Exact exchange kernel for time-dependent density-functional theory

An exact expression for the exchange kernel of time-dependent density-functional theory, the frequency-dependent functional derivative of the exchange potential with respect to the density, is derived. The expression is simple enough to be applied in practice. A simple and transparent derivation of the coupled Kohn-Sham equation of time-dependent density-functional theory is given. Modified coupled Kohn-Sham equations are presented that are especially well suited for an "exact-exchange" treatment of excitation energies, polarizabilities, and other linear response properties. (C) 1998 John Wiley & Sons, Inc.