Kinetic isotope effects for nonadiabatic proton transfer reactions in a polar environment 1. Interpretation of tunneling kinetic isotopic effects

Journal of Physical Chemistry A

Volumn 108, Issue 52, 2004, Pages 11793-11808

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

^a UNIVERSITY OF COLORADO   (United States)

^b ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARRHENIUS ACTIVATION ENERGY; KINETIC ISOTOPE EFFECTS (KIE); PROTON TRANSFER (PT); TEMPERATURE DEPENDENCE;

ACTIVATION ENERGY; COMPLEXATION; HYDROGEN BONDS; ISOTOPES; RATE CONSTANTS; SOLVENTS; THERMAL EFFECTS;

CHARGE TRANSFER;

EID: 11344269742     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp040497p     Document Type: Article

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73. 24 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 Id).
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83. Some PT systems will undoubtedly contain a mixture of nonadiabatic and adiabatic behavior. For example, the proton could be thermally excited where the proton vibrational state is above the barrier in the proton coordinate or it can tunnel through the proton barrier. The rate for the mixed case is the sum of the adiabatic and nonadiabatic PT rates, and the KIEs would thus be a convolution of adiabatic and nonadiabatic PT KIEs. See examples in ref 6.
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89. 5d.18 Henceforth, we assume the linear exponential form in eq 2.4.
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91. -1, a value also consistent with the mass dependence.
92. 30 Here we consider a linear H-bond system, where any bending contributions have been renormalized into the single H-bond mode frequency and separation. For simulation examples where the proton coordinate is treated with a stretch and bend, see ref 6.
93. 5d, e
94. 5a
95. The H-bond vibrational mode is assumed in this paper to remain significantly unchanged while the reaction coordinate fluctuates from the 0-0 TS to either the 0-1 or 1-0 TS.
96. p) term in eq 2.21 is an estimate for the decrease in barrier height for excited states.
97. eqL are based on model calculations by the present authors. Furthermore, these approximations are key provisions that allow for the development of the quantitative analysis in section 3, specifically those that indicate explicit contributions from excited proton states. While slight deviations from these approximations are possible and likely for real systems, the quantitative trends that result from the present analysis are not significantly altered by such deviations.
98. 13,14for nontunneling PT states that for a symmetric reaction the TS mode is purely classical proton motion, so that the TS mode includes more of the donor-acceptor mode as the reaction becomes more a symmetric. Thus, the TS mode mass increases with reaction asymmetry, and tunneling by H (or D) is less with increasing asymmetry, giving a maximal KIE for pure H (or D) motion for symmetric reaction and lower KIEs for less H (or D) tunneling at TS.
99. 44 demonstrate that an 'inverted' regime is possible for PT, the physical aspects of these systems that allow for observation of an 'inverted' regime remain to be clarified.
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104. RXN = 0.
105. Of course, in the solution case, the solvent would need to remain liquid and classical. More generally, the environment would have to remain classical.
106. 34 we have included the T dependence of the dielectric constant ε of water and find (i) a ∼20% reduction of the rale Arrhenius slopes and (ii) only a slight effect (<5%) on the KIE Arrhenius slope.
107. This is particularly true for H atom transfer reactions because they are weakly coupled to a polar environment, i.e., small reorganization energies (cf. the H atom transfer reaction in ref 5e).
108. ≠ = 9.25 kcal/mol, the proton or deuteron could be excited to a vibrational state above the proton barrier, and PT would then proceed via a nontunneling process. At this low T, however, the rate constant for such a process is many order of magnitudes smaller (for both H and D) than the tunneling rate constants.
109. o}. If a PT system was in the nontunneling regime at high temperatures one might expect that lowering the temperature would put the PT system in the tunneling regime, and thus one would expect a large Swain-Schaad ratio at low temperatures that progressively decreases toward the expected value eq 3.19 as T is increased. Figure 12c, however, displays the T dependence for a PT system that remains in the tunneling regime at all the displayed temperatures.
110. Se where the coupling to the solvent is weak, and e.g., the temperature dependence and KIE magnitude are quite different from those found in the present work.