Iently smaller Vkn, a single can use the piecewise approximation(Ek En) k ad kn (Ek En) nEp,ad(Q)(5.63)and eq 5.42 is valid inside each and every diabatic power range. Equation five.63 supplies a very simple, constant conversion among the diabatic and adiabatic photographs of ET in the Unoprostone Formula nonadiabatic limit, where the smaller electronic couplings involving the diabatic electronic states trigger decoupling with the different states with the proton-solvent subsystem in eq 5.40 and on the Q mode in eq 5.41a. Even so, when modest Vkn values represent a sufficient situation for vibronically nonadiabatic behavior (i.e., ultimately, VknSp kBT), the smaller overlap between reactant and kn product 474922-26-4 In stock proton vibrational wave functions is often the cause of this behavior within the time evolution of eq five.41.215 In fact, the p distance dependence of the vibronic couplings VknSkn is p 197,225 determined by the overlaps Skn. Detailed discussion of analytical and computational approaches to acquire mixed electron/proton vibrational adiabatic states is identified within the literature.214,226,227 Here we note that the dimensional reduction from the R,Q for the Q conformational space in going from eq 5.40 to eq 5.41 (or from eq five.59 to eq five.62) will not imply a double-adiabatic approximation or the choice of a reaction path inside the R, Q plane. The truth is, the above process treats R and Q on an equal footing as much as the solution of eq five.59 (for instance, e.g., in eq five.61). Then, eq five.62 arises from averaging eq five.59 more than the proton quantum state (i.e., overall, more than the electron-proton state for which eq 5.40 expresses the rate of population transform), in order that only the solvent degree of freedom remains described in terms of a probability density. Having said that, when this averaging does not mean application of your double-adiabatic approximation inside the common context of eqs five.40 and 5.41, it leads to the identical resultwhere the separation of the R and Q variables is allowed by the harmonic and Condon approximations (see, e.g., section 9 and ref 180), as in eqs 5.59-5.62. Inside the typical adiabatic approximation, the effective prospective En(R,Q) in eq five.40 or Ead(R,Q) + Gad (R,Q) in eq five.59 provides the effective possible energy for the proton motion (along the R axis) at any offered solvent conformation Q, as exemplified in Figure 23a. Comparing parts a and b of Figure 23 offers a hyperlink involving the behavior of your method around the diabatic crossing of Figure 23b as well as the overlap of the localized reactant and item proton vibrational states, since the latter is determined by the dominant selection of distances between the proton donor and acceptor allowed by the powerful prospective in Figure 23a (let us note that Figure 23a can be a profile of a PES landscape like that in Figure 18, orthogonal to the Q axis). This comparison is similar in spirit to that in Figure 19 for ET,7 but it also presents some essential variations that merit additional discussion. Inside the diabatic representation or the diabatic approximation of eq 5.63, the electron-proton terms in Figure 23b cross at Q = Qt, where the prospective energy for the motion of the solvent is E p(Qt) and the localization of the reactive subsystem within the kth n or nth potential effectively of Figure 23a corresponds to the exact same energy. In reality, the potential energy of every effectively is given by the average electronic power Ej(R,Qt) = j(R,Qt)|V(R ,Qt,q) + T q| j(R,Qt) (j = k, n), along with the proton vibrational energies in both wells are p|Ej(R,Qt)|p + Tp = E p(Qt). j j j j In reference.