Nd doubleadiabatic 54-28-4 Biological Activity approximations are distinguished. This treatment starts by thinking about the frequencies in the method: 0 describes the motion in the medium dipoles, p describes the frequency on the bound reactive proton in the initial and final states, and e is the frequency of electron motion in the reacting ions of eq 9.1. Around the basis in the relative order of magnitudes of these frequencies, which is, 0 1011 s-1 p 1014 s-1 e 1015 s-1, two achievable adiabatic separation schemes are regarded within the DKL model: (i) The electron subsystem is separated in the slow subsystem composed in the (reactive) proton and solvent. That is the common adiabatic SI-2 medchemexpress approximation on the BO scheme. (ii) Aside from the common adiabatic approximation, the transferring proton also responds instantaneously towards the solvent, as well as a second adiabatic approximation is applied for the proton dynamics. In each approximations, the fluctuations of your solvent polarization are necessary to surmount the activation barrier. The interaction on the proton using the anion (see eq 9.2) would be the other issue that determines the transition probability. This interaction appears as a perturbation within the Hamiltonian of the method, which is written in 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 inside the initial and final states, respectively. qA and qB will be the electron coordinates for ions A- and B-, respectively, R is the proton coordinate, Q can be a set of solvent normal coordinates, and the perturbation terms VpB and VpA are the energies from the proton-anion interactions in the two proton states. 0 involves the Hamiltonian of the solvent subsystem, I as well as the energies in the AH molecule and also the B- ion inside the solvent. 0 is defined similarly for the products. Within the reaction F of eq 9.1, VpB determines the proton jump after the method is near the transition coordinate. In actual fact, Fermi’s golden rule provides a transition probability density per unit timeIF2 | 0 |VpB| 0|two F F I(9.three)exactly where and are unperturbed wave functions for the initial and final states, which belong for the identical energy eigenvalue, and F would be the final density of states, equal to 1/(0) in the model. The rate of PT is obtained by statistical averaging over initial (reactant) states with the technique and summing more than finaldx.doi.org/10.1021/cr4006654 | Chem. Rev. 2014, 114, 3381-0 I0 FChemical Evaluations (product) states. Equation 9.3 indicates that the differences involving models i and ii arise in the approaches used to create the wave functions, which reflect the two unique levels of approximation for the physical description from the program. Applying the normal adiabatic approximation, 0 and 0 within 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 results in 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 )2 p exp – 4kBT(9.7)where A(qA,R,Q)B(qB,Q) and also a(qA,Q)B(qB,R,Q) would be the electronic wave functions for the reactants and merchandise, respectively, plus a (B) would be 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.
