Electron Correlation and Augmented Separated-Pair Expansion

As a refinement over the separated‐pair approximation, the augmented separated‐pair expansion is developed. The wavefunction is expanded in a series of augmented separated‐pair configurations. The leading term is the separated‐pair approximation. Each of the higher terms is an antisymmetrized product of separated space geminals and spin harmonics. The spin harmonics are eigenfunctions of ${\mathfrak{S}}^2$ and ${\mathfrak{S}}_z$ and, moreover, span irreducible one‐dimensional representations of the geminal subgroups. The separated space geminals are constructed from the natural orbitals of the separated‐pair approximation. It is expected that only relatively few augmented separated‐pair configurations contribute significantly and that they can be readily identified. The additional correlation energy recovered by the augmented separated‐pair expansion beyond the separated‐pair approximation can be classified as correlation between different strongly orthogonal geminals. It can be analyzed by a partitioning of the energy in terms of contributions from the various separated‐pair configurations.