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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.
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Discussion of the influence of bending on these results can be found in Refs [14] and [15]
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Discussion of the influence of bending on these results can be found in Refs [14] and [15].
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113
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77955162698
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The expression in Eqns (3) and (4) is similar in form to that for weakly electronically coupled (electronically nonadiabatic) electron transfer [95-98], in that the proton coupling C is analogous to the electronic resonance coupling and the reorganization energy ES is 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 Fig. 3b).
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77955131335
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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 1-10 TS
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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 1-10 TS.
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116
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77955148155
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The barrier height dependence V‡ in expression in Eqn (17) was derived from a semiclassical description for the proton resonance splitting [145-147]. Model calculations for OH O systems [2, 15,16] and quantum chemistry calculations of NH N systems[148] show that the change in the V‡ versus Q is predominantly linear (see Ref. 33 in Ref. [15]). This result yields the linear exponential expression for C in Eqns (5) and (16)
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The barrier height dependence V‡ in expression in Eqn (17) was derived from a semiclassical description for the proton resonance splitting [145-147]. Model calculations for OH O systems [2,15,16] and quantum chemistry calculations of NH N systems[148] show that the change in the V‡ versus Q is predominantly linear (see Ref. 33 in Ref. [15]). This result yields the linear exponential expression for C in Eqns (5) and (16).
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77955135203
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The difference between H-atom, hydride, and proton transfer reactions is primarily governed by their difference in charge rearrangement, which translates into a difference in the amount of reorganization required by the environment. H-atom transfer, for example, will have a smaller charge rearrangement than that of proton transfer, and will thus couple less to the environment, yielding a smaller reorganization energy.
-
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123
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77955165087
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While within the stated restrictions, the theory is generally applicable to H-atom, hydride, and proton transfer, there are important differences between solution and enzymatic reactions. In particular, the nature of the 'solvent' coordinate will be different in a biological environment, where 'solvation' is associated with an 'environmental' coordinate that modulates the symmetry of the hydrogenic species' potential, which should include the fields of charged, polar/polarizable groups and explicit solvent molecules present in (at least) the reactive site. The 'environmental' reorganization energy will thus concern their rearrangement. Similarly, the single H-bond coordinate Q needs to be generalized to a number of coordinates in the active site that modulate the proton barrier width.
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77955170134
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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 [5])[122]
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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 [5])[122].
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130
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77955133931
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o are obtained
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o are obtained.
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77955161100
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77955166194
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Further remarks on the T dependence of the Swain-Schaad ratio can be found in Section 3c of Ref. [15, 16]
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Further remarks on the T dependence of the Swain-Schaad ratio can be found in Section 3c of Ref. [15,16].
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