Nd doubleadiabatic approximations are distinguished. This treatment begins by thinking about the frequencies in the

Nd doubleadiabatic approximations are distinguished. This treatment begins by thinking about the frequencies in the system: 0 describes the motion from the medium dipoles, p describes the frequency with the bound reactive proton inside the initial and final states, and e will be the frequency of electron motion within the reacting ions of eq 9.1. Around the basis from the relative order of magnitudes of those frequencies, that’s, 0 1011 s-1 p 1014 s-1 e 1015 s-1, two doable adiabatic separation schemes are considered within the DKL model: (i) The electron subsystem is separated from the slow subsystem composed from the (reactive) proton and solvent. This is the normal adiabatic approximation from the BO scheme. (ii) Apart from the regular adiabatic approximation, the transferring proton also responds instantaneously towards the solvent, plus a second adiabatic approximation is applied for the proton dynamics. In each approximations, the fluctuations with the 935666-88-9 Description solvent polarization are required to surmount the activation barrier. The interaction in the proton with all the anion (see eq 9.two) could be the other factor that determines the transition probability. This interaction appears as a perturbation inside the Hamiltonian with the method, that is written inside the two equivalent types(qA , qB , R , Q ) = =0 F(qA , 0 I (qA ,qB , R , Q ) + VpB(qB , R )(9.two)qB , R , Q ) + VpA(qA , R )by using the unperturbed (channel) Hamiltonians 0 and 0 F I for the method in the initial and final states, respectively. qA and qB are the electron coordinates for ions A- and B-, respectively, R may be the proton coordinate, Q is a set of solvent normal coordinates, and also the perturbation terms VpB and VpA would be the energies from the proton-anion interactions in the two proton states. 0 contains the Hamiltonian from the solvent subsystem, I also as the energies on the AH molecule and also the B- ion inside the solvent. 0 is defined similarly for the merchandise. Within the reaction F of eq 9.1, VpB determines the proton jump once the program is near the transition coordinate. Actually, Fermi’s golden rule provides a transition probability density per unit timeIF2 | 0 |VpB| 0|two F F I(9.3)where and are unperturbed wave functions for the initial and final states, which Acid-PEG2-SS-PEG2-acid site belong to the same power eigenvalue, and F could be the final density of states, equal to 1/(0) in the model. The price of PT is obtained by statistical averaging more than initial (reactant) states on the system and summing over finaldx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-0 I0 FChemical Evaluations (item) states. Equation 9.3 indicates that the differences among models i and ii arise in the tactics utilised to create the wave functions, which reflect the two distinctive levels of approximation for the physical description of the method. Making use of the typical adiabatic approximation, 0 and 0 inside the DKL I F model are written as0(qA , I 0 (qA , F qB , R , Q ) = A (qA , R , Q ) B(qB , Q ) A (R , Q )(9.4a)Reviewseparation of eqs 9.6a-9.6d, validates the classical limit for the solvent degrees of freedom and leads to the rate180,k= VIFexp( -p) kBT p exp – (|n| + n) |n|! 2kBT| pn|n =-qB , R , Q ) = A (qA , Q ) B(qB , R , Q ) B (R , Q )(9.4b)( + E – n )two p exp – 4kBT(9.7)where A(qA,R,Q)B(qB,Q) and also a(qA,Q)B(qB,R,Q) are the electronic wave functions for the reactants and merchandise, respectively, and also a (B) is the wave function for the slow proton-solvent subsystem in the initial and final states, respectively. The notation for the vibrational functions emphasizes179,180 the.