To the electronically adiabatic surfaces in Figure 23b, their splitting at Qt just isn’t 520-33-2 site neglected, and eqs five.62a-5.62d are hence applied. The minimum splitting is Ep,ad(Qt) – E p,ad(Qt) + G p,ad(Qt) – G p,ad(Qt), 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 and the corresponding electron-proton power eigenvalue. G p,ad(Qt) – G p,ad(Qt) is zero for any model including that shown in Figure 24 with (R,Q). Hence, averaging Ead(R,Q) – 2R2/2 and Ead(R,Q) – 2R2/2 more than the respective proton wave 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 2 p,ad |p,ad (R )|2 + | (R )|2kn (R , Q t) + 4Vkn 2 dR(5.64)If pure ET occurs, p,ad(R) = p,ad(R). Thus, Tp,ad = Tp,ad and also the minima in the PFESs in Figure 18a (assumed to become approximately elliptic paraboloids) lie at the identical R coordinate. As such, the locus of PFES intersection, kn(R,Qt) = 0, is perpendicular to the Q axis and occurs for Q = Qt. Thus, eq five.64 reduces leading,ad p,ad E (Q t) – E (Q t) = two|Vkn|(five.65)(where the Condon approximation with respect to R was utilized). Figure 23c is obtained in the solvent coordinate Q , for which the adiabatic reduce and upper curves are every indistinguishable from a diabatic curve in a single PES basin. Within this case, Ek(R,Q ) and En(R,Q ) would be the left and proper potential wells for protondx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical Reviews motion, and Ep,ad(Q ) – E p,ad(Q ) Ep(Q ) – E p(Q ). Note that k n Ep,ad(Q) – Ep,ad(Q) could be the power difference amongst the electron-proton terms at every Q, which includes 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 therefore only the reduced adiabatic surface in Figure 23, or the upper a single following excitation, is at play. The diabatic electron-proton terms in Figure 23b have already been connected, inside the above evaluation, for the proton vibrational levels in the electronic successful possible for the nuclear motion of Figure 23a. When compared with the case of pure ET in Figure 19, the concentrate in Figure 23a is on the proton coordinate R soon after averaging over the (reactive) electronic degree of freedom. On the other hand, this parallelism cannot be extended for the relation involving the minimum adiabatic PES gap and the level splitting. In reality, PT takes spot amongst the p,ad(R) and p,ad(R) proton k n vibrational states which might be 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 these are not the proton states involved in the adiabatic electron-proton PESs of Figure 23b. The latter are, rather, p,ad, which is the vibrational element from the ground-state adiabatic electron-proton wave function ad(R,Q,q)p,ad(R) and is equivalent towards the lower-energy linear mixture of p,ad and p,ad shown in Figure 22b, and p,ad, k n that is the lowest vibrational function belonging to the upper adiabatic electronic wave function ad. Two electron-proton terms with all the same electronic state, ad(R,Q,q) p1,ad(R) and ad(R,Q,q) p2,ad(R) (right here, p can also be the quantum 475207-59-1 Autophagy quantity for the proton vibration; p1 and p2 are oscillator quantum numbers), is usually exploited to represent nonadiabatic ET inside the limit Vkn 0 (exactly where eq five.63 is valid). ad In fact, within this limit, the.