To the electronically adiabatic surfaces in Figure 23b, their splitting at Qt will not be neglected, and eqs 5.62a-5.62d are therefore utilised. The minimum splitting is Ep,ad(Qt) – E p,ad(Qt) + G p,ad(Qt) – G p,ad(Qt), 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 which include 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)|two – |p,ad (R)|two ]+ Ek (R , Q t) + En(R , Q t)dR 2 p,ad |p,ad (R )|two + | (R )|2kn (R , Q t) + 4Vkn two dR(five.64)If pure ET happens, p,ad(R) = p,ad(R). As a result, Tp,ad = Tp,ad plus the minima from the PFESs in Figure 18a (assumed to become roughly elliptic paraboloids) lie at the same R coordinate. As such, the locus of PFES intersection, kn(R,Qt) = 0, is perpendicular for the Q axis and occurs for Q = Qt. Thus, eq five.64 reduces top,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 at the solvent coordinate Q , for which the adiabatic decrease 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 ideal possible 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) will be the energy distinction involving the electron-proton terms at every Q, including the transition-state area, for electronically adiabatic ET (and therefore also for PT, as 832115-62-5 In stock discussed in section 5.two), 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 happen to be associated, inside the above evaluation, for the proton vibrational levels within the electronic powerful potential for the 64485-93-4 MedChemExpress 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 right after averaging over the (reactive) electronic degree of freedom. Nevertheless, this parallelism cannot be extended to the relation in between the minimum adiabatic PES gap and the level splitting. In actual fact, PT takes location involving the p,ad(R) and p,ad(R) proton k n vibrational states that happen to be localized in 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, as an alternative, p,ad, which can be the vibrational element in the ground-state adiabatic electron-proton wave function ad(R,Q,q)p,ad(R) and is similar to 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 to the upper adiabatic electronic wave function ad. Two electron-proton terms using 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 number for the proton vibration; p1 and p2 are oscillator quantum numbers), is often exploited to represent nonadiabatic ET in the limit Vkn 0 (exactly where eq five.63 is valid). ad Actually, within this limit, the.