Interpretation of primary kinetic isotope effects for adiabatic and nonadiabatic proton-transfer reactions in a polar environment

Isotope Effects in Chemistry and Biology

Volumn , Issue , 2005, Pages 549-578

  Kiefer, Philip M ^a   Hynes, James T ^a  

^a UNIVERSITY OF COLORADO   (United States)

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[No Author keywords available]

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EID: 84870028316     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1201/9781420028027     Document Type: Chapter

References (132)

1. Borgis, D. and Hynes, J. T., A curve crossing approach for proton transfer reactions in solution, J. Phys. Chem., 100, 1118-1128, 1996.
2. Borgis, D. and Hynes, J. T., Dynamical theory of proton tunnelling transfer rates in solution: general formulation, Chem. Phys., 170, 315-346, 1993.
3. Borgis, D. J., Lee, S., and Hynes, J. T., A dynamical theory of nonadiabatic proton and hydrogen atom transfer reaction rates in solution, Chem. Phys. Lett., 162, 19-26, 1989.
4. Borgis, D. and Hynes, J. T., Molecular dynamics simulation for a model nonadiabatic proton transfer reaction in solution, J. Chem. Phys., 94, 3619-3628, 1991.
5. Lee, S. and Hynes, J. T., Intramolecular hydrogen atom transfer rates in solution, J. Chim. Phys., 99, 7557-7567, 1996.
6. Ando, K. and Hynes, J. T., Molecular mechanism of HCl acid ionization in water. Ab initio potential energy surfaces and monte carlo simulations, J. Phys. Chem. B, 101, 10464-10478, 1997.
7. Ando, K. and Hynes, J. T., Molecular mechanism of HF acid ionization in water: an electronic structure-monte carlo study, J. Phys. Chem. A, 103, 10398-10408, 1999.
8. Staib, A., Hynes, J. T., and Borgis, D., Proton transfer in hydrogen-bonded acid-base complexes in polar solvents, J. Chem. Phys., 102, 2487-2505, 1995.
9. Ando, K. and Hynes, J. T., Acid-base proton transfer and ion pair formation in solution, Adv. Chem. Phys., 110, 381-430, 1999.
10. Kiefer, P. M. and Hynes, J. T., Nonlinear free energy relations for adiabatic proton transfer reactions in a polar environment I fixed proton donor-acceptor distance, J. Phys. Chem. A, 106, 1834-1849, 2002.
11. Kiefer, P. M. and Hynes, J. T., Nonlinear free energy relations for adiabatic proton transfer reactions in a polar environment. II Inclusion of proton donor-acceptor vibration, J. Phys. Chem. A, 106, 1850-1861, 2002.
12. Kiefer, P. M. and Hynes, J. T., Kinetic isotope effects for adiabatic proton transfer reactions in a polar environment, J. Phys. Chem. A, 107, 9022-9039, 2003.
13. Kiefer, P. M. and Hynes, J. T., Kinetic isotope effects for nonadiabatic proton transfer reactions in a polar environment I. Interpretation of tunneling kinetic isotope effects, J. Phys. Chem. A, 108, 11793-11808, 2004.
14. Kiefer, P. M. and Hynes, J. T., Kinetic isotope effects for nonadiabatic proton transfer reactions in a polar environment II. Comparison with an electronic diabatic description, J. Phys. Chem. A, 108, 11809-11818, 2004.
15. Timoneda, J. J. and Hynes, J. T., Nonequilibrium free energy surfaces for hydrogen-bonded proton transfer complexes in solution, J. Phys. Chem., 95, 10431-10442, 1991.
16. Gertner, B. J. and Hynes, J. T., Model molecular dynamics simulation of hydrochloric acid ionization at the surface of stratospheric ice, Faraday Soc. Discuss., 110, 301-322, 1998.
17. Bell, R. P., The proton in chemistry, 2nd ed., Cornell University Press, Ithaca, NY, 1973.
18. Caldin, E. and Gold, V., Proton Transfer Reactions, Chapman and Hall, London, 1975.
19. Kresge, A., What makes proton transfer fast? J. Acc. Chem. Res., 8, 354-360, 1975.
20. Hibbert, F., Mechanisms of proton transfer between oxygen and nitrogen acids and bases in aqueous solution, Adv Phys. Org. Chem., 22, 113-212, 1986.
21. Hibbert, F., Hydrogen bonding and chemical reactivity, Adv. Phys. Org. Chem., 26, 255-379, 1990.
22. Kreevoy, M. M. and Konasewich, D. E., The Brønsted a and the primary hydrogen isotope effect Adv. chem. phys., 21, 243-252, 1972.
23. Kreevoy, M. M. and Oh, S.-w., Relations between rate and equilibrium constants for proton-transfer reactions, J. Am. Chem. Soc., 95, 4805-4810, 1973.
24. Kresge, A. J. and Silverman, D. N., Application of marcus rate theory to proton transfer in enzymecatalyzed reactions, Meth. Enz., 308, 276-297, 1999.
25. Kresge, A. J., Chen, H. J., and Chiang, Y., Vinyl ether hydrolysis. 7. Isotope effects on catalysis by aqueous hydrofluoric acid, J. Am. Chem. Soc., 99, 802-805, 1977.
26. Kresge, A. J., Sagatys, D. S., and Chen, H. L., Vinyl ether hydrolysis. 9. Isotope effects on proton transfer from the hydronium ion, J. Am. Chem. Soc., 99, 7228-7233, 1977.
27. McLennan, D. J. and Wong, R. J., The carbanion mechanism of olefin-forming elimination. VII theoretical analysis of substituent and isotope effects in proton transfer from 2,2-diaryl-1,1,1- trichloroethanes, Aust. J. Chem., 29, 787-798, 1976.
28. Lee, I.-S. H., Jeoung, E. H., and Kreevoy, M. M., Primary kinetic isotope effects on hydride transfer from 1,3-dimethyl-2-phenylbenzimidazole to NAD + analogues, J. Am. Chem. Soc., 123, 7492-7496, 2001.
29. Bell, R. P. and Goodall, D. M., Kinetic hydrogen isotope effects, Proc. Roy. Soc. London Series A, 294, 273-297, 1966.
30. Dixon, J. E. and Bruice, T. C., Dependence of the primary isotope effect (k H/k D) on base strength for the primary amine catalyzed ionization of nitroethane, J. Am. Chem. Soc., 92, 905-909, 1970.
31. Pryor, W. A. and Kneipp, K. G., Primary kinetic isotope effects and the nature of hydrogen-transfer transition states. The reaction of a series of free radicals with thiols, J. Am. Chem. Soc., 93, 5584-5586, 1971.
32. Bell, R. P. and Cox, B. G., Primary kinetic isotope effects and the rate of ionization of nitroethane in mixtures of water and dimethyl sulphoxide, J. Chem. Soc. B, 783-785, 1971.
33. Bordwell, F. G. and Boyle, W. J., Kinetic isotope effects for nitroalkanes and their relationship in proton transfer reactions, J. Am. Chem. Soc., 97, 3447-3452, 1975.
34. Cha, Y., Murray, C. J., and Klinman, J. P., Hydrogen tunneling in enzyme reactions, Science, 243, 1325-1330, 1989.
35. Kohen, A. and Klinman, J. P., Enzyme catalysis: beyond classical paradigms, Acc. Chem. Res., 31, 397-404, 1998.
36. Kohen, A. and Klinman, J. P., Hydrogen tunneling in biology, Chem. Biol., 6, R191-R198, 1999.
37. Kohen, A., Cannio, R., Bartolucci, S., and Klinman, J. P., Enzyme dynamics and hydrogen tunneling in thermophilic alcohol dehydrogenase, Nature, 399, 496-499, 1999.
38. Kresge, A. J., Magnitude of primary hydrogen isotope effects, In Isotope Effects on Enzyme-Catalyzed Reactions, Cleland, W. W., O’Leary, M. H., and Northrop, D. B., Eds., University Park Press, Baltimore, MD, pp. 37-63, 1977.
39. 14,15
40. Cukier, R. I., Proton-coupled electron transfer reactions: evaluation of rate constants, J. Phys. Chem., 100, 15428-15443, 1996.
41. Cukier, R. I. and Nocera, D., Proton-coupled electron transfer, Ann. Rev. Phys. Chem., 49, 337-369, 1998.
42. Soudackov, A. and Hammes-Schiffer, S., Derivation of rate expressions for nonadiabatic protoncoupled electron transfer reactions in solution, J. Chem. Phys., 113, 2385-2396, 2000.
43. Iordanova, N., Decornez, H., and Hammes-Schiffer, S., Theoretical study of electron, proton, and proton-coupled electron transfer in iron bi-imidazole complexes, J. Am. Chem. Soc., 123, 3723-3733, 2001.
44. Iordanova, N. and Hammes-Schiffer, S., Theoretical investigation of large kinetic isotope effects for proton-coupled electron transfer in ruthenium polypuridyl complexes, J. Am. Chem. Soc., 124, 4848-4856, 2002.
45. Hammes-Schiffer, S., Theoretical perspectives on proton-coupled electron transfer reactions, Acc. Chem. Res., 34, 273-281, 2001.
46. Melander, L. and Saunders, W. H., Reaction Rates of Isotopic Molecules, Wiley, New York, 1980.
47. Westheimer, F. H., The magnitude of the primary kinetic isotope effect for compounds of hydrogen and deuterium, Chem. Rev., 61, 265-273, 1961.
48. Melander, L., Isotope Effects on Reaction Rates, The Ronald Press Co., New York, 1960.
49. Hammond, G. S., A correlation of reaction rates, J. Am. Chem. Soc., 77, 33-338, 1955.
50. Lowry, T. H. and Richardson, K. S., Mechanism and Theory in Organic Chemistry, 3rd ed., Harper Collins Pubs., New York, 1987.
51. More O’Ferral, R. A., Substrate isotope effects, In Proton Transfer Reactions, Caldin, E. and Gold, V., Eds., Chapman and Hall, London, pp. 201-261, 1975.
52. Bell, R. P., The Tunnel Effect in Chemistry, Chapman and Hall, New York, 1980.
53. Bell, R. P., Sachs, W. H., and Tranter, R. L., Model Calculations of Isotope Effects in Proton Transfer Reactions, Trans Far Soc., 67, 1995-2003, 1971.
54. 8,11,20as well as assumes that the proton primarily resides in it ground (stretching and bending) vibrational state.
55. Swain, G. G., Stivers, E. C., Reuwer, J. F., and Schaad, L. J., Use of hydrogen isotope effects to identify the attacking nucleophile in the enolization of ketones catalyzed by acetic acid, J. Am. Chem. Soc., 80, 5885-5893, 1958.
56. Babamov, V. K. and Marcus, R. A., Dynamics of hydrogen atom and proton transfer reactions. Symmetric case, J. Chem. Phys., 74, 1790-1798, 1981.
57. Hiller, C., Manz, J., Miller, W. H., and Römelt, J., Oscillating reactivity of collinear symmetric heavy + light 2 heavy atom reactions, J. Chem. Phys., 78, 3850-3856, 1983.
58. Miller, W. H., Tunneling corrections to unimolecular rate constants, with application to formaldehyde, J. Am. Chem. Soc., 101, 6810-6814, 1979.
59. Skodje, R. T., Truhlar, D. G., and Garrett, B. C., Vibrationally adiabatic models for reactive tunneling, J. Chem. Phys., 77, 5955-5976, 1982.
60. 2+ H, J. Chem. Phys., 67, 2609-2613, 1977.
61. Garrett, B. C. and Truhlar, D. G., A least action variational method for calculating multidimensional tunneling probabilities for chemical reactions, J. Chem. Phys., 79, 4931-4938, 1983.
62. Kim, Y. and Kreevoy, M. M., The experimental manifestations of corner-cutting tunneling, J. Am. Chem. Soc., 114, 7116-7123, 1992.
63. Calculations of KIEs derived from a classical reaction path (e.g., the MEP) in the presence of a solvent or polar environment typically add quantum corrections to that path.
64. 25e25 For numerical calculations consistent with the stanadard view, see (a) Alhambra, C., Corchado, J. C., Sánchez, M. L., Gao, J., and Truhlar, D. G., Quantum dynamics of hydride transfer in enzyme catalysis, J. Am. Chem. Soc., 122, 8197-8203, 2000.
65. Hwang, J.-K. and Warshel, A., A quantized classical path approach for calculations of quantum mechanical rate constants, J. Phys. Chem., 97, 10053-10058, 1993.
66. Hwang, J.-K., Chu, Z. T., Yadav, A., and Warshel, A., Simulations of quantum mechanical corrections for rate constants of hydride- transfer reactions in enzymes and solutions, J. Phys. Chem., 95, 8445-8448, 1991.
67. Hwang, J.-K. and Warshel, A., How important are quantum mechanical nuclear motions in enzyme catalysis? J. Am. Chem. Soc., 118, 11745-11751, 1996.
68. Alhambra, C., Gao, J., Corchado, J. C., Villa, J., and Truhlar, D. G., Quantum mechanical dynamical effects in an enzyme catalyzed proton transfer reaction, J. Am. Chem. Soc., 121, 2253-2258, 1999.
69. Cui, Q. and Karplus, M., Quantum mechanics/molecular mechanics studies of triosephosphate isomerase-catalyzed reactions: Effect of geometry and tunneling on proton-transfer rate constants, J. Am. Chem. Soc., 124, 3093-3124, 2002.
70. Garrett, B. C. and Truhlar, D. G., Generalized transition state theory. Bond energy-bond order method for canonical variational calculations with application to hydrogen atom transfer reactions, J. Am. Chem. Soc., 101, 4534-4547, 1979.
71. Saunders, W. H., Calculations of isotope effects in elimination reactions. New experimental criteria for tunneling in slow proton transfers, J. Am. Chem. Soc., 107, 164-169, 1985.
72. For examples of the equilibrium solvation picture for PT in a complex system, see (a) Bash, P. A., Field, M. J., Davenport, R. C., Petsko, G. A., Ringe, D., and Karplus, M., Computer simulation and analysis of the reaction pathway of triosephosphate isomerase, Biochemistry, 30, 5826-5832, 1991.
73. Cui, Q. and Karplus, M., Triosephosphate isomerase: a theoretical comparison of alternative pathways, J. Am. Chem. Soc., 123, 2284-2290, 2001.
74. Alhambra, C., Corchado, J., Sánchez, M. L., Garcia-Viloca, M., Gao, J., and Truhlar, D. G., Canonical variational transition state theory for enzyme kinetics with the protein mean force and multidimensional quantum mechanical tunneling dynamics. Theory and application to liver alcohol dehydrogenase, J. Phys. Chem. B, 105, 11326-11340, 2001.
75. Cui, Q., Elstner, M., and Karplus, M., A theoretical analysis of the proton and hydride transfer in liver alcohol dehydrogenase (LADH), J. Phys. Chem. B, 106, 2721-2740, 2002.
76. Dogonadze, R. R., Kuznetzov, A. M., and Levich, V. G., Theory of hydrogen-ion discharge on metals: case of high overvoltages, Electrochim. Acta, 13, 1025-1044, 1968.
77. German, E. D., Kuznetzov, A. M., and Dogonadze, R. R., Theory of kinetic isotope effect in proton transfer reactions in a polar medium, J. Chem. Soc. Farad. Trans II, 76, 1128-1146, 1980.
78. Kuznetzov, A. M., Charge Transfer in Physics, Chemistry and Biology: Physical Mechanisms of Elementary Processes and an Introduction to the Theory, Gordon and Breach Publishers, Amsterdam, 1995.
79. Kuznetzov, A. M. and Ulstrup, J., Proton and hydrogen atom tunneling in hydrolytic and redox enzyme catalysis, Can. J. Chem., 77, 1085-1096, 1999.
80. Sühnel, J. and Gustav, K., Theory of proton-transfer reactions. The influence of adiabaticity on free energy relations, Chem. Phys., 87, 179-187, 1984.
81. Basilevsky, M. V., Soudackov, A., and Vener, M. V., Electron proton free energy surfaces for proton transfer reaction in polar solvents: test calculations for carbon-carbon reaction centres, Chem. Phys., 200, 87-106, 1995.
82. Basilevsky, M. V., Vener, M. V., Davidovich, G. V., and Soudackov, A., Dynamics of proton transfer reactions in polar solvent in the nonadiabtic two-state approximation: test calculations for carbon-carbon centre, Chem. Phys., 208, 267-282, 1996.
83. Vener, M. V., Rostov, I. V., Soudackov, A., and Basilevsky, M. V., Semiemperical modeling free energy surfaces for proton transfer in polar aprotic solvents, Chem. Phys., 254, 249-265, 2000.
84. Agarwal, P. K., Billeter, S. R., and Hammes-Schiffer, S., Nuclear quantum effects and enzyme dynamics in dihydrofolate reductase catalysis, J. Phys. Chem. B, 106, 3283-3293, 2002.
85. Agarwal, P. K., Billeter, S. R., Rajagopalan, P. T., Benkovic, S. J., and Hammes-Schiffer, S., Network of coupled promoting motions in enzyme catalysis, PNAS, 99, 2794-2799, 2002.
86. Hammes-Schiffer, S., Comparison of hydride, hydrogen atom, and proton-coupled electron transfer reactions, Chem. Phys. Chem., 3, 33-42, 2002.
87. Hammes-Schiffer, S. and Billeter, S. R., Hybrid approach for the dynamical simulation of proton and hydride transfer in solution and proteins, Int. Rev. Phys. Chem., 20, 591-616, 2001.
88. Billeter, S. R., Webb, S. P., Agarwal, P. K., Iordanov, T., and Hammes-Schiffer, S., Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and the role of enzyme motion, J. Am. Chem. Soc., 123, 11262-11272, 2001.
89. Billeter, S. R., Webb, S. P., Iordanov, T., Agarwal, P. K., and Hammes-Schiffer, S., Hybrid approach for including electronic and nuclear quantum effects in molecular dynamics simulations of hydrogen transfer reactions in enzyme, J. Chem. Phys., 114, 6925-6936, 2001.
90. While these two regimes are distinctly separated, there may exist real systems where different isotopes will be in different regimes. For example, the proton potential barrier at the solvent TS configuration may be small enough such that the proton ground vibration state may be above the barrier, but still large enough such that the deuteron ground vibration state, with a smaller ZPE, may be below the barrier. The present discussion assumes that all isotopes transfer in the same regime.
91. 1b
92. 2pair in low polarity solvents, J. Phys. Chem. A, 105, 2582-2590, 2001.
93. Cleland, W. W. and Kreevoy, M. M., Low-barrier hydrogen bonds and enzymic catalysis, Science, 264, 1887-1890, 1994.
94. Cleland, W. W., Frey, P. A., and Gerlt, J. A., The low barrier hydrogen bond in enzymatic catalysis, J. Biol. Chem., 273, 25529-25532, 1998, For adiabatic PT, the “low barrier H-bond” situation occurs at an activated TS configuration in the solvent coordinate.
95. Kiefer, P. M., Leite, V. P. B., and Whitnell, R. M., A simple model for proton transfer, Chem. Phys., 194, 33-44, 1995.
96. Hynes, J. T., The role of the environment in chemical reactions, In The Enzyme Catalysis Process, Cooper, A., Houben, J. L., and Chien, L. C., Eds., Plenum NATO ASI Series, New York, pp. 283-292, 1989.
97. Hynes, J. T., The theory of reactions in solution, In The Theory of Chemical Reaction Dynamics, Vol. IV, Baer, M., Ed., CRC Press, Boca Raton, FL, pp. 171-234, 1985, Remarks about recrossing corrections to TST can be found in Ref. 41 of Ref. 4.
98. 2a
99. RXNis defined throughout as the free energy difference between reactant and product H-bond complexes, a free energy difference that is rarely experimentally determined. The full connection to experimentally determined quantities is discussed in Ref. 43 of Ref. 4.
100. Evans, M. G. and Polanyi, M., Further considerations on the thermodynamics of chemical equilibria and reaction rates, Trans. Faraday Soc., 32, 1333-1360, 1936.
101. Evans, M. G. and Polanyi, M., Inertia and driving force of chemical reactions, Trans. Faraday Soc., 34, 11-24, 1938, The Evans-Polanyi relations were developed mainly for gas phase reactions but are also useful in solution in the context of the standard picture.
102. Kiefer, P. M. and Hynes, J. T., Temperature dependent solvent polarity effects on adiabatic proton transfer rate constants and kinetic isotope effects, Israel J. Chem., 44, 171-184, 2004.
103. ois not expected to be exactly 0.5 due to ‘intrinsic’ asymmetry, but the deviation from 0.5 for either H or D is not expected to be significant. For further discussion, see Ref. 45 of Ref. 4.
104. Novak, A., Hydrogen bonding in solids. Correlation of spectroscopic and crystallographic data, Struct. Bond., 18, 177-216, 1974.
105. Zeegers-Huyskens, T. and Huyskens, P., Proton transfer and ion transfer complexes, In Molecular Interactions, Vol. 2, Ratajcak, H. and Orville-Thomas, W. J., Eds., Wiley, New York, pp. 1-106, 1980.
106. 5
107. Pimentel, G. C. and McClellan, A. L., The Hydrogen Bond, W.H. Freeman, New York, 1960.
108. Personal communication from E. Pines. For preliminary KIEs of photo-acids, see. (a) Krishnan, R., Lee, J., and Robinson, G. W., Isotope effect on weak acid dissociation, J. Phys. Chem., 94, 6365-6367, 1990.
109. Pines, E., Pines, D., Barak, T., Magnes, B.-Z., Tolbert, L. M., and Haubrich, J. E., Isotope and temperature effects in ultrafast proton-transfer from a strong excited-state acid, Ber. Bunsenges. Phys. Chem., 102, 511-517, 1998.
110. 2O, and while this change in solvent introduces other possible solvent isotope effects (i.e., viscosity), the rate limiting step in each case has been shown to be a PT step (or a series of PT steps), and thus the measured KIE corresponds to PT.
111. 4
112. Siebrand, W., Wildman, T. A., and Zgierski, M. Z., Golden-rule treatment of hydrogen-transfer reactions. 1. Principles, J. Am. Chem. Soc., 106, 4083-4089, 1984.
113. Siebrand, W., Wildman, T. A., and Zgierski, M. Z., Golden-rule treatment of hydrogen-transfer reactions. 2. Applications, J. Am. Chem. Soc., 106, 4089-4096, 1984.
114. Cukier, R. I., A theory that connects proton-coupled electron-transfer and hydrogen-atom transfer reactions, J. Phys. Chem. B, 106, 1746-1757, 2002.
115. Cukier, R. I. and Zhu, J., Simulation of proton transfer reaction rates: the role of solvent electronic polarization, J. Phys. Chem. B, 101, 7180-7190, 1997.
116. Sis analogous to the electronic diabatic solvent reorganization energy. Even though the reorganization energies and couplings are analogous, the physical picture behind the two reaction types is quite different. The reorganization energy for proton tunneling is the free energy difference associated with a Franck-Condon-like excitation (all nuclear and solvent modes other than the proton mode are held fixed) of the ground diabatic proton vibrational state at the equilibrium reactant solvent position to the ground product diabatic proton vibrational state, followed by relaxation along the solvent coordinate to the equilibrium solvent product position (see Figure 21.7d).
117. Marcus, R. A., On the theory of oxidation-reduction reactions involving electron transfer. I, J. Chem. Phys., 24, 966-978, 1956.
118. Marcus, R. A., Electrostatic free energy and other properties of states having nonequilibrium polarization. I, J. Chem. Phys., 24, 979-988, 1956.
119. Marcus, R. A. and Sutin, N., Electron transfer in chemistry and biology, Biochim. Biophys. Acta, 811, 265-322, 1985.
120. Sutin, N., Theory of electron transfer reactions: insights and hindsights, Prog. Inorg. Chem., 30, 441-498, 1983.
121. Discussion of the influence of bending on these results can be found in Refs. 4 and 5a.
122. The H-bond vibrational mode is assumed to remain significantly unchanged while the reaction coordinate fluctuates from the 0-0 TS to either the 0-1 or 1 -0 TS.
123. This is particularly true for H atom transfer reactions because they are weakly coupled to a polar environment, i.e., small reorganization energies (cf. H atom transfer reaction in Ref. 1e).
124. oare obtained.
125. Antoniou, D. and Schwartz, S. D., Large kinetic isotope effects in enzymatic proton transfer and the role of substrate oscillations, PNAS, 94, 12360-12365, 1997.
126. Antoniou, D. and Schwartz, S. D., A molecular dynamics quantum Kramers study of proton transfer in solution, J. Chem. Phys., 110, 465-472, 1999.
127. Karmacharya, R. and Schwartz, S. D., Quantum proton transfer coupled to a quantum anharmonic mode, J. Chem. Phys., 110, 7376-7381, 1999.
128. Further remarks on the T dependence of the Swain-Schaad ratio can be found in Section 3c of Ref. 5a.
129. Peters, K. S., Cashin, A., and Timbers, P., Picosecond dynamics of nonadiabatic proton transfer:A kinetic study of proton transfer within the contact radical ion pair of substituted benzophenones/n, ndimethylaniline, J. Am. Chem. Soc., 122, 107-113, 2000.
130. Peters, K. S. and Cashin, A., A picosecond kinetic study of nonadiabatic proton transfer within the contact radical ion pair of substituted benzophenones/n, n-diethylaniline, J. Phys. Chem. A, 104, 4833-4838, 2000.
131. Peters, K. S. and Kim, G., Solvent effects for nonadiabatic proton transfer in the benzophenone/n, n-dimethylaniline, J. Phys. Chem. A, 105, 4177-4181, 2001.
132. Andrieux, C. P., Gamby, J., Hapiot, P., and Saveant, J.-M., Evidence for inverted region behavior in proton transfer to carbanions, J. Am. Chem. Soc., 125, 10119-10124, 2003.