Determination of frequency-dependent polarizabilities using current density-functional theory

A time-dependent generalization of current density-functional theory in the form introduced by by Vignale, Rasolt and Geldart [Adv. Quantum Chem. 21, 235 (1990)] is used. This theory is then applied to the case where an external harmonic electric field is present, and the changes are considered by perturbation theory. Finally, expressions for the frequency-dependent polarizabilities are derived in terms of the so-called electric and magnetic hessians. The theory is contrasted with time-dependent coupled Hartree-Fock theory; this demonstrates how the theory can he implemented.