Nonadiabatic EPT. In eq ten.17, the cross-term containing (X)1/2 remains finite in the classical limit

Nonadiabatic EPT. In eq ten.17, the cross-term containing (X)1/2 remains finite in the classical limit 0 due to the expression for . This is a consequence with the dynamical correlation amongst the X coupling and splitting fluctuations, and may be related to the discussion of Figure 33. Application of eq ten.17 to Figure 33 (exactly where S is fixed) establishes that the motion along R (i.e., at fixed nuclear coordinates) is impacted by , the motion along X will depend on X, and the motion along oblique lines, which include the dashed ones (that is associated with rotation more than the R, X plane), is also influenced by (X)1/2. The cross-term (X)1/2 precludes factoring the rate expression into separate contributions in the two kinds of fluctuations. Regarding eq ten.17, 6893-26-1 Purity & Documentation Borgis and Hynes say,193 “Note the key feature that the apparent “activation energy” in the exponent in k is governed by the solvent and the Q-vibration; it can be not straight related to the barrier height for the proton, Chlorobenzuron custom synthesis because the proton coordinate is just not the reaction coordinate.” (Q is X in our notation.) Note, however, that IF seems in this productive activation power. It’s not a function of R, but it does depend on the barrier height (see the expression of IF resulting from eq ten.4 or the relatedThe average on the squared coupling is taken over the ground state on the X vibrational mode. The truth is, excitation on the X mode is forbidden at temperatures such that kBT and beneath the situation |G S . (W IF2)t is defined by eq 10.18c because the worth with the squared H coupling in the crossing point Xt = X/2 of your diabatic curves in Figure 32b for the symmetric case. The Condon approximation with respect to X would amount, as an alternative, to replacing WIF20 with (W IF2)t, which is typically inappropriate, as discussed above. Equation ten.18a is formally identical for the expression for the pure ET price constant, following relaxation from the Condon approximation.333 Furthermore, eq 10.18a yields the Marcus and DKL results, except for the more explicit expression of the coupling reported in eqs ten.18b and ten.18c. As inside the DKL model, the thermal energy kBT is considerably smaller than , but a lot bigger than the power quantum for the solvent motion. Inside 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|( – )2 X |G|G exp – kBT(G 0)(ten.19b)where |G| = G+ S and |G| = G- S. The activation barriers in eqs 10.18a and ten.19 are in agreement with these predicted by Marcus for PT and HAT reactions (cf. eqs 6.12 and 6.14, and also eq 9.15), while only the similarity in between eq ten.18a along with the Marcus ET rate has been stressed frequently in the previous literature.184,193 Rate constants quite similar to those above were elaborated by Suarez and Silbey377 with reference to hydrogen tunneling in condensed media around the basis of a spin-boson Hamiltonian for the HAT program.378 Borgis and Hynes also elaborated an expression for the PT price continuous inside the completely (electronically and vibrationally) adiabatic regime, for /kBT 1:kIF = Gact S exp – two kBTCondon approximation delivers the mechanism for the influence of PT at the hydrogen-bonded interface on the long-distance ET . The effects of your R coordinate around the reorganization power aren’t included. The model can bring about isotope effects and temperature dependence with the PCET rate continual beyond these.