To the electronically adiabatic surfaces in Figure 23b, their splitting at Qt is just not neglected, and eqs 5.62a-5.62d are hence used. The 486460-32-6 Formula 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 along with the corresponding electron-proton energy eigenvalue. G p,ad(Qt) – G p,ad(Qt) is zero to get a model like 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 two p,ad |p,ad (R )|2 + | (R )|2kn (R , Q t) + 4Vkn two dR(5.64)If pure ET occurs, p,ad(R) = p,ad(R). Hence, Tp,ad = Tp,ad plus the minima of your PFESs in Figure 18a (assumed to be around elliptic paraboloids) lie at the very same R coordinate. As such, the locus of PFES intersection, kn(R,Qt) = 0, is perpendicular to the Q axis and happens for Q = Qt. As a result, eq 5.64 reduces best,ad p,ad E (Q t) – E (Q t) = 2|Vkn|(five.65)(exactly where the Condon approximation with respect to R was applied). Figure 23c is obtained in the solvent coordinate Q , for which the adiabatic decrease and upper curves are every indistinguishable from a diabatic curve in 1 PES basin. In this case, Ek(R,Q ) and En(R,Q ) are the left and appropriate potential wells for protondx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-Chemical Evaluations 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 distinction between the electron-proton terms at each and every Q, Petunidin (chloride) FAK including the transition-state area, for electronically adiabatic ET (and therefore also for PT, as discussed in section five.two), exactly where the nonadiabatic coupling terms are negligible and hence only the decrease adiabatic surface in Figure 23, or the upper one following excitation, is at play. The diabatic electron-proton terms in Figure 23b have already been connected, within the above analysis, for the proton vibrational levels in the electronic successful prospective for the nuclear motion of Figure 23a. In comparison to the case of pure ET in Figure 19, the concentrate in Figure 23a is on the proton coordinate R right after averaging more than the (reactive) electronic degree of freedom. On the other hand, this parallelism can not be extended towards the relation involving the minimum adiabatic PES gap plus the level splitting. Actually, PT requires place in between the p,ad(R) and p,ad(R) proton k n vibrational states which are localized within the two wells of Figure 23a (i.e., the localized vibrational functions (I) and (II) within the D A notation of Figure 22a), but they are not the proton states involved in the adiabatic electron-proton PESs of Figure 23b. The latter are, rather, p,ad, that is the vibrational element on the 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 is the lowest vibrational function belonging towards the upper adiabatic electronic wave function ad. Two electron-proton terms using the exact 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 number for the proton vibration; p1 and p2 are oscillator quantum numbers), is usually exploited to represent nonadiabatic ET in the limit Vkn 0 (exactly where eq five.63 is valid). ad In truth, in this limit, the.