Time-Dependent Density Functional Theory of Polarization Relaxation under External Field

A new inhomogeneous time-dependent density functional theory is proposed to study an effect of external field on the polarization relaxation of molecular liquids. The effect of external field is considered by the number density of solvent molecules, and the homogeneous approximation introduced by many previous studies is not employed. To demonstrate the validity of the theory, the spatial distribution of the relaxation time is calculated in a polar solvent system with an ion. The calculated results show a notable effect of translational diffusion on the spatial distribution of the polarization relaxation time.