To the electronically adiabatic surfaces in Figure 23b, their splitting at Qt is not neglected, and eqs five.62a-5.62d are as a result made use of. The minimum splitting is Ep,ad(Qt) – E p,ad(Qt) + G p,ad(Qt) – G p,ad(Qt), exactly where the derivatives with respect to Q in the diagonal interaction terms G p,ad(Qt) and G p,ad(Qt) are taken at Q = Qt and marks the upper adiabatic electronic state plus the corresponding electron-proton power eigenvalue. G p,ad(Qt) – G p,ad(Qt) is zero to get a model for example that shown in Figure 24 with (R,Q). Thus, averaging Ead(R,Q) – 2R2/2 and Ead(R,Q) – 2R2/2 over the respective proton wave 545380-34-5 Protocol functions givesp,ad p,ad E (Q t) – E (Q t) p,ad p,ad = T – T +[|p,ad (R)|2 – |p,ad (R)|two ]+ Ek (R , Q t) + En(R , Q t)dR two p,ad |p,ad (R )|two + | (R )|2kn (R , Q t) + 4Vkn two dR(5.64)If pure ET happens, p,ad(R) = p,ad(R). Therefore, Tp,ad = Tp,ad and the minima with the PFESs in Figure 18a (assumed to become approximately elliptic paraboloids) lie in the similar R coordinate. As such, the locus of PFES intersection, kn(R,Qt) = 0, is perpendicular to the Q axis and occurs for Q = Qt. Hence, eq five.64 reduces top rated,ad p,ad E (Q t) – E (Q t) = 2|Vkn|(five.65)(where the Condon Methenamine Bacterial approximation with respect to R was employed). Figure 23c is obtained in the solvent coordinate Q , for which the adiabatic reduced and upper curves are every single indistinguishable from a diabatic curve in a single PES basin. Within this case, Ek(R,Q ) and En(R,Q ) are the left and suitable prospective wells for protondx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical Testimonials motion, and Ep,ad(Q ) – E p,ad(Q ) Ep(Q ) – E p(Q ). Note that k n Ep,ad(Q) – Ep,ad(Q) is the energy distinction involving the electron-proton terms at each and every Q, such as the transition-state region, for electronically adiabatic ET (and hence also for PT, as discussed in section five.2), where the nonadiabatic coupling terms are negligible and thus only the reduce adiabatic surface in Figure 23, or the upper one particular following excitation, is at play. The diabatic electron-proton terms in Figure 23b have already been related, in the above evaluation, towards the proton vibrational levels within the electronic powerful possible for the nuclear motion of Figure 23a. Compared to the case of pure ET in Figure 19, the focus in Figure 23a is on the proton coordinate R after averaging over the (reactive) electronic degree of freedom. On the other hand, this parallelism can not be extended for the relation among the minimum adiabatic PES gap plus the level splitting. In truth, PT takes place in between the p,ad(R) and p,ad(R) proton k n vibrational states that are localized within the two wells of Figure 23a (i.e., the localized vibrational functions (I) and (II) inside the D A notation of Figure 22a), but they are not the proton states involved within the adiabatic electron-proton PESs of Figure 23b. The latter are, instead, p,ad, which is the vibrational component of the ground-state adiabatic electron-proton wave function ad(R,Q,q)p,ad(R) and is similar towards the lower-energy linear combination of p,ad and p,ad shown in Figure 22b, and p,ad, k n which can be the lowest vibrational function belonging to the upper adiabatic electronic wave function ad. Two electron-proton terms with all the very same electronic state, ad(R,Q,q) p1,ad(R) and ad(R,Q,q) p2,ad(R) (here, p is also the quantum quantity for the proton vibration; p1 and p2 are oscillator quantum numbers), may be exploited to represent nonadiabatic ET within the limit Vkn 0 (where eq five.63 is valid). ad In actual fact, in this limit, the.