Nonadiabatic EPT. In eq 10.17, the cross-term containing (X)1/2 remains finite within the classical limit

Nonadiabatic EPT. In eq 10.17, the cross-term containing (X)1/2 remains finite within the classical limit 0 because of the expression for . This is a consequence with the dynamical correlation amongst the X coupling and splitting fluctuations, and can be associated with the discussion of Figure 33. Application of eq ten.17 to Figure 33 (where S is fixed) establishes that the motion along R (i.e., at fixed nuclear coordinates) is affected by , the motion along X is dependent upon X, plus the motion along oblique lines, for instance the dashed ones (that is associated with rotation over the R, X plane), is also influenced by (X)1/2. The cross-term (X)1/2 precludes factoring the price expression into separate contributions in the two sorts of fluctuations. Relating to eq ten.17, Borgis and Hynes say,193 “Note the key function that the apparent “activation energy” inside the exponent in k is governed by the solvent along with the Q-vibration; it is not directly associated with the barrier height for the proton, because the proton coordinate just isn’t the reaction coordinate.” (Q is X in our notation.) Note, nevertheless, that IF appears in this productive activation energy. It 69-57-8 supplier really is not a function of R, but it does depend on the barrier height (see the expression of IF resulting from eq ten.four or the relatedThe average in the squared coupling is taken more than the ground state in the X vibrational mode. In reality, excitation on the X mode is forbidden at temperatures such that kBT and below the condition |G S . (W IF2)t is defined by eq 10.18c as the value from the squared H coupling in the crossing point Xt = X/2 of your diabatic curves in Figure 32b for the symmetric case. The 108341-18-0 Autophagy Condon approximation with respect to X would quantity, as an alternative, to replacing WIF20 with (W IF2)t, which can be commonly inappropriate, as discussed above. Equation 10.18a is formally identical to the expression for the pure ET rate constant, soon after relaxation of your Condon approximation.333 In addition, eq 10.18a yields the Marcus and DKL results, except for the additional explicit expression in the coupling reported in eqs 10.18b and 10.18c. As within the DKL model, the thermal energy kBT is significantly smaller than , but substantially bigger than the energy quantum for the solvent motion. Within the limit of weak solvation, S |G 165,192,kIF = WIF|G| h exp |G||G|( + )two X |G|(G 0)(10.19a)dx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical ReviewskIF = WIFReview|G| h exp |G||G|( – )two X |G|G exp – kBT(G 0)(10.19b)exactly where |G| = G+ S and |G| = G- S. The activation barriers in eqs 10.18a and ten.19 are in agreement with those predicted by Marcus for PT and HAT reactions (cf. eqs 6.12 and 6.14, and also eq 9.15), although only the similarity among eq 10.18a as well as the Marcus ET price has been stressed normally inside the previous literature.184,193 Rate constants really equivalent to these above were elaborated by Suarez and Silbey377 with reference to hydrogen tunneling in condensed media on the basis of a spin-boson Hamiltonian for the HAT program.378 Borgis and Hynes also elaborated an expression for the PT price constant within the completely (electronically and vibrationally) adiabatic regime, for /kBT 1:kIF = Gact S exp – two kBTCondon approximation supplies the mechanism for the influence of PT at the hydrogen-bonded interface on the long-distance ET . The effects from the R coordinate on the reorganization energy are not included. The model can result in isotope effects and temperature dependence on the PCET rate constant beyond those.