Theory of Correlated Wavefunctions. III. Alternative Initial Approximations

The perturbation treatment of electron correlation is generalized to include an initial orbital approximation Ψ0 in which the orbitals are arbitrary within a unitary transformation which leaves Ψ0 unchanged. Various methods are considered for the partitioning of the total Hamiltonian into zeroth- and first-order parts consistent with a given zeroth-order Ψ0. One particular partitioning is discussed in detail which leads to simple and physically significant expressions for the second- and third-order energies, and for which the second-order energy gives a good estimate of the correlation energy when the orbitals are well localized and when no near-degeneracies are present. A calculation of the angular correlation in the ground state of the beryllium atom serves to investigate the validity of a number of concepts.