LBL-10594 [Til Lawrence Berkeley Laboratory fewi UNIVERSITY OF CALIFORNIA Materials & Molecular Research Division #tffc EFFECT OF NUCLEAR SPIN ON CHEMICAL REACTIONS AND INTERNAL MOLECULAR ROTATION Larry Lee Sterna (Ph.D. thesis) December 1980 Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48 EFFECT OF NUCLEAR SPIN ON CHEMICAL REACTIONS AND INTERNAL MOLECULAR ROTATION Larry Lee Sterna Materials and Molecular Research Division Lawrence Berkeley Laboratory University of California Berkelev, CA 94720 Ph.D. Thesis December 1980 This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract Number W-7405-ENG-48. EFFECT OF NUCLEAR SPIN ON CHEMICAL REACTIONS AND INTERNAL MOLECULAR ROTATION Larry Lee Sterna Materials and Molecular Research Division Lawrence Berkeley Laboratory University of California Berkeley, CA 94720 Abstract Through the hyperfine interaction, nuclear spins can cause rapid O10 Hz) singlet-triplet intersystem crossing in the electronic states of a pair of free radicals. Since, in general, two radicals can form a chemical bond only if the two unpaired electrons have singlet spin correlation, the nuclear spins have an influence (magnetic isotope effect) on the chemical reactivity of the pair. This effect is largest for radical pairs which are prepared with pure triplet electron spin correlation and which recombine in isolaLion from other radicals (geminate recombination). Part I of this dissertation is a study of the magnetic isotope 13 effect, and results are presented for the separation of C and 22 C isotopes. Two models are included in the theoretical treatment of the effect. In the first model the spin states evolve quantum mechanically, and geminate recombination is calculated by numerically integrating the collision probability times the probability the radical pair is in a singlet state. Although it is difficult to b include more than three collisions of the radical pair, a closed- form solution, accounting for all possible collisions, is obtained when the singlet state radical pairs have unit probability of bonding during a collision. In the second model the intersystem crossing is treated via first-order rate constants which are average values of the hyperfine couplings. Using these rate constants and hydrodynamic diffusion equations, an analytical solution, which accounts for all collisions, Is obtained for the geminate recombination. This model was extended to treat the case of recombination within a spherical reflecting boundary, such as a micelle. Both models contain terms which account for loss of radicals due to competitive chemical reactions. The two reactions studied are photolysis of benzophenone and toluene and the photolytic decomposition of dibenzylketone (l,3-diphenyl-2-propanone). No magnetic isotope effect was observed in the benzophenone reaction, and this is shown to be consistent with the operation of spin-orbit coupling (which is 13 estimated) in the radical pair. C enrichment was observed for the dibenzylketone reaction, and this enrichment was substantially enhanced at intermediate viscosities and low temperatures. Part II of this dissertation is a presentation of theory and results for the use of Zeeman spin-lattice relaxation as a probe of methyl group rotation in the solid state. The coupling between spin and spatial degrees of freedom is a result of the c Faull principle and is analogous to the behavior of ortho and para hydrogen. This coupling is associated with a spin degree of freedom termed rotational polarization, and its size is related to the non-exponentiality of the Zeeman relaxation. The theory is presented for the relaxation of methyl groups coupled by fast spin diffusion and it is extended to treat the case of adjacent methyl groups which are geared together. Experimental results are presented for the time and angular dependences of rotational polarization, the methyl group magnetic moment, and methyl-methyl steric interactions. The compounds studied are 2,6-dimethylphenol, methyl iodide, 1,4,5,8- tetramethylanthracene, 1,4,5,8-tetramethylnaphthalene, 1,2,4,5- tetramethylbenzene, and 2,3-dimethylmaleicanhydride. Calculations are presented to show the relationship between the tunneling frequency and rotation rate of a hindered methyl group. ACKNOWLEDGEMENTS Several years of work have gone into producing this dissertation, and I hope to express some measure of my gratitude here to those who have had a part in it. Professor Alex Pines has been most generous in his support and encouragement throughout this work. His ideas and inspiration were an essential part in the success of any experiment. I am grateful to Dr. Soemi Emid who was my mentor in the understanding of methyl groups and rotational polarization and who participated, as did Dr. Shan Hsi, in the methyl iodide experiments. The work on the magnetic isotope effect greatly benefited from Dr. David Ronis' help in developing the Continuous Diffusion Model. For many discussions and arguments on NMR and help with experiments, I am grateful to my fellow graduate students Gary Drobny, Dick Eckman, Joel Garbow, Jim Murdoch, Steve Sinton, George Wolf, and Yu-Sze Yen as well as to Drs. Dave Wemmer, Warren Warren, and Luciano Mueller. Special thanks are due to Dan weitekamp and Jau Tang for their willingness to devote much of their time to resolving problems related to my research. Sidney Wolfe and Herbert Zimmerman contributed a tremendous amount in the synthesis of compounds and growing of single crystals, as did the people of the departmental shops who either constructed or repaired much of the equipment used in the experiments. Sanford Bustamante, Jon Sessler, Harry Weeks, and Paul Mayeda helped with the magnetic isotope experiments. Dione Carmichael and Carol Hacker ii are to be thanked for their excellent typing abilities in producing the first and final drafts of this manuscript. Marshall Tuttle did an outstanding job in turning my sketches into flawless drawings. My parents Hugo and Dorothy Sterna deserve a wealth of gratitude for their support of me during all my years of study. To all of my friends and colleagues, including those 1 have neglected to mention, this work is dedicated. This research was supported in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Department of Energy under Contract Number W-7405-ENG-48 and by a grant from the Dreyfus Foundation. Berkeley March 1981 L.L. Sterna Ill INTRODUCTORY BOTE Parts I and II of this dissertation contain very different subject matter, and with the exception of Appendix F, they were designed to be read independently of one another. Consequently, the reader is forewarned that there are instances where the same symbols are used in the two parts but with different meanings. The references are marked with square brackets [ ] , and the reference lists contain only publications, no footnotes. iv And whatsoever ye do, in Word or deed, do all in the name of the Lord Jesus, giving thanks to God the Father through him. Colossians S.I? CONTENTS PAST I INTERACTION BETWEEN NUCLEAR SPIN AND CHEMICAL REACTIONS MAGNETIC ISOTOPE EFFECT 2 1. INTRODUCTION 4 1.1. Free Radical Reaction Scheme 5 1.2. Geminate Recombination 7 1.3. Diffusion 11 1.4. Electron Spin States 14 1.5. Electron Spin State Interconversion 17 2. FIRST COLLISION MODEL 19 2.1. Recombination Yield 19 2.2. First Collision Probability function 22 2.3. Chemical React'vity 26 2.4. Spin Hamiltonian 28 2.4.1. Two-Electron Hamiltonian Terms 31 2.4.2. One-Electron Hamiltonlan Terms 35 2.4.3. Spin-Orbit Coupling 37 2.5. Time Evolution of the Spin States 43 2.5.1. Basis Functions 43 2.5.2. Initial Conditions 46 2.5.3. Time Evolution up to the First Collision 47 2.5.4. Time-Dependent Singlet Character 53 2.5.5. First Collision and Thereafter 57 vi 2.5.6. Spin-Orbit Coupling 61 2.6. Competitive Channels and Radical Lifetimes 70 2.7. Special Case of High Singlet Reactivity 73 3. CONTINUOUS DIFFUSION MODEL 76 3.1. Diffusion 77 3.2. Classical Treatment of Intersystem Crossing 78 3.3. Chemical Loss 81 3.4. Time Evolution Equations and Boundary Conditions 82 3.5. Recombination Yield 84 3.6. Restricted Volume and Micelles 88 4. PHOTOCHEMISTRY 91 4.1. Benzophenone and Toluene 91 4.2. Dibenzylketone 99 5. EXPERIMENTAL DETAILS 104 5.1. Benzophenone and Toluene 104 5.2. Dibenzylketone 109 5.3. Benzaldehyde 122 6. CALCULATIONS AND EXPERIMENTAL RESULTS 124 6.1. Betvzoptvei\c*ie and Tol\ie,na 125 6.1.1. Geminate Recombination 125 6.1.2. Isotope Enhancement Factor 135 6.2. Dibenzylketone 144 6.2.1. Geminate Recombination 144 6.2.2. Isotope Enrichment Factor 147 7. SUMMARY AND DISCUSSION 162 REFERENCES 165 vil PART II INTIiRACTIONS BETWEEN NUCLEAR SPIN AND METHYL GROUP ROTATIONAL AND TORSIONAL DEGREES OF FREEDOM 8. INTRODUCTION 171 8.1. Partitioning of States In Space and Spin 172 9. SPIN THERMODYNAMICS 175 9.1. Grand Canonical Ensemble 177 9.2. Quasl-Equilibrium 180 9.3. Number Operators 183 10. METHYL GROUP DESCRIPTION 187 10.1. Spatial Hamlltonian 187 10.2. Spin Hamlltonian 194 10.2.1. Zeeman Hamiltonian 194 10.2.2. Dipolar Hamiltonian 197 10.3. The Pauli Principle and the Tunneling System 201 11. SPIN DIFFUSION AND SPIN-LATTICE RELAXATION 204 11.1. Symmetry Restricted Spin Diffusion 204 11.2. Rotational Polarization 207 11.3. Spin-Lattice Relaxation 211 11.3.1. Independent Methyl Groups 211 11.3.2. Coupled Methyl Groups 217 12. EXPERIMENTAL DETAILS 226 12.1. Samples 226 12.2. Signal to Noise 228 viii 12.3. 106 MHz Spectrometer 230 12.3.1. Magnet 230 12.3.2. Pulse Generation 230 12.3.3.