Variational approximations to time-dependent Hartree-Fock theory

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Abstract
A product ansatz for the first-order perturbed Fock-Dirac one-matrix is employed to investigate coupled and uncoupled variational approximations to time-dependent Hartree-Fock theory. Simple differential equations are obtained in each case for a single pair of variational functions which describe completely the response of an N-electron system to external radiation, obviating the customarily required 2N first-order Hartree-Fock spin-orbitals. Connections with previously described variational approximations for studying the interactions of radiation and matter are discussed and clarified and the frequency-dependent dipole polarizabilities of some simple atomic systems are computed to illustrate the approximations considered. Accurate results are obtained for the polarizabilities and their associated resonance frequencies from the fully coupled method and from the simpler of the uncoupled approximations. The latter approximation, which is closely related to an earlier approach of Pople and Schofield in the static case, entails no self-consistency requirement or two-electron integral computations and can provide a highly convenient theoretical technique for investigating the optical properties of atoms and molecules.