Perturbation theory of the electron correlation cusp based on a partitioning of the electron–electron interaction into long- and short-range components

Abstract

We propose a method, using low order, Rayleigh Schrödinger perturbation theory (RSPT), for systematically increasing the accuracy of traditional, orbital-based, ab initio electronic structure computations. The method is designed to be equally applicable to closed- or open-shell systems. The interelectron interaction is partitioned into long- and short-range components using an expression containing an arbitrary smoothing parameter, γ. The smooth, nonsingular, long-range component of the interelectron interaction is retained in the reference Hamiltonian, and the exponentially-short-range component is included in the perturbation. Modified Fock operators are introduced to prevent spurious core shrinkage. Orbital-based methods are employed for the reference problem. Explicitly correlated Gaussian geminal basis functions are used for variational solution of the RSPT equations. The computational burden shifts from solution of the reference problem to that of the RSPT equations as the extent of smoothing is increased, i.e., as γ is decreased. It is shown that smoothing the interelectron interaction out to a distance of about one Bohr for the helium atom is a reasonable compromise yielding satisfactory rates of convergence of both CI and RSPT expansions. The accuracy of the computed energy increases by two decimal digits for each additional perturbation order in the wave function. Expanding the wave function through third order for γ=2 bohr−1 yields the helium atom energy in error by only 4 nanohartrees.