To the electronically adiabatic surfaces in Figure 23b, their splitting at Qt is not neglected, and eqs five.62a-5.62d are thus 1187856-49-0 References utilised. 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 and also the corresponding electron-proton power eigenvalue. G p,ad(Qt) – G p,ad(Qt) is zero for a model for example that shown in Figure 24 with (R,Q). Hence, averaging Ead(R,Q) – 2R2/2 and Ead(R,Q) – 2R2/2 over 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 happens, p,ad(R) = p,ad(R). As a result, Tp,ad = Tp,ad plus the minima of your PFESs in Figure 18a (assumed to be roughly elliptic paraboloids) lie in the very same R coordinate. As such, the locus of PFES intersection, kn(R,Qt) = 0, is perpendicular Alpha-Ketoglutaric acid (sodium) salt site towards the Q axis and happens for Q = Qt. Hence, eq five.64 reduces major,ad p,ad E (Q t) – E (Q t) = 2|Vkn|(five.65)(where the Condon approximation with respect to R was utilised). Figure 23c is obtained at the solvent coordinate Q , for which the adiabatic lower and upper curves are every single indistinguishable from a diabatic curve in one particular PES basin. In this case, Ek(R,Q ) and En(R,Q ) will be the left and ideal 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 energy distinction among the electron-proton terms at every Q, including the transition-state region, for electronically adiabatic ET (and therefore also for PT, as discussed in section 5.two), where the nonadiabatic coupling terms are negligible and as a result 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 been connected, in the above evaluation, towards the proton vibrational levels in the electronic efficient possible for the nuclear motion of Figure 23a. In comparison to the case of pure ET in Figure 19, the concentrate in Figure 23a is around the proton coordinate R after averaging over the (reactive) electronic degree of freedom. Nevertheless, this parallelism can’t be extended for the relation involving the minimum adiabatic PES gap and also the level splitting. In reality, PT takes place among 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) in 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, instead, p,ad, which is the vibrational element of your ground-state adiabatic electron-proton wave function ad(R,Q,q)p,ad(R) and is similar towards the lower-energy linear mixture 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 the same electronic state, ad(R,Q,q) p1,ad(R) and ad(R,Q,q) p2,ad(R) (right here, p is also the quantum quantity for the proton vibration; p1 and p2 are oscillator quantum numbers), might be exploited to represent nonadiabatic ET within the limit Vkn 0 (where eq five.63 is valid). ad Actually, in this limit, the.