Exact exchange in linear-response theory

An exact formalism for excitation energies of any interacting N-electron sy stem has recently been derived from the linear-response limit of time-depen dent Kohn-Sham theory. A response kernel is determined in this theory by th e functional derivative of the ground-state Kohn-Sham potential function wi th respect to electron density. It is shown here that the exchange part of this response kernel is a linear operator determined exactly by the underly ing second-quantized Hamiltonian:If correlation response is neglected, the theory reduces to the random-phase approximation including exchange. This f ormalism justifies methods that combine this exact exchange kernel with den sity-functional approximations to the correlation kernel. [S1050-2947(99)50 111-X].