Polarization response of a dielectric continuum to a motion of charge

In cases where dielectric relaxation dominates the time scale of molecular processes which involve the motion of charge (e.g., solvation dynamics, electron transfer reactions, or chemical reactions), the relevant time scale is the longitudinal relaxation time τ_L, which is generally faster than the dielectric relaxation time τ_D. Numerical calculations of the polarizations P_D(t) with dE(t)/dt = 0 and P_E(t) with dD(t)/dt = 0 for an electrical RC network equivalent to an arbitrary dielectric function ε*(ω) are performed in order to generalize the relation between τ_L and τ_D which only for the Debye case reads τ_L = τ_Dε_∞/ε_s. The results for non-Debye systems as a function of relaxation time dispersion and relaxation strength are that 〈τ_L〉 ≪ 〈τ_D〉ε_∞/ε_s whereas the decay profiles for P_D(t) and P_E(t) are similar. The normalized field decay P_E(t) represents a continuum model prediction for the Stokes shift correlation function C(t) observed in solvation dynamics experiments.