In]; R , X ) = [Pin] +n([P ]; inR , X)(12.10)(n =

In]; R , X ) = [Pin] +n([P ]; inR , X)(12.10)(n = Ia, Ib, Fa, Fb)Figure 47. Schematic representation from the system and its interactions in the SHS theory of PCET. De (Dp) and Ae (Ap) are the electron (proton) donor and acceptor, respectively. Qe and Qp are the solvent collective coordinates linked with ET and PT, respectively. denotes the overall set of solvent degrees of freedom. The power terms in eqs 12.7 and 12.8 plus the nonadiabatic coupling matrices d(ep) and G(ep) of eq 12.21 are depicted. The interactions between cis-ACPD manufacturer solute and solvent components are denoted utilizing double-headed arrows.where would be the self-energy of Pin(r) and n includes the solute-solvent interaction along with the energy in the gas-phase solute. Gn defines a PFES for the nuclear motion. Gn can also be written when it comes to Qp and Qe.214,428 Offered the solute electronic state |n, Gn is214,Gn(Q p , Q e , R , X ) = |Hcont(Q p , Q e , R , X )| n n (n = Ia, Ib, Fa, Fb)(12.11)where, inside a solvent continuum model, the VB matrix yielding the cost-free energy isHcont(R , X , Q p , Q e) = (R , Q p , Q e)I + H 0(R , X ) 0 0 + 0 0 0 0 Qp 0 0 0 Qe 0 0 Q p + Q e 0and interactions in the PCET reaction system are depicted in Figure 47. An Mivacurium (dichloride) site efficient Hamiltonian for the method is often written asHtot = TR + TX + T + Hel(R , X , )(12.7)exactly where will be the set of solvent degrees of freedom, plus the electronic Hamiltonian, which depends parametrically on all nuclear coordinates, is given byHel = Hgp(R , X ) + V(R , X ) + Vss + Vs(R , X , )(12.eight)(12.12)In these equations, T Q denotes the kinetic energy operator for the Q = R, X, coordinate, Hgp would be the gas-phase electronic Hamiltonian from the solute, V describes the interaction of solute and solvent electronic degrees of freedom (qs in Figure 47; the BO adiabatic approximation is adopted for such electrons), Vss describes the solvent-solvent interactions, and Vs accounts for all interactions from the solute with the solvent inertial degrees of freedom. Vs contains electrostatic and shortrange interactions, but the latter are neglected when a dielectric continuum model of your solvent is utilized. The terms involved inside the Hamiltonian of eqs 12.7 and 12.eight is often evaluated by using either a dielectric continuum or an explicit solvent model. In both instances, the gas-phase solute power plus the interaction of your solute with the electronic polarization of the solvent are offered, inside the four-state VB basis, by the 4 four matrix H0(R,X) with matrix elements(H 0)ij = i|Hgp + V|j (i , j = Ia, Ib, Fa, Fb)(12.9)Note that the time scale separation involving the qs (solvent electrons) and q (reactive electron) motions implies that the solvent “electronic polarization field is generally in equilibrium with point-like solute electrons”.214 In other words, the wave function for the solvent electrons features a parametric dependence around the q coordinate, as established by the BO separation of qs and q. Furthermore, by utilizing a strict BO adiabatic approximation114 (see section five.1) for qs with respect to the nuclear coordinates, the qs wave function is independent of Pin(r). Ultimately, this implies the independence of V on Qpand the adiabatic totally free power surfaces are obtained by diagonalizing Hcont. In eq 12.12, I is the identity matrix. The function is the self-energy in the solvent inertial polarization field as a function on the solvent reaction coordinates expressed in eqs 12.3a and 12.3b. The initial solute-inertial polarization interaction (cost-free) energy is contained in . In actual fact,.