants.

109 ' Conformer G1 G2

Conformer G1G2

Conformer T1G2

Expt. spectrum of band B

Conformer T1T2

Conformer G1T2

Figure 6.6: Comparison of the experimental spectrum of band B of 1-butoxy with the simulations of the B − X transitions of the ﬁve conformers of 1-butoxy using calculated and rotation and spin-rotation constants.

110 ' Conformer G1 G2

Conformer G1G2

Conformer T1G2

Expt. spectrum of band C

Conformer T1T2

Conformer G1T2

Figure 6.7: Comparison of the experimental spectrum of band C of 1-butoxy with the simulations of the B − X transitions of the ﬁve conformers of 1-butoxy using calculated and rotation and spin-rotation constants.

111 of 1-butoxy has Cs symmetry, only four of the possible six spin-rotation constants can

41 be determined since for a molecule with Cs symmetry, the constants c and e vanish.

Furthermore, the constant ˜cc=0 unless there are contributions to the spin-rotation tensor from excited electronic states. However, these contributions will be so small that it is unlikely that they will be determined by our experiment. In Chapter 5 we demonstrated that there are certain linear combinations of the diagonal components of the spin-rotation tensor that cause certain transitions to split. Transitions involving

K =0 are split by the amount (N +1/2)(a0 − a) while those involving K =±1and

3 N =1 are split by the amount 2 (a0 + a/2). Using the calculated values of these constants, we may predict the magnitude of the splittings to serve as a guide in

making assignments. The constants a0 and a are diagonal in K and should thus be well determined from the spectrum. The constant b mixes levels with ∆K = ±2 which will be strongly mixed by the asymmetric part of the rotational Hamiltonian and should thus be determined as well. Thus we should be able to well determine all three diagonal components of the spin-rotation tensor from the spectrum.

Fit

The analysis of this spectrum was carried out in a manner very similar to that of the corresponding band (band B) in 1-propoxy. In order to complete the line assignments, it is important identify all the spin-rotation splittings. The calculated value of the spin-rotation constant (a0 +a/2) is large (2.1 GHz) and it was fairly trivial to identify spin-rotation splittings caused by this constant. These splittings are shown in Fig.

6.8. However, the claculated value of the constant (a0 − a) is quite small (0.12 GHz).

Thus the eﬀect of this constant on the spectrum is much less, although it can still be

112 determined from the spectrum as demonstrated in Fig. 6.9. The K=0 transitions

(which are aﬀected uniquely by this spin-rotation constant) are barely split (they look

broadened rather than split). However the eﬀect of this spin-rotation constant on the

spectrum is still observable for the high N (N >2) transitions as shown in Fig. 6.9.

Furthermore, this constant will have a small aﬀect on the splitting of the N =0,

K =0↔|K| = 1 transitions and thus can be well determined. The simulated ﬁt

spectrum of band B from the ﬁt constants is shown in Fig. 6.10.

The resulting ﬁt spectrum of band B is shown in Fig. 6.10. The vibrationally

excited bands D and F were ﬁt independently. The ground state constants obtained

from the ﬁts of all three bands were found to be within two standard deviations. The

resulting constants for the vibrationless levels of the X and B states of conformer

T1T2 are given in Table 6.2. The ground state constants reported are those obtained by weighting the constants obtained from the ﬁts of the origin and vibrationally excited bands by the inverse of the corresponding standard deviation. The results of the individual ﬁts of bands B, D, and F are given in Table 6.3.

113 a)

c) 114

29094.0 29094.2 29094.3 29094.5 29094.7 29094.8 29095.0 Frequency (cm-1)

Figure 6.8: a) Low frequency end of the experimental spectrum of band B, b) Simulation of the B˜ − X˜ transition of T1T2 conformer of 1-butoxy (relative intensity of dipole components, µα,a:b:c=0:0:1), c) Addition of calculated value of one spin-rotation constant (a0 + a/2) that splits transitions with |K |=1, d) Simulation after fitting two linear combinations of the rotational constants, e) Simulation after fitting five linear combinations of the rotational constants and the spin-rotation constant (a0 + a/2). a)

d) *

R2 R1 R3

a) R4

29096.0 29096.2 29096.3 29096.5 29096.7 Frequency (cm-1)

Figure 6.9: a) Portion of experimental spectrum of band B of 1-butoxy, b) Simulation of the B˜ − X˜ transition of T1T2 conformer showing the |K | =1↔ K =0Rbranch transitions using a rigid-rotor Hamiltonian with no spin-rotation, c) simulation upon adding the calculated value of the spin-rotation constant a0 − a; the splitting of the R2 and R3 transitions is noticeable, d) Simulation after adding the calculated value of the spin-rotation constant d.TheR4 transition (marked with an asterisk) which was more split before adding this constant looks more like the experimental transition due to the addition of this oﬀ-diagonal constant. Thus these two spin-rotation constants can be determined from this portion of the spectrum.

115 Const. (GHz) Fit Calc. A 20.19(2) 20.14 B 2.044(6) 2.00 C 1.934(4) 1.90 a0 − a 0.125(9) 0.08 a0 + a/2 2.918(8) 2.77 b -0.13(3) 0.08 d 0.64(4) 1.60 A 18.07(1) 18.56 B 2.049(3) 2.02 C 1.916(3) 1.91 −1 T0(cm ) 29095.28(1) -

Table 6.2: Experimentally determined molecular constants of conformer T1T2 of 1- butoxy. The calculated constants are those predicted from the quantum chemistry calculations. Experimental ground state constants were obtained by averaging over all the vibrational bands (D and F) observed while the excited state constants are those for the vibrationless level obtained from ﬁtting the origin band B.

116 a)

29093 29094 29095 29095 29096 29097 29097 29098 29099 Frequency (cm-1)

Figure 6.10: Comparison of experimental sepctrum and simulation based upon ﬁt constants (Table 6.2) for band B and conformer T1T2 of 1-butoxy. a) Experimental spectrum of band B, b) Simulation using ﬁt constants. The ratio of the square of the transition electric dipole moment a:b:c=0:0:1 and the rotational temperature is 1.15 K.

117 Const. (GHz) Band B Band D Band F 79 transitions assigned 79 transitions assigned 107 transitions assigned σ=51 MHz σ=96 MHz σ=86 MHz A 20.19(2) 20.24(2) 20.16(2) B 2.054(6) 2.040(8) 2.029(3) C 1.922(8) 1.955(7) 1.936(3) a0 − a 0.14(1) 0.11(1) 0.114(8) a0 + a/2 2.918(8) 2.927(9) 2.910(6) 118 b -0.13(2) -0.09(3) -0.15(4) d 0.68(4) 0.64(6) 0.60(2) A 18.067(5) 18.51(1) 17.996(6) B 2.049(3) 2.043(4) 2.018(2) C 1.916(3) 1.934(4) 1.916(2)

−1 Table 6.3: Results of the independent ﬁts of bands B, D, and F of 1-butoxy. T00 (cm )=29095.28(1), −1 −1 T0D(cm )=T00+168.55(1), T0F (cm )=T00+670.91(1). 6.1.3 Conformer G1T2 -BandA Rotational Structure

It has been postulated that the likely conformational assignment for band A is conformer G1T2 based upon the good agreement between the simulation of the B − X transition using the calculated molecular constants of conformer G1T2 and the experimental spectrum of band A (see Fig. 6.5). Conformer G1T2 has C1 symmetry and thus transitions will be allowed by all three components of the electric dipole moment. The spectrum is therefore expected to have fairly complicated rotational structure. Conformer G1T2 of 1-butoxy is analogous to the gauche conformer (G) of

1-propoxy which has already been discussed in detail in the previous chapter.

Spin-Rotation

Since conformer G1T2 has only C1 symmetry, all six components of the spin-rotation tensor should be determinable. Using the calculated values of these constants, we may predict the magnitude of the splittings to serve as a guide in making assignments.

The constants a, a0,andb are diagonal in K and should thus be well determined from the experimental spectrum. The effect of the spin-rotation constants d and e which are off-diagonal in K should be smaller, however their effect should increase with increasing N . The constant c mixes states with ∆K = ±2, i.e., the same states that are mixed by the asymmetric part of the rotational Hamiltonian and should thus be determinable from the spectrum.

Fit

The simulated spectrum shown in Fig. 6.5 was used as the starting point in the analysis of band A. It is quite clear from Fig. 6.5 that the overall correlation between

119 the experimental spectrum and the simulation is quite good. This implies that the

calculated molecular constants used to generate the simulation are rather close to the

experimental values. However, in order to carry out a ﬁt to obtain the molecular

constants, it is necessary to identify spin-rotation eﬀects in the spectrum to make the

correct line assignments. In the following analysis, line assignments were made based

upon the good correspondence between the simulated and experimental spectra.

It is easier to pick out splittings in the high N transitions (extremes of the

spectrum) because the splitting increases with increasing N . This is demonstrated

in Fig. 6.11. Fig. 6.11a shows a simulation using calculated rotational constants only

with no spin-rotation. Clearly the transitions shown using solid lines appear to be

split. The splitting indeed occurs upon adding the calculated values of all the spin-

rotation constants as can be seen in Fig. 6.11b. The assignments shown in Fig. 6.11b

using solid lines were made to ﬁt one linear combination of the rotational constants in

the excited state to yield the improved simulation shown in Fig. 6.11c. The relative

weights of the a, b,andc transition dipole moments were varied (from their ab initio

values) to get better relative intensities.

The eﬀect of the diagonal components of the spin-rotation tensor, namely (a0 +

a/2) and (a0 − a) is illustrated in Fig. 6.12. The assignments shown are those corresponding to |K| =1↔ K = 0 transitions in a Q-branch and N =1,K =0↔

|K| = 1 transitions in another Q-branch. By making these assignments in addition to those already made in Fig. 6.11, more linear combinations of the rotational constants can be ﬁt as shown in the simulation 6.12c) obtained by ﬁtting all three linear combinations in the excited state. This simulation clearly looks closer to the experimental spectrum than the simulation 6.12b). We can then make additional

120 a

28647.6 28647.8 28648.0 28648.2 28648.4 Frequency (cm-1)

Figure 6.11: Spin-rotation in 1-butoxy conformer G1T2 : a) Simulation using calculated rotational constants without spin-rotation, b) splitting of transitions upon adding the calculated values of all six spin-rotation constants, c) ﬁt of one linear combination of the rotational constants in the excited state, d) Experimental spectrum.

121 assignments shown in Fig. 6.12c) and in other parts of the spectrum as well, to progressively fit all the linear combinations of the rotational constants in the ground state as shown in Fig. 6.12d). It is evident that this simulation resembles the experimental spectrum even more. Thus by progressively refining the rotational constants, more and more assignments can be made unambiguously to then fit the diagonal components of the spin-rotation tensor, namely, (a0 + a/2), (a0 − a)andb (whose effect on the spectrum is the greatest of all the spin-rotation constants) to obtain simulation 6.12e). At this stage, approximately 130 assignments could be made and all the rotational constants and five spin-rotation constants ((a0 + a/2), (a0 − a), b, d,andc) could be fit to yield simulation 6.12f).

In the final fit obtained by assigning 146 transitions, all rotational and spin- rotation constants were determined. The resulting simulation spectrum of band A is shown in Fig. 6.13 and the results of the fit are given in Table 6.4.

122 a)

28649.0 28649.2 28649.3 28649.5 28649.7 Frequency (cm-1)

' ↔ " |K'|=1 ↔ K"=0 Q-branch K=0 |K |=1 Q-branch

Figure 6.12: Spin-rotation coupling in conformer G1T2 of 1-butoxy: a) expanded view of experimental spectrum of band A showing two Q-branches (in boxes), b) simulation using refined (fit) rotational constants as demonstrated in Fig. 6.11, c) Simulation obtained after fitting all three linear combinations of the rotational constants in the ground state, d) simulation after fitting all six linear combinations of rotational constants in the ground and excited states, e) Simulation after fitting the spin-rotation constants (a0 +a/2), (a0 −a)andb, f) Simulation after fitting six linear combinations of the rotational constants and five spin-rotation constants (see text for details).

123 Expt.

Fit

28648 28649 28649 28650 28651 28651 28652

Frequency (cm-1)

Figure 6.13: Comparison of the experimental spectrum with the simulation based upon ﬁt constants (Table 6.4) for band A and conformer G1T2 fo 1-butoxy. The ratio of the square of the transition electric dipole moment a:b:c is 10:2:9 (the calculated values are 17:1:8) and the rotational temperature is 1.2 K.

124 Const. (GHz) Fit Calc. A 13.419(6) 13.53 B 2.397(2) 2.34 C 2.240(1) 2.19 a0 − a 0.328(4) 0.31 a0 + a/2 0.709(9) 0.72 b -0.20(1) -0.23 d 0.69(5) 1.10 c 0.13(5) 0.20 e 0.39(7) 0.43 A 11.821(3) 12.33 B 2.462(1) 2.42 C 2.247(1) 2.22 −1 T0(cm ) 28649.47(1)

Table 6.4: Molecular constants of conformer G1T2 from the ﬁt of band A of 1-butoxy.

125 6.1.4 1-Butoxy Conformer T1G2

Conformer T1G2 of 1-butoxy has C1 symmetry and thus six rotational and six spin- rotation constants should be obtainable from the spectrum as in the case of band A.

The ﬁt of this band was thus carried out in a manner analogous to that of band A.

The identiﬁcation of transitions that are split by spin-rotation is easily done at the ends of the spectrum where the rotational structure and spin-rotation structure can be distinguished. Fig. 6.14b) shows that the correlation between the experimental spectrum and the simulation using just the calculated rotational constants and no spin-rotation is quite good. The transitions labeled R0, R1,andR2 are R-branch transitions with |K| =1↔ K = 0. It is clear that these transitions correlate very well with the experimental spectrum and thus their assignment is unambiguous.

There is no observable splitting of these transitions which implies that the magnitude of the spin-rotation constant (a0 − a) that uniquely determines the splitting of these transition is very small and indeed the calculated value of this constant is 0.03 GHz.

The transitions assigned using the solid lines correspond to those with K =0↔

|K| = 1. It is clear from Figs. 6.14 a) and b) that these transitions appear to be split in the experimental spectrum. The splittings appear upon adding the calculated values of the spin-rotation constants as shown in Fig. 6.14 c). The major contribution to this splitting is from the constant (a0 + a/2) since the other diagonal spin-rotation constants (a0 − a)andb are very small. Thus (a0 + a/2) can be well determined from the spectrum.

It can be seen from a comparison of Figs. 6.14 a) and b) that the details in the

Qbranchwith|K| =1↔ K = 0 are not exactly reproduced in the simulation.

126 In order to make correct line assignments herein, the assignments for the R-branch shown and those in the blue end of the spectrum shown in Fig. 6.14 c) were made

B+C to fit 2 . The result of this fit is shown in Fig. 6.14 d). This simulation is clearly an improved one using which more assignments can be made to progressivly fit the rotational constants. The simulations after fitting all three linear combinations of the rotational constants in the excited state and ground state respectively are shown in Figs. 6.14 e) and f). This enabled more assignments to be made. Fig. 6.14 g) shows the simulation after fitting the spin-rotation constant (a0 + a/2). At this point, the Q-branch shown almost exactly reproduces the experimental spectrum so that assignments within it could be made to fit (a0 − a)andb. Although (a0 − a)is very small, it could be determined from the spectrum. This is because this constant does have an effect upon the Q-branch and also on transitions with N > 1and

K =0↔|K| = 1 and moreover, the eﬀect of this constant increases with increasing

N . The constant b was also determined from the spectrum as expected because it mixes levels that are already mixed by the asymmetric part of the Hamiltonian.

At this point, ≈ 130 transitions were assigned to ﬁt all the molecular constants.

The calculated values of the constants d and e are 0.00 GHz and indeed could not be determined from the ﬁt. The comparison of the experimental spectrum and the simulation using the ﬁt constants (Table 6.5) is shown in Fig. 6.15.

The vibrational band due to conformer T1G2 , namely band E was also independently ﬁt. A comparison of the ﬁts of bands C and E revealed that the ground state constants were within two standard deviations. Thus following the same procedure as described for conformer T1T2 , the ground state constants were weighted by the inverse of the standard deviation and the weighted average values are given in Table

127 Const. (GHz) Fit Calc.. A 12.42(2) 12.40 B 2.443(2) 2.41 C 2.242(6) 2.21 a0 − a 0.043(7) 0.03 a0 + a/2 2.16(1) 2.01 b -0.035(1) -0.03 d 0.00 0.00 c 0.00 0.00 e 0.59(4) 0.68 A 12.64(1) 12.73 B 2.331(5) 2.35 C 2.183(4) 2.18 −1 T0(cm ) 29163.73(1)

Table 6.5: Molecular constants of conformer T1G2 of 1-butoxy. The ground state constants are the standard deviation weighted average of the constants obtained from the ﬁts of bands C and E while the excited state constants are those corresponding to the vibrationless level obtained from ﬁtting the origin band C.

6.5. The results of the individual ﬁts of bands C and E are give in Table 6.6. The molecular constants of the vibrationless levels of the X and B states are given in

Table 6.5. The results of the individual ﬁts of bands C and E are given in Table 6.6.

128 a) h) g) f)

R R0 1

R2 a)

29164 29164 29165 29165 29165 29166 Frequency (cm-1)

K"=0 <−> K'=1 Q-branch

Figure 6.14: a) Experimental spectrum of band C, b) Simulation of B−X transition of conformer T1G2 of 1-butoxy using only calculated rotational constants, c) Simulation with spin-rotation turned on using the calculated values of the spin-rotation constants, d) Simulation after fitting one linear combination of the rotational constants in the excited state, e) Simulation after fitting all three linear combination of the rotational constants in the excited state, f) Simulation after fitting all six linear combinations of the rotational constants in the ground and excited states, g) Simulation after fitting all six rotational constants and the spin-rotation constant (a0 + a/2), h) Simulation after fitting all six rotational constants and four spin-rotation constants.

129 Fit

Expt.

29163 29163 29164 29165 29165 Frequency (cm-1)

Figure 6.15: Comparison of experimental sepctrum and simulation based upon ﬁt constants (Table 6.5) for band C and conformer T1G2 of 1-butoxy. The ratio of the squares of the transition electric dipole moments a:b:c=3:7:7 (the calculated values are 1:14:13) and the rotational temperature is 1.0 K.

130 Const. (GHz) Band C Band E 223 transitions assigned 119 transitions assigned σ=60 MHz σ=73 MHz A 12.41(1) 12.44(2) B 2.439(2) 2.449(6) C 2.240(1) 2.246(2) a0 − a 0.028(5) 0.038(7) a0 + a/2 2.15(1) 2.20(1) b -0.022(9) -0.05(1) d - - c - - e 0.56(3) 0.55(5) A 12.510(5) 12.635(2) B 2.334(2) 2.331(2) C 2.174(3) 2.183(3)

Table 6.6: Results of the independent ﬁts of bands C and E. The spin-rotation con- −1 stants d and c could not be determined from the ﬁts. T00(cm )=29163.73(1) and −1 T0E(cm )=T00+199.83(1).

131 Band Conformer Vibrational Interval Assignment 0 A G1T2 - 00 0 B T1T2 - 00 D T1T2 169 νCCO F T1T2 671 νCO 0 C T1G2 - 00 E T1G2 200 νCCO

Table 6.7: Vibrational assignments of the bands of 1-butoxy. νCO is the C-O stretch and νCCO is the backbone C-C-O deformation.

6.1.5 Discussion Vibrational Assignments

Table 6.1 indicates that both the rotational and spin-rotation constants are important parameters in establishing the conformational identity of the carrier of the spectrum.

This is clearly illustrated by considering conformers G1T2 and T1G2 whose rotational constants diﬀer by 8% whereas the spin-rotation constants diﬀer 72%. However the calculated and experimental rotational constants for a particular conformer given in Tables 6.1, 6.2, 6.4, and 6.5 agree to within 3%. A similar trend is observed in the spin-rotation constants, although the reliability of the predictions is much lower.29

Thus it is expected that the rotational structure together with the fine structure of a given vibrational band unambiguously “bar-codes” for the conformer carrying that band. The results of the fits of the vibronic bands A through E of 1-butoxy collected in Tables 6.4, 6.3, and 6.6 firmly establish the presence of three different conformers based upon the comparison with calculated values of the molecular constants.

132 Conformer G1T2 has the simplest vibrational spectrum with only one band (band

A) bearing its rotational structure. It is reasonable to consider this band as the origin of the B˜ − X˜ transition because a search for any bands up to 1000 cm−1 to the red of band A yielded no signal. No excited vibrational bands of conformer G1T2 could be identiﬁed, although it is evident from Fig. 6.1 that there are a few bands, other than bands A-E, that are too weak to rotationally resolve.

On the other hand, conformer T1T2 of 1-butoxy, which is analogous to the trans

(T) conformer of 1-propoxy, has three vibrational bands, the lowest of which (band

B) is considered to be the origin. Band F at 672 cm−1is the only one in the C-

O stretch region; its frequency is also in reasonably good agreement with ab initio calculations29 which while not particularly accurate for the B˜ state, are qualitatively useful in making vibrational assignments. As per the calculations, the remaining strong band D is assigned to a low frequency C-C-O backbone bend or deformation.

Finally, for conformer T1G2 , we have two lines with the lowest one (C) assumed to be the origin. Band E at 200 cm−1is assigned as a C-C-O backbone deformation which is in good agreement with ab initio calculations. No band is detected in the

C-O stretch region.

The remaining lines in the survey spectrum are too weak to rotationally resolve and assign deﬁnitely. Furthermore, we have scanned 1500 cm−1to the blue of band F and observed nothing. The LIF spectra of the three diﬀerent conformers thus seem to

−1 end abruptly; the maximum extent is < 700 cm for conformer T1T2 , which alone contains one quantum of C-O stretch excitation. A similar behaviour was observed in the case of the analogous trans conformer of 1-propoxy.49 This is in sharp contrast to the previously reported spectra of the smaller alkoxies like methoxy, ethoxy and

133 2-propoxy in which the predominant feature of the spectrum is a strong progression

in the C-O stretch due to a large increase in the C-O bond in the B˜ state. Those LIF spectra terminated 3000 cm−1above the origin. In methoxy, the termination of the

LIF spectrum is believed to be by predissociation from repulsive states asymtotically

approaching the R·+O dissociation limit. Our ab initio calculations and the observed

B˜ − X˜ excitation frequencies places the B˜ state vibrationless level of methoxy above

the X˜ state dissociation limit to CH3+O. In ethoxy, 2-propoxy, and all other observed

conformers of 1-propoxy and 1-butoxy, the B state vibrationless level is well below the

dissociation limit. Therefore it is unlikely that the termination of the LIF spectra in

these radicals is due to predissociation from repulsive states. In the case of 1-propoxy,

the abrupt termination of the spectrum was attributed to rapid internal conversion

to the X˜ state that occurs upon vibrational excitation which likely accounts for the

similar behaviour in 1-butoxy.

6.1.6 Electronic Origins

The lowest frequency origin band is that of conformer G1T2 (band A) which is shifted

−1 -446 cm with respect to the origin of conformer T1T2 while the origin of conformer

−1 T1G2 is shifted +68 cm with respect to the same reference. As Table 6.1 indi-

cates, according to our ab initio calculations the lowest energy conformer is conformer

−1 G1T2 which is lower than conformer T1T2 only 10 cm . If we consider conformer

T1T2 as a reference, then this implies that the B˜ state of conformer G1T2 is stabilized

−1 −1 by 400 cm and the B state of conformer T1G2 is destabilized by 50 cm as compared to the B state of conformer T1T2 . We can rationalize this observation

as follows. In the case of conformer G1T2 the stabilization may be attributed to a

134 non-classical C-H···O hydrogen bond which is more important in the B˜ state because

of the larger volume of the p-orbitals on the oxygen atom. A similar observation was

observed in the analogous gauche conformer of 1-propoxy (see chapter 5). This kind

of hydrogen bonding is not possible in the other two conformers which have local Cs

symmetry around the oxygen atom. It is probable that the conformer T1G2 is desta-

bilized due to steric repulsion between the the end hydrogens in both the X˜ and B˜

states as compared to the X˜ and B˜ states of conformer T1T2 . The additional small

destabilization ( 50 cm−1)oftheB˜ state may be due to a small increase in the electron density on the Cα hydrogen atoms in the B state which leads to an increase

in the steric repulsion.

Rotation and Spin-Rotation Constants

Based upon the good agreement between calculated and experimentally obtained

rotational constants in both the X and B states, one can arrive at a simple model to describe the geometry changes upon electronic excitation to be an increase in the

C-O bond length and a decrease in the C-C-O bond angle which is consistent with the large change in the C-O bonding character in the two states. Increases in the

C-O bond length of 0.19 A0,0.20A0, and 0.19 A0 and decreases in the C-C-O bond

0 0 0 angles of 8.0 ,7.7 ,and7.8 respectively for conformers G1T2 ,T1T2 ,andT1G2 were

deduced from the observed rotational constants.

The values for the components (˜αβ) of the spin-rotation tensor are give in Table

6.8 which indicates that the predicted spin-rotation constants agree well with the

experimentally determined ones. This further conﬁrms that the the simple semi-

empirical model used to predict the spin-rotation constants29 is reasonable. This

135 Conformer G1T2 Conformer T1T2 Conformer T1G2

Const. (GHz) Fit Calc. Fit Calc. Fit Calc ˜ aa -1.09(1) -1.13 -5.71(4) -5.47 -4.31(2) -3.99 ˜ bb -0.53(1) -0.54 -0.25(2) -0.15 -0.006(9) 0.00 ˜ cc -0.13(1) -0.08 0.00 0.00 -0.050(8) -0.06 |˜ ab| = |˜ ba| 0.69(5) 1.10 0.64(4) 1.60 0.00 0.00 |˜ bc| = |˜ cb| 0.15(5) 0.20 0.00 0.00 0.00 0.00 |˜ ac| = |˜ ca| 0.40(5) 0.43 0.00 0.00 0.59(4) 0.68

Table 6.8: Spin-rotation constants of conformers G1T2 ,T1T2 ,andT1G2 of 1-butoxy

model assumes that the nature of the orbital carrying the unpaired electron on the oxygen atom does not change signiﬁcantly from ethoxy to any other 1-alkoxy radical.

Furthermore, as shown by Tables 6.4 and 6.5, two conformers (G1T2 and T1G2 )which have very similar rotational constants can be unambiguously distinguished from each other because of their very diﬀerent spin-rotation constants which the model predicts.

6.1.7 Conformational Selectivity

It is well known that at room temperature conversion among conformers is very facile. However at the very low jet temperatures (<1.5K rotational temperatures) such interconversion is exceedingly unlikely on the time scale of the experiment.

136 Presumably in the initial photolysis that produces the alkoxy radical there is suﬃcient energy to populate all (or at least most) of the possible conformers.∗ As the jet cools, many of the higher energy conformers relax. However clearly equilibrium is not reached since at the low jet temperature only the lowest energy conformer would be populated at equilibrium. Rather some conformers are “trapped” in higher energy conformations. The question is then raised as to which conformers relax and which are trapped.

For 1-butoxy we can compare Table 6.7 of the observed conformers with Fig.

3.5 which shows the possible conformer structures. It is clear that two of the three observed conformers (G1T2 and T1T2) are of the straight chain variety. Of the 3 possible conformers to at least approach a cyclic structure only T1G2 is observed.

It is also interesting to note that the conformer G1G2 closely resembles the cyclic transition state that converts 1-butoxy to the hydroxy butyl (·CH-(CH2)2−CH2OH) radical which would not be expected to be observable by LIF spectroscopy. The

◦ other unobserved conformer, G1G2,diﬀersfromG1G2 by only 120 rotation of the

O-containing methyl and might rapidly relax to G1G2 which could be an eﬀective sink for 1-butoxy radicals.

∗While there is suﬃcient energy in the photolysis to populate the various alkoxy conformer, there is no guarantee that this energy is randomized in the molecule. It is also possible that there is a propensity for the alkoxy conformer to be determined by the conformational geometry of the alkyl nitrite precursor. If we assume the precursor is at room temperature, a number of its conformations will be well populated but some of the higher energy ones will not. Following this argument one might expect a clear preference for the lower energy conﬁrmers of the alkoxy radicals. While the lowest energy conformers do seem to be observed in all cases, there is seemingly a random-like sampling of the higher energy conformers. For instance in 1-butoxy the two lowest energy conformers (G1T2 and T1T2) are observed. The other three conformers are all comparably and substantially higher in energy (from calculations ≈2kT, where T is room temperature) yet only one T1G2 is observed.

137 CHAPTER 7

High-Resolution Spectroscopy of 1-Pentoxy

7.1 Introduction

The electronic spectroscopy of 1-pentoxy will be discussed in this chapter. As in the

case of 1-propoxy and 1-butoxy, the high-resolution rotationally resolved spectra of

the vibronic bands in the survey LIF spectrum of the B − X transition were recorded and analyzed to obtain the structural and vibrational assignments. The method of analysis is similar to what has been described in the previous two chapters for 1- butoxy and 1-propoxy and will not be described for 1-pentoxy. Only the results of the analyses will be presented.

7.2 Results

The survey spectra of 1-pentoxy is shown in Fig. 7.1. The bands labled a through

K were studied under high resolution to rotationally resolve their structure. As expected, the situation gets even more complicated in the case of 1-pentoxy. Figs. 7.2 and 7.3 show the rotationally resolved spectra of bands a through K of 1-pentoxy.

138 Six groups of bands can be distinguished based upon vastly diﬀerent rotational

structure with bands A and G belonging to one group, bands C, F, J, and K belonging

to the second, bands B and I in the third, bands E and H in the fourth, band a in the

ﬁfth, and band D in the sixth. Thus the high-resolution spectra of 1-pentoxy shows

the presence of at least six diﬀerent conformers.

The rotationally resolved spectra a through K of 1-pentoxy were analyzed along the same principles as described in the previous chapters for 1-butoxy and 1-propoxy.

There are fourteen unique conformations for 1-pentoxy as shown in Fig. 7.4. The B−

X transition of all the conformers were simulated using the calculated rotational and spin-rotation constants. Then, as was done in the case of 1-butoxy, the experimentally obtained spectra were matched against the simulations to start the ﬁtting procedure.

The conformational assignment for band C (as well as F, J, and K) was quite obvious as being T1T2T3 because this conformer has unique rotational constants.

Fig. 7.5 shows the simulations of ﬁve conformers of 1-pentoxy which most closely

match the experimentally obtained rotational structure of the the B˜ − X˜ transitions

of the remaining four groups of bands shown in Figs. 7.2 and 7.3. (see Tables 7.1

and 7.2 for the calculated rotational and spin-rotational constants). A similarity in

the gross features is evident, although upon closer examination, they are certainly

distinguishable from each other.

It can be observed in Figs. 7.2 and 7.3 that bands A, B, and a, though by no

means identical, have a somewhat similar rotational structure which can immediately

be recognized in the simulations shown in Fig. 7.5. A closer inspection of the sim-

ulations and the experimental spectra of bands A, B, and a allows us to conclude

that the conformational identity of these bands are respectively conformers G1T2T3,

139 J

C B

I E

FG A H D 140 K

28600 28800 29000 29200 29400 29600 29800 30000 Frequency (cm-1)

Figure 7.1: 1-pentoxy survey LIF spectrum K

29810.0 29810.5 29811.0 29811.5 29812.0 29812.5

29682.5 29683.0 29683.5 29684.0 29684.5 29685.0 29685.5 J

29140.0 29140.5 29141.0 29141.5 29142.0 29142.5 141

F 29012.0 29012.5 29013.0 29013.5 29014.0 29014.5

29226.5 29227.0 29227.5 29228.0 29228.5 29229.0

C 28642.0 28642.5 28643.0 28643.5 28644.0 28644.5 28645.0 Frequency (cm -1 )

Figure 7.2: Rotationally resolved spectra of bands A, G, C, F, J, and K of 1-pentoxy G

A D

E 29100.0 29100.5 29101.0 29101.5 29102.0 29102.5

29231.5 29232.0 29232.5 29233.0 29233.5 29234.0 a

29121.0 29121.5 29122.0 29122.5 29123.0 29123.5 142

I 28639.5 28640.0 28640.5 28641.0 28641.5 28642.0

29652.5 29653.0 29653.5 29654.0 29654.5 29655.0 B

28986.0 28986.5 28987.0 28987.5 28988.0 28988.5 28989.0 Frequency (cm -1 )

Figure 7.3: Rotationally resolved spectra of bands B, I, a,E,H,andDof1-pentoxy T1T2T3

G1T2T3 T1T2G3

H C H H

2 5 H CH

H O 3

H H

CH H O H C H H H 3 2 5 H H H

C3H7 H C2H5 H O

H H H H H

H H H

HHH H H H H C H CH O H C H O 3 7 2 C2H4O H CH2O 2 4 C H CH3 C H O 3 7 CH2O 2 4 ' T1G2T3 G1T2G 3

G1T2G3

H H

C H H O CH H C H H 3 2 5 H O 2 5 H H

O H H C H

C3H7 H H 3 7 H H

H H

H H HH H C H H CH3 H 2 5 HH H CH O H C H C2H4O CH3 C H O 2 C H O 3 7 CH2O H 2 4 2 4 CH2O ' ' ' T1G2G 3 G1G 2G3 G1G 2T3

H H HH

O H

H H H H H H C H CH H O H O H

3 7 H 3 H C H H

H H 3 7 H

H H

H HH H C H H HC2H5 HH H 2 5 H CH C2H5 CH C3H7 CH2O 3 C2H4O 3 C2H4O CH2O C2H4O H CH2O '

G1G2T3 G1G2G 3 T1G2G3

H H HH

H H H H H H O H

O CH3 O H H H

C H C3H7 H H

H 3 7 H H

H H

H HCH H CH H H C H HH 2 5 H HC2H5 3 2 5 CH3 C H O C H H CH2O 2 4 3 7 H CH2O C2H4O H CH2O C2H4O

G1G2G3 G 1G2G3

H H H

H O

H H

O H H H C3H7 H

C3H7 H H

HH H HH HCH CH C H 2 5 H 3 2 5 CH C H O H CH O 3 2 4 H CH2O C2H4O 2

Figure 7.4: Structures of fourteen unique conformers of 1-pentoxy at their local minima. The corresponding Newman projections of are also shown.

143 Conformer A B C A B C G1T2T3 9.788 1.356 1.271 9.140 1.394 1.293 T1T2T3 16.383 1.153 1.114 15.808 1.163 1.121 T1T2G3 9.666 1.357 1.266 9.130 1.382 1.280 G1T2G3 7.965 1.505 1.460 7.604 1.533 1.489 T1G2T3 10.578 1.342 1.269 9.292 1.490 1.375 G1T2G3 9.845 1.456 1.356 6.755 1.672 1.547 G1G2T3 7.137 1.609 1.498 6.702 1.648 1.522 T1G2G3 6.693 1.653 1.527 6.235 1.808 1.787 G1G2G3 6.788 1.716 1.699 6.373 1.801 1.527 G1G2T3 6.270 1.885 1.574 4.971 4.971 1.864 G1G2G3 4.994 2.339 1.915 6.356 1.745 1.507 T1G2G3 6.244 1.778 1.510 4.506 2.530 1.859 G1G2G3 4.481 2.667 1.877 5.661 1.928 1.740 G1G2G3 5.603 1.974 1.745 5.661 1.928 1.740

Table 7.1: Calculated ground and excited state rotational constants in GHz of the diﬀerent conformers of 1-pentoxy as obtained at the B3LYP/6-31+G* level of theory.

Conformer ãa ˜bb ˜cc |ãb| = |˜ba||ãc| = |˜ca||˜bc| = |˜cb| G1T2T3 -0.46 -0.33 -0.08 0.58 0.30 0.16 T1T2T3 -4.85 -0.06 -0.00 1.10 0.05 0.00 T1T2G3 -2.18 -0.15 -0.02 0.87 0.30 0.05 G1T2G3 -0.42 -0.23 -0.22 0.42 0.22 0.22 T1G2T3 -3.47 -0.00 -0.03 0.14 0.47 0.01 G1T2G3 -1.30 -0.30 -0.02 0.93 0.23 0.07 G1G2T3 -0.26 -0.31 -0.19 0.35 0.28 0.24 T1G2G3 -1.77 -0.10 -0.04 0.53 0.33 0.06 G1G2G3 -0.98 -0.32 -0.04 0.69 0.23 0.11 G1G2T3 -0.02 -0.60 -0.05 0.09 0.02 0.16 G1G2G3 -0.06 -0.78 -0.01 0.24 0.03 0.08 T1G2G3 -1.76 -0.04 -0.07 0.32 0.44 0.05 G1G2G3 -0.03 -0.74 -0.13 0.14 0.06 0.31 G1G2G3 -0.59 -0.01 -0.42 0.08 0.58 0.06

Table 7.2: Predicted ground-state electron spin-molecular rotation constants (in GHz) of the 14 conformers of 1-pentoxy.

144 Conformer G 1 T 2 G 3 28638.7 28639.3 28640.0 28640.7 28641.3 28642.0

Conformer T 1 T 2 G 3 28985.3 28986.0 28986.7 28987.3 28988.0 28988.7

Conformer T 1 G 2 T 3 145 29120.0 29120.7 29121.3 29122.0 29122.7 29123.3

' Conformer G 1 T 2 G 3 28642.0 28642.7 28643.3 28644.0 28644.7

Conformer G 1 T 2 T 3

28642.0 28642.7 28643.3 28644.0 28644.7 Frequency (cm -1 )

Figure 7.5: Simulations of the B − X transition using the calculated rotational and spin-rotation constants of ﬁve conformers of 1-pentoxy. The similarity in the overall rotational proﬁles is evident. T1T2G3,andG1T2G3. The conformational assignment for band C (as well as F, J, and K) was quite obvious as being T1T2T3 because this conformer has unique rotational constants. A comparison of Figs. 7.5 and 7.3 shows that the conformational assignment for band E (and H) is conformer T1G2T3. Since the S/N ratio for band

D is very poor, a unique conformer assignment (or a rigorous analysis) could not be carried out for this band.

From an inspection of the rest of the bands, it was concluded that only these six diﬀerent conformers of 1-pentoxy were observed. The calculated rotational constants of the X and B states of all 14 conformers of 1-pentoxy are collected in Table 7.1 and the X state spin-rotation constants are given in Table 7.2. Figs. 7.6 and 7.7 shows comparisons between experimental and simulated spectra for 6 bands. We will not detail the rotational analysis for 1-pentoxy, but only summarize the results.

The conformational assignment for bands A and G is conformer G1T2T3 .A comparison of the experimental and ﬁt spectra of band A is shown in Fig. 7.6 A and it is evident that the agreement between these two spectra is very good. The corresponding molecular constants for the vibrationless levels of the X˜ and B˜ states are given in Table 7.3. It is evident from this table that all the six rotational constants and six spin-rotation constants are rather well determined.

The conformational assignment for bands C, F, J, and K is conformer T1T2T3 with its molecular constants being determined from the ﬁts of bands C, F, and J.

This conformer has Cs symmetry and hence pure c-type transitions are observed.

Furthermore, only four spin-rotation constants can be determined for this conformer and ˜cc ≈ 0 because of the Cs symmetry. The ﬁt spectrum of band B is shown in Fig.

7.7 C and the molecular constants for the vibrationless levels of the X˜ and B˜ states

146 are given in Table 7.3. This table shows that all six rotational constants and the four spin-rotation constants a, a0, b,andd, were determined from the spectrum.

The conformational assignment for bands B and I is conformer T1T2G3 . Fig.

7.7 B shows that the correlation between the experimental and ﬁt spectra of band

C is very good. The experimentally obtained molecular constants of conformer

T1T2G3 are given in Table 7.3 which indicates that all the rotational constants and

five of six spin-rotation constants are determined from the spectrum. The spin- rotation constant c could not be determined probably because its magnitude is very small (0.06 GHz) as indicated by the predictions and also because its effect on the spectrum is small. The final fit was carried out by freezing this constant at the calculated value.

The conformational assignment for band a is conformer G1T2G3 . The comparison of the experimental and fit spectra of this band is shown in Fig. 7.6a.Amismatch between the experimentally observed and fit spectra of band a is apparent in the blue end of Fig. 7.6a. This is because the origin frequency of bands a and A differ by only

≈90 GHz while the width of band A is ≈70 GHz. Thus there is an overlap between the blue and red ends of bands a and A respectively. The agreement between the rest of the experimental and fit spectra of band a is however so good that a definite conformational assignment can be made. The results of the fit are summarized in

Table 7.3 which indicates that all the rotational constants and ﬁve of six spin-rotation constants were determine from the spectrum. The spin-rotation constant b could not be determined probably because of its very small in magnitude (-0.005 GHz as per predictions). The ﬁt was thus carried out by freezing this constant at its calculated value.

147 The conformational assignment for bands E and H is conformer T1G2T3 .As

indicated by Fig. 7.6E, there is very good agreement between the ﬁt and experimen-

tal spectra of band E. The results of the ﬁt are collected in Table 7.3 which shows

that all rotational constants and three of six spin-rotation constants were determined

from the fit. The final fit was performed by freezing the constants c, d,ande at the

predicted values. None of these oﬀ-diagonal spin-rotation constants were determined

probably because the eﬀect of these constants on the spectrum increases with increas-

ing rotational quantum number N many of which are buried in the baseline due to

the relatively poor S/N ratio. Nonetheless, the conformational assignment for this

band is quite unambiguous.

As already mentioned, the poor S/N ratio of band D prevented a detailed ro-

tational analysis of this band. The comparison of the B˜ − X˜ transition simulation using the calculated rotational and spin-rotation constants of all 14 conformers of

1-pentoxy and the experimental spectrum of band D showed that there are ﬁve conformers which are comparably good candidates for this spectrum. These constitute

the cyclic conformers T1G2G3 ,G1G2T3 ,T1G2G3 ,andG1G2G3 whichareshownin

Fig. 7.8 and which have very similar rotational constants as can be seen in Table 7.1.

Thus no conclusive conformation assignment could be made for this band.

148 E Fit

Expt.

Fit a

29120.7 29121.3 29122.0 29122.7Expt. 29123.3

28639.3 28640.0 28640.7 28641.3 28642.0 149

A Fit

28642.0 28642.7 28643.3 28644.0 28644.7 28645.3-1 Frequency (cm ) Expt.

Figure 7.6: Comparison of experimental spectra with simulations based upon ﬁt constants (Table 7.3) for band A and conformer G1T2T3 of 1-pentoxy, band a and conformer G1T2G3 , and band E and conformer T1G2T3. The ratio of the square of the electric dipole moments a:b:c are respectively 3:1:2, 1:4:6, and 1:8:10 for bands A, a, and E (the calculated values are respectively 2:1:4, 1:8:12, and 1:10:13). The rotational temperatures are 1.5, 1.3, and 1.3 K respectively for bands A, a,andE. C Fit

Expt.

29012.0 29012.7 29013.3 29014.0 29014.7

150 B Fit

28986.0 28986.7 28987.3 28988.0 28988.7 Frequency (cm -1 )

Figure 7.7: Comparison of experimental spectra with simulationsExpt. based upon ﬁt constants (Table 7.3) band B and conformer T1T2G3, and band C and conformer T1T2T3. The ratio of the square of the electric dipole moments a:b:c are respectively 1:2:4 and 0:0:1 for bands B and C (the calculated values are respectively 1:6:2 and 0:0:1). The rotational temperature is 1.3 K for both bands. G'1G2G3

T1G2G3

Expt. spectrum of band D

G1G2T3

T1G2G3'

29099.3 29100.0 29100.7 29101.3 29102.0 29102.7 29103.3 Frequency (cm-1)

Figure 7.8: Comparison of experimental spectrm of band D with simulations using the calculated rotational and spin-rotation condtants and ratio of the square of the electric dipole moment a:b:c of 4 “cyclic” conformers of 1-pentoxy having similar rotational constants in both the ground and excited states (Tables 7.1 and 7.2). The poor S/N ratio of band D and the large number of possible conformer candidates prevented a deﬁnite assignment for this band from being made.

151 Const. Band A [G1T2T3 ] Band C [T1T2T3 ] Band B 164 lines 79 lines 137 lines σ=52 MHz σ=51 MHz σ=71 MHz A 9.66(2)[9.79] 16.30(2) [16.38] 9.65(1) [9.67] B 1.386(2) [1.36] 1.192(2) [1.15] 1.390(4) [1.36] C 1.288(1) [1.27] 1.142(2) [1.11] 1.274(3) [1.27] ãa -0.46(2) [-0.46] -5.21(5) [-4.85] -2.331(7) [-2.18] ˜bb -0.30(1) [-0.33] -0.09(2) [-0.06] -0.14(2) [-0.15] ˜cc -0.14(1) [-0.08] 0.00 [0.00] -0.01(1) [-0.02] |ãb =˜ba| 0.22(4) [0.58] 0.52(1) [1.10] 0.44(2) [0.87] |˜bc =˜cb| 0.19(4) [0.16] 0.00 [0.00] - [0.05] |ãc =˜ca| 0.11(3) [0.30] 0.00 [0.00] 0.20(2) [0.30] A 8.730(2) [9.14] 15.316(8) [15.81] 8.852(4) [9.13] B 1.414(1) [1.39] 1.173(2) [1.16] 1.392(1) [1.38] C 1.305(1) [1.29] 1.149(1) [1.12] 1.289(1) [1.28] −1 T00(cm ) 28643.38(1) 29012.82(1) 28986.98(1)

Const. Band a [G1T2G3 ] E[T1G2T3 ] 103 lines 103 lines σ=110 MHz σ=117 MHz A 7.932(6) [7.97] 10.56(2) [10.58] B 1.548(6) [1.51] 1.335(3) [1.34] C 1.509(5) [1.46] 1.279(4) [1.27] ãa -0.34(1) [-0.42] -3.72(3) [-3.47] ˜bb -0.261(9) [-0.23] -0.03(1) [-0.00] ˜cc -0.271(9) [-0.22] -0.03(1) [-0.03] |ãb =˜ba| 0.41(3) [0.42] -[0.14] |˜bc =˜cb| 0.22(2) [0.22] - [0.01] |ãc =˜ca| 0.23(2) [0.22] - [0.47] A 7.427(7) [7.60] 10.96(7) [11.15] B 1.577(3) [1.53] 1.308(3) [1.32] C 1.524(1) [1.49] 1.269(1) [1.26] −1 T00(cm ) 28640.35(1) 29121.57(1)

Table 7.3: Experimentally determined rotational and spin-rotation constants (in GHz) from ﬁve sets of rotational bands of 1-pentoxy. The ground state constants correspond to an average of the values from all bands, weight inversely by the standard deviation, σ. The excited state constants correspond to the vibrationless level obtained from the ﬁts of the origin bands A, C, B, a, and E respectively. The calculated constants of the assigned conformers (whose calculated values most closely match the experimental ones) are given in brackets.

152 Const. (GHz) Band A Band G 164 transitions assigned 86 transitions assigned σ=52 MHz σ=56 MHz A 9.638(5) 9.70(5) B 1.386(1) 1.385(3) C 1.285(1) 1.291(3) a0 − a 0.217(3) 0.214(3) a0 + a/2 0.332(6) 0.35(3) b -0.095(8) -0.07(1) d 0.20(3) 0.25(5) c 0.15(4) 0.24(4) e 0.07(5) - A 8.730(2) 8.796(7) B 1.414(1) 1.429(2) C 1.302(1) 1.308(1)

Table 7.4: Results of the independent ﬁts of bands A and G of 1-pentoxy. The spin-rotation constants e could not be determined from the ﬁt of band G and was 0 −1 frozen at the calculated value given in Table 7.3 for conformer G1T2T3 .T0(cm ) 0 −1 = 28643.38(1), TG(cm ) = 29277.65(1)

153 al .:Rslso h needn t fbnsC ,adJo -etx.The 1-pentoxy. ˜ of freezing J by and done F, C, were bands bands of three ﬁts all independent of the of ﬁts Results 7.5: Table T F 0 (cm − 1 =94.01,T )=29140.80(1),

J 0 Const. (GHz) Band C Band F Band J (cm 79 transitions assigned 79 transitions assigned 107 transitions assigned −

1 σ=51 MHz σ=96 MHz σ=86 MHz )=29683.47(1) A 16.31(3) 16.24(4) 20.32(2) B 1.192(3) 1.195(4) 1.191(1) 154 C 1.147(1) 1.142(4) 1.139(1) a0 − a = −b 0.047(9) 0.03(2) 0.050(5)

a0 + a/2 2.59(4) 2.65(5) 2.64(1) cc d 0.22(2) 0.28(3) 0.277(6) t00.T 0.00. at A 15.316(8) 15.82(1) 15.521(4) B 1.173(2) 1.177(5) 1.175(1) C 1.149(2) 1.160(2) 1.160(1) 0 0 (cm − 1 )=29012.82(1), Const. (GHz) Band B Band I 137 transitions assigned 51 transitions assigned σ=71 MHz σ=40 MHz A 9.62(1) 9.66(2) B 1.380(2) 1.396(6) C 1.275(1) 1.274(3) a0 − a 0.074(5) 0.077(7) a0 + a/2 1.185(7) 1.214(3) b -0.06(1) -0.07(2) d 0.48(3) 0.41(2) c - - e 0.20(4) - A 8.852(4) 8.978(4) B 1.392(1) 1.415(2) C 1.289(1) 1.297(2)

Table 7.6: Fits of bands B and I of 1-pentoxy. The spin-rotation constants c could not be determined from the ﬁt of band B, while the spin-rotation constants c and e could not be determined from the ﬁt of band I. These constants were frozen at the 0 −1 calculated values given in Table 7.3 for conformer G1T2G3 .T0(cm )=28986.98(1), 0 −1 TI (cm )=29653.41(1)

155 Const. (GHz) Band E Band H 103 transitions assigned 90 transitions assigned σ=117 MHz σ=125 MHz A 10.53(2) 10.57(2) B 1.340(4) 1.332(3) C 1.275(2) 1.281(5) a0 − a 0.032(9) 0.024(1) a0 + a/2 1.90(3) 1.83(2) b - - d - - c - - e - - A 8.852(4) 11.17(1) B 1.392(1) 1.266(4) C 1.289(1) 1.285(3)

Table 7.7: Fits of bands E and H of 1-pentoxy. The spin-rotation constants c could not be determined from the ﬁt of band B, while the spin-rotation constants b, d, c and e could not be determined from the ﬁts of bands E and H and were frozen at the 0 −1 calculated values given in Table 7.3 for conformer T1G2T3 .T0(cm ) = 29121.57(1), 0 TH = 29232.21(1).

156 7.2.1 Discussion Vibrational Assignments

Table 7.3 shows that the calculated and experimentally determined rotational constants for each of the five observed conformers of 1-pentoxy agree to <3% and while the rotational constants of the different conformers differ by as much as 70%. The same can be said about the spin-rotation constants although the predictions are worse than the predictions of the rotational constants as expected given the semi-empirical model used to calculate the former.29 Thus we conclude that the carriers of the spectral bands a through K of 1-pentoxy are the five different conformers.

The vibrational assignments for the bands are summarized in Table 7.8. It is clear from this table that as in the case of 1-propoxy, and 1-butoxy, a maximum of only one quantum C-O stretch excitation is observed (all bands other than a through K are too weak to rotationally resolve and assign). This abrupt termination of the LIF spectra of the diﬀerent conformers is again attrubuted to rapid internal conversion upon vibrational excitation in the B˜ state based upon similar arguments given for

1-butoxy.

Electronic Origins

It is interesting to note that the electronic origins of the ﬁve observed conformers of 1-pentoxy fall into two broad groups depending on whether or not the local symmetry around the oxygen atom is Cs or not. The origins of conformers G1T2T3 and

G1T2G3 in which the oxygen atom is rotated out of plane are almost identical at

−1 ≈28640 cm whereas the origins of conformers T1T2T3 ,T1T2G3 ,andT1G2T3 which

157 Band Conformer Vibrational Interval Assignment 0 A G1T2T3 - 00 G G1T2T3 584 νC−O 0 C T1T2T3 - 00 F T1T2T3 128 νC−C−O J T1T2T3 671 νC−O K T1T2T3 128 νC−OνC−C−O 0 B T1T2G3 - 00 I T1T2G3 667 νC−O 0 a G1T2G3 - 00 0 E T1G2T3 - 00 H T1G2T3 110 νC−C−O

Table 7.8: Vibrational assignments of the bands of 1-pentoxy. νC−O is the C-O stretch and νC−C−O is the backbone C-C-O deformetion.

−1 have local Cs symmetry are higher by 370, 347, and 482 cm respectively. As men-

tioned previously in the case of 1-butoxy, the origin band of the corresponding “oxygen

−1 out of plane” conformer was lower by 446 cm as compared to the Cs conformer and

this diﬀerence was attributed to stabilization of the B state of the former due to

C-H···O hydrogen bonding. Clearly this trend continues in 1-pentoxy as well. The

origins of conformers 2 and 3 diﬀer by only 26 cm−1 which implies that both the

X˜ and B˜ states of of conformer T1T2G3 are shifted by practically identical amounts

with respect to the same states of the Cs conformer (T1T2T3 ). This is reasonable

because conformer T1T2G3 has the end ethyl group twisted out of the plane which

is quite far away from the oxygen chromophore and hence the electronic transition

should have hardly any eﬀect on the B˜ state energy. On the other hand, the origin

158 −1 of conformer T1G2T3 is higher than that of conformer T1T2T3 by ≈ 100 cm . Con- former T1G2T3 is analogous to conformer T1G2 of 1-butoxy in which the end ethyl group is rotated out of the plane and a similar shift (+68 cm−1) in the origin bands was observed. This was attributed to the destabilization of the B˜ state of conformer

T1G2 . The destabilization of the B˜ state of conformer T1G2T3 of 1-pentoxy is attributed to an increase in steric repulsion upon electronic excitation as argued in the case of 1-butoxy.

Rotation and Spin-Rotation Constants

Table 7.3 indicates that the agreement between the calculated and experimentally determined rotation and spin-rotation constants of all ﬁve conformers is quite good.

Indeed not only can different conformers be distinguished based upon different rotational constants but also based upon different spin-rotation constants as illustrated by conformers G1T2T3 and T1T2G3 . Based upon the simple model that describes the geometry changes that occurs upon electronic excitation (as described in the case of 1-butoxy), one can deduce the changes in the C-O bond lengths and C-C-O bond angles from the rotational constants. The increase in the C-O bond length upon excitation for conformers G1T2T3 ,T1T2T3 ,T1T2G3 ,G1T2G3 ,andT1G2T3 are respectively 0.19, 0.18, 0.16, 0.16, and 0.17 A˚ and the decrease in the C-C-O bond angle is respectively 7.8, 7.5, 7.5, 7.7, and 7.70.

7.2.2 Conformational Selectivity

In the previous chapter, a rationalization for the fact that some conformers of 1- butoxy are observed while others are not, was presented based upon the idea that the conformer G1G2 can be an eﬀective sink for the 1-butoxy radicals because this

159 conformer closely resembles the cyclic transition state that converts 1-butoxy to the hydroxy butyl (·CH-(CH2)2−CH2OH) radical which would not be expected to be observable by LIF spectroscopy. Conformers that can easily relax to this structure were not observed.

Similar, although somewhat less deﬁnitive, conclusions for 1-pentoxy can be reached by comparing Table 7.8 and Fig. 7.4. We note that the 5 observed conformers are all straight-chain or nearly so. Furthermore of this “category” of conformers (ﬁrst

two rows of Fig. 7.4) only G1T2G3 has not been observed. Generally speaking these conformers that have (or resemble) a cyclic structure (last 3 rows of Fig. 7.4) have not been definitely observed (excluding one spectrum (D) whose assignment is uncer- tain). Of course once again the transition state for the tautomerization reaction to produce the hydroxy pentyl (CH3-CH-(CH˙ 2)2-CH2OH) radical has a cyclic structure so it might be argued that the absence of these conformers is due to efficient relaxation to a conformation closely resembling the transition state, which retains sufficient energy from the photolysis to continue the tautomerization reaction. The extreme weakness and poor S/N ratio of band D may be attributed to such a relaxation which is nonetheless not so efficient for this particular cyclic conformer.

Further experiments are certainly necessary to conﬁrm or disprove this hypothesis. However it is interesting to note that the postulated existence and accessibility of a tautomerization sink for the alkoxy radicals also would largly rationalize some previously reported, somewhat contradictory results. Dibble and co-workers carried out ﬂow experiments with T>200 K on all 14 structural isomers of butoxy, pentoxy, and hexoxy. He reported observing assignable, structured spectra for only 4 of the 14 isomers, namely, 2-butoxy, t-butoxy, 2-pentoxy and 3-pentoxy. On the other

160 hand, we have observed strong LIF spectra for all 13 structural isomers that we have investigated under jet cooled conditions (T<1.5 K). (The isomer neo-pentoxy was not observed because we were unable to synthesize the precursor by the standard procedures referenced in chapter 2 as revealed by FTIR absorption spectra.) The key observation is that of the 14 possible structural isomers of butoxy, pentoxy and hexoxy, only the 4 for which Dibble and co-workers observed LIF spectra, do not have cyclic conformers and cannot form a 6-member ring transition state. We would expect that conformer conversion would remain facile on the temperature and time scale of the experiments of Dibble and co-workers. Ergo, a tautomerization sink might well have destroyed the population of the 10 isomers whose LIF spectra could not be observed in those experiments.

On the other hand, in our jet experiment, it is clear that conformers get “frozen out” far from equilibrium. Furthermore our detailed rotational analyses demonstrated that most, if not all, our observed LIF spectra, are assignable to conformers whose geometries are quite diﬀerent from the cyclic transition state required for tautomerization. This may well be the explanation of why we have observed good LIF spectra from all these structural isomers when previous experiments have not.

161 CHAPTER 8

Conclusions

The alkoxy radicals have been of extreme interest from both the fundamental as well as well as practical standpoint. The smallest alkoxy radical methoxy has been spectroscopically investigated in great detail by both experimentalists as well as the- oreticians in the past and continues to be of great interest even now. However, the spectrocopy of the larger alkoxy radicals has been virtually unexplored. From the practical standpoint, the alkoxy radicals are key intermediates in the tropospheric degradation of volatile organic compounds and the combustion of fossil fuels. Hence an understanding of their chemistry is very important in modeling the chemistry of the atmosphere.

The work described in this dissertation is a detailed description of laser induced

ﬂuorescence studies of more than twenty large alkoxy radicals, many of which have never been observed before. This document also describes high-resolution rotationally resolved LIF experiments on the primary alkoxy radicals to obtain structural information on the carrier of the spectra. The detailed rotational and vibrational analysis provide the hitherto unavailable data set which will serve as a diagnostic for detecting the alkoxy radicals. This data set also serves as a benchmark for ab initio calculations.

162 We have seen from the moderate resolution studies that all investigated alkoxy

radicals show structured and sharp LIF spectra. The largest investigated radical, 1-

dodecoxy, has a hydrocarbon chain containing 12 carbon atoms. It is surprising that

a radical of this size ﬂuoresces at all considering that it has 108 vibrational modes

and hence one might expect the excited electronic state to decay via a non-radiative

mechanism like internal conversion.

These studies also showed that the origin frequencies fall into distinct groups based

upon the nature of the branching in the hydrocarbon chain, i.e, diﬀerent structural

isomers of a particular radical have distinctly diﬀerent origin frequencies. For a

particular structural isomer, the origin frequencies progressively shift to the red with

increasing number of carbon atoms (n). This red shift is most signiﬁcant up to n=3

after which the red shift gets progressively much smaller.

Moderate resolution spectra of some of the bands that appeared in the the sur-

vey spectra of the primary and secondary alkoxy species revealed noticeably diﬀerent

rotational contours. These were attributed to diﬀerent conformers of the particu-

lar structural isomer. To verify this, high-resolution rotationally resolved spectra of

selected strong bands in the survey spectra of the primary alkoxy radicals from 1-

propoxy to 1-pentoxy were obtained. Five bands of the B −X excitation spectrum of

1-propoxy, six in 1-butoxy and 11 in 1-pentoxy had their rotational and spin-rotation structure resolved and analyzed by high-resolution spectroscopy. The rotational constants in both the B˜ and X˜ states and components of the spin-rotation tensor in the

X˜ state (the spin-rotation splitting in the B˜ state is beyond our experimental resolu-

tion) were determined. By comparing these experimentally determined constants to

ones determined from quantum chemistry calculations, we have identiﬁed the spectra

163 of 2 distinct conformers of 1-propoxy, 3 conformers of 1-butoxy, and 5 conformers of

1-pentoxy. A transition of a sixth conformer is observed in the spectrum of 1-pentoxy

but not deﬁnitely assigned due to low signal/noise.

From the measured constants some things can be said about the electronic and

geometric structure of the radicals. As has been the case with previously reported

alkoxy radicals, the X − B excitation causes a signiﬁcant lengthening (≈ 0.20 A)˚ and a decrease (≈ 8◦) in the C-C-O bond angle. Good estimates of X˜ state spin-rotation

constants can be obtained from those of ethoxy, by rotating (via coordinates from

quantum chemistry calculations) from a coordinate system ﬁxed on the O atom to

the inertial coordinate system.

By a combination of experimental electronic origins and computational results,

we can learn a considerable amount about subtle stabilization eﬀects on molecular

geometry, which may have implications for molecules as large as proteins.

Besides the direct structural information we obtain from the spectra, our isomer

and conformer speciﬁc diagnostic allows us to conclude some interesting facts about

the radicals dynamics. The survey LIF spectra reveal some interesting dynamical

behavior; the spectra of 2-propoxy and t-butoxy are strikingly diﬀerent from the

spectra of all other investigated spectra in that the former show a long progression

in the C-O stretch with at least 5 quanta being observable. A similar behavior was

observed in the case of the two smallest alkoxy radicals methoxy and ethoxy. The

spectra of all other alkoxies show limited vibrational structure, before a non-radiative

decay channel opens to quench the ﬂuoresence (and the LIF spectra). The diﬀerence

in behavior can likely be attributed to the presence of C-C-C linkages in the latter that

have been shown to dramatically accelerate IVR in comparably sized hydrocarbons.

164 High-resolution, rotationally resolved studies of the primary alkoxy radicals showed that vibronic assignments can be made because the rotational structure of a vibronic band barcodes for the conformer carrying that band. The vibrational analysis revealed that one quantum excitation in the C-O stretch is observed for both conformers of

1-propoxy. The C-O stretch of the G conformer is much weaker than the Cs symmetry T conformer. However in 1-butoxy we observe a single C-O stretch band for the

Cs conformer while no C-O stretches are observed for any of the other conformers.

Similarly for 1-pentoxy a C-O stretch is observed for the Cs conformer (T1T2T3 ) and also for the T1T2G3 conformer which has local Cs symmetry at the O end of the radical. A C-O stretch is also observed for the G1T2T3 conformer, but it is very weak, and it is missing in the other conformers. This indicates that the excited state dynamics is not only isomer speciﬁc for a particular radical, but is also (albeit weakly) conformer speciﬁc.

Finally it is clear that the sample of conformers that we observe is far from equilibrium, where only the lowest energy conformer would be observable at the ≈1K rotational temperature. Rather a number of higher energy conformers appear to be frozen out, but certainly some comparably energetic conformers are “missing”. We postulate that a possible sink for these “missing” conformers during the relaxation process is the tautomerization reaction to from hydroxy alkyl radicals. Conformers with geometries comparable to the cyclic transition state of this reaction would most likely be consumed, and there seems to be a fairly good correlation of the missing conformers with these geometries.

165 In conclusion, this dissertation describes the detailed characterization of large alkoxy radicals. A database of valuable information on these very important chemical intermediates has been established which has led to a detailed description of the structure and dynamics of these radicals.

166 APPENDIX A

As noted in the text, when HSR is included the H matrix has both real and

imaginary parts although of course it remains Hermitian. Thus H may be written as

the sum of real and imaginary parts:

H = Hreal + iHim (1)

where the elements of both Hreal and Him are all real.

There exist computer programs that can directly diagonalize the complex H, but they are generally slow and do not easily interface with our analysis program. There- fore we adopt the following approach. If the eigenvectors of H are denoted by u+iv, the n × n complex eigenvalue problem can be written as

(A + iB) · (u + iv)=λ(u + iv)(2)

where A=Hreal,B=Him and the matrix λ contains the eigenvalues along its diagonal.

Expanding

Au + iAv + iBu − Bv = λu + iλv (3)

Since the real and imaginary parts must be independently equal

Au − Bv = λu (4)

Bu + Av = λv (5)

These two equations can be summarized in matrix notation, as

167 u A −B u u W · = · = λ (6) v BA v v

where the matrix W is now of order 2n.IfW is real symmetric then standard

routines can be used to ﬁnd its eigenvalues λ and the real (u) and imagining (v)

parts of its eigenvector. Since A and B are real by construction, we need only show

W is symmetric, i.e., WT=W or

T T T T A −B A B A −B W = = = = W (7) BA (−B)T AT BA

which holds if BT = −B since A is real symmetric. However BT must equal -B since

H is Hermitian and

∗ T T (Hmk) =(A − iB)mk = Akm − iBkm (8)

But,

H† =(H∗)T = H (9)

therefore

Akm − iBkm = Amk + iBmk (10)

Thus, the complex problem reduces to the straightforward diagonalization of the real,

symmetric matrix, W. Corresponding to a given eigenvalue λ, the vector -v u is also a solution and thus λ is doubly degenerate. Pairs of the form (u+iv)and i(u+iv) are the eigenvectors of H . One eigenvalue and eigenvector is chosen from

168 each pair to give the eigenvalues and eigenvectors of H. Thus the eigenvectors and eigenvalues of the “true”, complex Hamiltonian matrix (H) can be obtained using the same numerical recipe as used for a real matrix.

Once this is done, the eigenfunctions of Hreal are matched against those of H and the corresponding eigenvalues of H were used to evaluate the transition frequencies.

The above process is carried out so that real eigenfunctions may be used to calculate

the intensities of the transitions while the transition frequencies may be calculated

from the eigenvalues of the complete Hamiltonian matrix.

169 APPENDIX B

The data files comprising the rotationally resolved spectra of 1-propoxy, 1-butoxy, and 1-pentoxy are attached in this appendix. These are ASCII files with a .DAT extension and any data processing program like Microsoft Excel, Sigmaplot, Origin etc. may be used to plot these spectra. Each file consists of two columns of numbers - the first column is the frequency (in cm−1) and the second is the intensity (in arbitrary units). The file name is self-explanatory; it consists of the name of the radical and the label of the vibronic band for that radical as described in the text.

The line positions may be determined easily in Excel or Origin using the mouse. In the analysis described in this thesis, the GUI program SpecView which was developed in our lab was used to determine the line positions and simultaneously assigning them.

This program runs on Windows and line positions were determined by just using the mouse.

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