Dependence on the different proton localizations ahead of and following the transfer reaction. The initial and final PESs inside the DKL model are elliptic paraboloids inside the two-dimensional space from the proton coordinate in addition to a collective solvent coordinate (see Figure 18a). The reaction path on the PESs is interpreted inside the DKL assumption of negligible solvent frequency dispersion. Two assumptions simplify the computation of the PT price in the DKL model. The first is the Condon approximation,117,159 neglecting the dependence in the electronic couplings and overlap integrals on the nuclear coordinates.333 The coupling involving initial and final electronic states induced by VpB is computed at the R and Q values of maximum overlap integral for the slow subsystem (Rt and Qt). The second simplifying approximation is the fact that each the proton and solvent are described as harmonic oscillators, as a result allowing one to write the (standard mode) 23007-85-4 Technical Information factored nuclear wave functions asp solv A,B (R , Q ) = A,B (R ) A,B (Q )In eq 9.7, p is often a (dimensionless) measure of your coupling between the proton and the other degrees of freedom that is certainly accountable for the equilibrium distance R AB in between the proton donor and acceptor: mpp two p p = -2 ln(SIF) = RAB (9.8) two Right here, mp may be the proton mass. would be the solvent reorganization power for the PT method:= 0(Q k A – Q k B)k(9.9)exactly where Q kA and Q kB are the equilibrium generalized coordinates from the solvent for the initial and final states. Finally, E is definitely the energy difference among the minima of two PESs as in Figure 18a, with all the valueE = B(RB , Q B) + A (Q B) – A (RA , Q A ) – B(Q A ) + 0 Q k2B – two k(9.10)Q k2Ak(9.five)The PT matrix element is given byp,solv p solv WIF F 0|VpB|I 0 = VIFSIFSIF(9.6a)withVIF A (qA , Q t) B(qB , R t , Q t) VpB(qB , R t) A (qA , R t , Q t) B(qB , Q t)dqA dqBp SIF(9.6b) (9.6c) (9.6d)Bp(R) Ap (R)dR Bsolv(Q ) Asolv (Q )dQsolv SIFThe rate of PT is obtained by statistical averaging more than initial (reactant) states in the method and summing more than final (item) states. The factored type with the proton coupling in eqs 9.6a-9.6d results in substantial simplification in deriving the price from eq 9.3 because the summations more than the proton and solvent vibrational states can be carried out separately. At room temperature, p kBT, so the quantum nature on the transferring proton cannot be neglected regardless of approximation i.334 The fact that 0 kBT (high-temperature limit with respect towards the solvent), collectively using the vibrational modeHere, B(R B,Q B) plus a(Q B) would be the energies with the solvated molecule BH and ion A-, respectively, in the final equilibrium geometry from the proton and solvent, plus a(R A,Q A) and B(Q A) are the respective quantities for AH and B-. The power quantities subtracted in eq 9.ten are introduced in refs 179 and 180 as potential energies, which appear inside the Schrodinger equations of the DKL remedy.179 They may be interpreted as successful possible energies that involve entropic contributions, and therefore as cost-free energies. This interpretation has been used consistently using the Schrodinger equation formalism in elegant and much more basic approaches of Newton and co-workers (inside the context of ET)336 and of Hammes-Schiffer and co-workers (inside the context of PCET; see Felypressin Purity section 12).214,337 In these approaches, the no cost energy surfaces which can be involved in ET and PCET are obtained as expectation values of an efficient Hamiltonian (see eq 12.11). Returning to the analysis in the DKL remedy, a different.