Ted during the PCET reaction. BO separation from the q coordinate is then utilised to

Ted during the PCET reaction. BO separation from the q coordinate is then utilised to obtain the initial and final electronic states (from which the electronic coupling VIF is obtained) as well as the corresponding energy levels as functions on the nuclear coordinates, that are the diabatic PESs VI(R,Q) and VF(R,Q) for the nuclear motion. VI and VF are used to construct the model Hamiltonian inside the diabatic representation:two gQ 1 two 2 PQ + Q Q – 2 z = VIFx + 2 QThe first (double-adiabatic) method described in this section is associated towards the 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 is also 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 constant might be given exactly the same formal expression because the ET price continuous for an electron coupled to two harmonic nuclear modes. In the coupled ET-PT reaction, the internal nuclear coordinate (i.e., the proton) experiences a double-well potential (e.g., in hydrogen-bonded interfaces). Thus, the energies and wave functions of the transferring proton differ from those of a harmonic nuclear mode. Inside the diabatic representation acceptable for proton levels drastically beneath the top with the proton tunneling barrier, harmonic wave functions can be used to describe the localized proton vibrations in each potential nicely. However, proton wave functions with diverse peak positions appear in the 29700-22-9 custom synthesis quantitative description of the reaction rate constant. Moreover, linear combinations of such wave functions are needed to describe proton states of power near the leading of your tunnel barrier. But, if the use on the proton state in constructing the PCET price follows the same formalism because the use of the internal harmonic mode in constructing the ET price, the PCET and ET prices have the exact same formal dependence on the electronic and nuclear modes. In this case, the two rates differ only within the physical which means and quantitative values from the cost-free energies and nuclear wave function overlaps incorporated inside the prices, considering the fact that these physical parameters correspond to ET in 1 case and to ET-PT inside the other case. This observation is in the heart of Cukier’s strategy and matches, in spirit, our “ET interpretation” of the DKL price continuous determined by the generic character from the DKL reactant and item states (inside the original DKL model, PT or HAT is studied, and as a result, the initial and final-HI(R ) 0 G z + two HF(R )(11.5)The quantities that refer towards the single collective solvent mode involved are defined in eq 11.1 with j = Q. In contrast towards the Hamiltonian of eq 11.1, the Condon approximation is employed for the electronic coupling. Within 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 in between the electron and proton dynamics, since the PES for the proton motion depends on the electronic state in these Hamiltonians. The combination of solvent-proton, solvent-electron, and electron-proton couplings embodied in eq 11.5 enables a a lot more intimate connection to be established involving ET and PT than the Hamiltonian model of eq 11.1. In the latter, (i) the exact same double-well possible Vp(R) co.