For the electronically adiabatic surfaces in Figure 23b, their splitting at Qt is not neglected, and eqs five.62a-5.62d are therefore 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 1260533-36-5 manufacturer electronic state and the corresponding electron-proton power eigenvalue. G p,ad(Qt) – G p,ad(Qt) is zero for any model like that shown in Figure 24 with (R,Q). As a result, 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)|2 ]+ Ek (R , Q t) + En(R , Q t)dR two p,ad |p,ad (R )|2 + | (R )|2kn (R , Q t) + 4Vkn two dR(five.64)If pure ET occurs, p,ad(R) = p,ad(R). Thus, Tp,ad = Tp,ad as well as the minima of the PFESs in Figure 18a (assumed to be about elliptic paraboloids) lie at the similar R coordinate. As such, the locus of PFES intersection, kn(R,Qt) = 0, is 405060-95-9 In Vivo perpendicular to the Q axis and happens for Q = Qt. Thus, eq five.64 reduces leading,ad p,ad E (Q t) – E (Q t) = two|Vkn|(5.65)(where the Condon approximation with respect to R was utilized). Figure 23c is obtained at the solvent coordinate Q , for which the adiabatic reduce and upper curves are each and every indistinguishable from a diabatic curve in one particular PES basin. In this case, Ek(R,Q ) and En(R,Q ) are the left and correct possible 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 definitely the energy difference between the electron-proton terms at every Q, which includes the transition-state area, for electronically adiabatic ET (and therefore also for PT, as discussed in section 5.2), where the nonadiabatic coupling terms are negligible and thus only the lower 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, within the above evaluation, for the proton vibrational levels in the electronic effective potential for the nuclear motion of Figure 23a. When compared with the case of pure ET in Figure 19, the focus in Figure 23a is around the proton coordinate R soon after averaging more than the (reactive) electronic degree of freedom. However, this parallelism can not be extended towards the relation between the minimum adiabatic PES gap plus the level splitting. Actually, PT takes place between the p,ad(R) and p,ad(R) proton k n vibrational states that happen to be localized inside 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 inside the adiabatic electron-proton PESs of Figure 23b. The latter are, rather, p,ad, which can be the vibrational component with 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 is the lowest vibrational function belonging for 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 is also the quantum quantity for the proton vibration; p1 and p2 are oscillator quantum numbers), is often exploited to represent nonadiabatic ET within the limit Vkn 0 (exactly where eq 5.63 is valid). ad Actually, within this limit, the.