Current-Density Functional Theory of Linear Response to Time-Dependent Electromagnetic Fields

Abstract

Local density approximations are known to be very useful in calculating the ground-state exchange and correlation (xc) energy of many-electron systems [1], and local approximations are gaining in importance for the description of xc effects in time-dependent situations also [2,3]. Most of the time-dependent work has dealt with a scalar time-dependent xc potential ${v_{xc}}(\vec r,\omega )$ approximated as a local functional of the time-dependent density $n(\vec r,\omega )$ as described in the chapter “Time-dependent density functional theory” in the introductory section of this Book. Despite much progress in this scalar approach, it will be shown in this Chapter that existing approximations for v _xc require modification. In particular, it will be shown that (i) there is no local density approximation for the scalar xc potential at finite frequency (ii) there is, however, a consistent local approximation for a vector xc potential ${{\vec a}_{xc}}(\vec r,\omega )$ in terms of the dynamic current density $\vec j(\vec r,\omega )$ and its space derivatives, as well as the ground-state density and its space derivatives. This approximation is valid, at a given frequency, for sufficiently slow spatial variations of the ground-state density and of the perturbing dynamic potential. The appropriately modified vector xc potential will be derived here in some detail, thus filling out the brief description published recently [4]. New material will also be presented, providing interpretation of the findings in the simple case of one dimensional inhomogeneity.