Rresponds for the initial and final electronic states and (ii) the coupling of electron and

Rresponds for the initial and final electronic states and (ii) the coupling of electron and FD&C Green No. 3 medchemexpress proton dynamics is restricted for the influence of the R worth around the electronic coupling VIF. In light of the analysis of section five.three, the effective prospective energies for the proton dynamics in the initial and final electronic states, V I(R) and V F(R), may very well be interpreted as (i) the averages from the diabatic PESs V I(R,Q) and V F(R,Q) more than the Q conformation, (ii) the values of these PESs at the reactant and product equilibrium Q values, or (iii) proton PESs that usually do not depend directly on Q, i.e., are determined only by the electronic state. The proton PESs V I(R) and V F(R) are known as “bond potentials” by Cukier, simply because they describe the bound proton via the entire R range, for the corresponding electronic states. In the event the bond potentials are characterized by a big asymmetry (see 7385-67-3 MedChemExpress Figure 41) and depend weakly on the localization with the transferring electron (namely, the dashed and solid lines in Figure 41 are extremely similar), then no PT happens: the proton vibrates approximately around the same position in the initial and final ET states. Conversely, verydx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical ReviewskPCET = VIF two SkBTReview|0I|nF|n(G+ + – )2 S Fn I0 exp – 4SkBT(p kBT )(11.7)Figure 41. Proton PESs that might represent VI(R,Q) and VF(R,Q) or V I(R) and V F(R). A robust dependence on the electronic state is illustrated. Just before ET (i.e., in electronic state I), the initial proton localization, that is centered on -R0, is strongly favored in comparison with its localization immediately after tunneling, i.e., around R0. The opposite case occurs following ET. Hence, PT is thermodynamically favored to happen immediately after ET. Note that the depicted PESs are qualitatively similar to these in Figure 2 of ref 116 and are comparable with these in Figure 27c.various V I(R) and V F(R) indicate powerful coupling with the electron and proton states, as shown in Figure 41. Primarily based around the above Hamiltonian, and applying regular manipulations of ET theory,149,343 the PCET rate constant iskPCET = VIF 2 SkBTPk |kI|nF|k n(G+ + – )2 S Fn Ik xp – 4SkBT = SkBTPv2 Wv(G+ + – )2 S v xp – 4SkBT(11.6a)whereWv = VIFk1|nF(11.6b)The quantum numbers = I,k and = F,n are utilised to distinguish the initial and final proton states, as well because the overall vibronic states. The rate constant is formally similar to that in eq 11.two. Nevertheless, the price reflects the vital differences between the Hamiltonians of eqs 11.1 and 11.five. On the one hand, the ET matrix element doesn’t rely on R in eq 11.6. However, the passage from Hp(R) to V I(R),V F(R) results in distinct sets of proton vibrational states that correspond to V I(R) and V F(R) (|kI and |nF, respectively). The harmonic approximation will need not be used for the vibrational states in eq 11.6, exactly where, actually, the initial and final proton energy levels are generically denoted by and , respectively. Nevertheless, within the derivation of kPCET, it really is assumed that the R and Q Franck-Condon overlaps may be factored.116 Note that eq 11.6 reduces to eq 9.17, obtained inside the DKL model, within the harmonic approximation for the vibrational motion of your proton in its initial and final localized states and contemplating that the proton frequency satisfies the situation p kBT, in order that only the proton vibrational ground state is initially populated. In factThe helpful potential energy curves in Figure 41 c.