Driven electron transfer in an environment with slow and fast degrees of freedom.

Abstract

Driven electron transfer in a polar medium with slow and fast degrees of freedom is studied in the framework of a spin-boson Hamiltonian. Evolution dynamics is rigorously found when omega(s)(c)/(Gamma(a))sqrt[E(rs)/kT]<<1, where omega(s)(c) is the Debye cutoff frequency in the spectral function for the slow modes, E(rs) is the reorganization energy of slow degrees of freedom, and Gamma(-1)(a) is the reaction time dependent on the laser intensity parameter a=muE(0)/Planck's over 2piomega. Here omega and E0 are the frequency and the amplitude of a cw electric field, and mu is the electron dipole moment difference between the initial and final states. The master equation is derived for an arbitrary driving force affecting both the transition matrix element and the potential energy. For a cw electric field, the time dependent probability of staying at the product state, P1(t), is shown to be strongly dependent on the field intensity parameter a: P1(a,t) approximately (Gamma(m(1),m(2))t)(-E(rf)/E(rs)) or P1(a,t) approximately (Gamma(m(0))t)(-E(rf)/E(rs)), double or single resonances, respectively. Here E(rf) is the reorganization energy of fast degrees of freedom, Gamma(m(1),m(2)) approximately J(2)(m(1))(a)+J(2)(m(2))(a), and Gamma(m(0)) approximately J(2)(m(0))(a), where J(a) is a Bessel function. By changing the parameter a, one is able to manipulate the rate and direction of the reaction. When J(2)(m(0))(a) is close to zero the reaction is slow. Hence, slow modes turn out to be fast. This changes the character of the evolution dynamics from non- to mono- exponential decay, respectively. For the double resonance, the equilibrium constant is studied with the field intensity. It is shown that the reaction is almost insensitive to temperature. However, it strongly depends on the reaction heat, which provides a condition for the resonance.