Self-consistent time-dependent Hartree-Fock scheme

We have derived a self-consistent time-dependent Hartree-Fock scheme based on a Green's function approach. The contour integral is performed analytically, which makes the computational effort per iteration comparable with a normal time-dependent Hartree-Fock calculation. The excitation energies are found as poles for the polarization propagator in the energy representation. The corresponding residues determine the transition moments. Comparison is made with other similar random-phase approximations. We have applied our scheme to the π-electron systems of trans-butadiene, pyridine, and benzene. The triplet spectra of those molecules especially are considerably improved over normal time-dependent Hartree-Fock results.