Time-dependent Hartree-Fock theory

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Abstract
The lowest singlet and triplet excited states of the two paired electrons in a chemical bond are treated by the time-dependent Hartree-Fock (H.F.) method, with the π electrons of the double bond in ethylene as an example. The results depend on a dimensionless parameter g which describes the strength of the electron correlation effects, and they are compared with a simple configuration interaction calculation. When g is small the frequencies and amplitudes of the Hartree-Fock oscillations give an accurate estimate of the energies and intensities of the two lowest transitions, the correlation energy and the pair distribution function of the gound state. The correlation energy is related to the zero-point energy of the oscillations. As g increases the H.F. method overestimates the correlation corrections and breaks down completely if g = 1. At this point the triplet oscillation becomes unstable, because the molecular orbital wave-function with two paired electrons ceases to be the state of lowest energy. When g is large the H.F. results violate spin conservation and the exclusion principle.