Ted during the PCET reaction. BO separation on the q coordinate is then made use

Ted during the PCET reaction. BO separation on the q coordinate is then made use of to get the initial and final electronic states (from which the electronic coupling VIF is obtained) along with the corresponding energy levels as functions from the nuclear coordinates, which are the diabatic PESs VI(R,Q) and VF(R,Q) for the nuclear motion. VI and VF are utilised to construct the model Hamiltonian within the diabatic representation:two gQ 1 two two PQ + Q Q – 2 z = VIFx + 2 QThe initial (double-adiabatic) strategy described in this section is related towards the 97657-92-6 web extended Marcus theory of PT and HAT, reviewed in section six, since the transferring proton’s coordinate is treated as an inner-sphere solute mode. The method can also be associated to the DKL model interpreted as an EPT model (see section 9). In Cukier’s PCET model, the reactive electron is coupled to a classical solvent polarization mode and to a quantum internal coordinate describing the reactive proton. Cukier noted that the PCET price 6451-73-6 Description continual could be provided precisely the same formal expression as the ET price continual for an electron coupled to two harmonic nuclear modes. Within the coupled ET-PT reaction, the internal nuclear coordinate (i.e., the proton) experiences a double-well possible (e.g., in hydrogen-bonded interfaces). Therefore, the energies and wave functions of the transferring proton differ from these of a harmonic nuclear mode. In the diabatic representation suitable for proton levels substantially below the prime from the proton tunneling barrier, harmonic wave functions could be made use of to describe the localized proton vibrations in each and every possible nicely. On the other hand, proton wave functions with unique peak positions appear within the quantitative description of the reaction rate constant. Furthermore, linear combinations of such wave functions are required to describe proton states of power near the top from the tunnel barrier. However, when the use of your proton state in constructing the PCET rate follows precisely the same formalism as the use in the internal harmonic mode in constructing the ET rate, the PCET and ET rates possess the similar formal dependence around the electronic and nuclear modes. Within this case, the two prices differ only within the physical which means and quantitative values on the totally free energies and nuclear wave function overlaps integrated within the prices, considering the fact that these physical parameters correspond to ET in one particular case and to ET-PT inside the other case. This observation is at the heart of Cukier’s method and matches, in spirit, our “ET interpretation” in the DKL rate continual determined by the generic character of the DKL reactant and solution states (inside the original DKL model, PT or HAT is studied, and thus, the initial and final-HI(R ) 0 G z + 2 HF(R )(11.five)The quantities that refer for the single collective solvent mode involved are defined in eq 11.1 with j = Q. In contrast for the Hamiltonian of eq 11.1, the Condon approximation is employed for the electronic coupling. Inside the Hamiltonian model of eq 11.5 the solvent mode is coupled to both the q and R coordinates. The Hamiltonians HI(R) = T R + V I(R) and HF(R) = T R + I F V F(R) express direct coupling involving the electron and proton dynamics, since the PES for the proton motion will depend on the electronic state in these Hamiltonians. The mixture of solvent-proton, solvent-electron, and electron-proton couplings embodied in eq 11.five allows a additional intimate connection to become established amongst ET and PT than the Hamiltonian model of eq 11.1. In the latter, (i) the same double-well possible Vp(R) co.