GENERALIZED PERTURBED HARTREE-FOCK THEORY

The conventional coupled perturbed Hartree-Fock theory is generalized to allow for an arbitrary independent-particle zero-order Hamiltonian and arbitrary perturbed Hartree-Fock Hamiltonian. The perturbation series for the resulting (unrestricted) Hartree-Fock wave function, density matrices, and energy are developed in diagrammatic form. A linked cluster expansion for the Hartree-Fock wave function is derived. It is shown that any expectation value for the perturbed Hartree-Fock state is represented by a precise subset of the diagrams contributing to the perturbation result for the exact perturbed electronic Hamiltonian but that this is not true for the wave funtion. Explicit results are given for the wave function through third order and the energy through fourth order. Further, general topological rules are presented which define the Hartree-Fock diagrams through all orders, and allow generalization of the formalism to particular applications. By comparison of the present results with those for the exact perturbation theory, it is shown that the subset of topologies which enter the Hartree-Fock perturbation expansion always correspond to contributions in which the electron-electron potential acts between uncorrelated one-electron terms, a result consistent with the usual interpretation of the Hartree-Fock approximation. © 1980 American Institute of Physics.