# Exact exchange in linear-response theory

## Abstract

An exact formalism for excitation energies of any interacting N-electron system has recently been derived from the linear-response limit of time-dependent Kohn-Sham theory. A response kernel is determined in this theory by the functional derivative of the ground-state Kohn-Sham potential function with respect to electron density. It is shown here that the exchange part of this response kernel is a linear operator determined exactly by the underlying second-quantized Hamiltonian. If correlation response is neglected, the theory reduces to the random-phase approximation including exchange. This formalism justifies methods that combine this exact exchange kernel with density-functional approximations to the correlation kernel. © 1999 The American Physical Society.