Perturbational approach to the electron correlation cusp applied to helium-like atoms

A recently proposed perturbational approach to the electron correlation cusp problem [Sirbu, I.; King, H. F. J Chem Phys 2002, 117, 6411-6416] is tested in the context of three spherically symmetrical two-electron systems: helium atom, hydride anion, and a solvable model system. The interelectronic interaction is partitioned into long- and short-range components. The long-range interaction, lacking the singularities responsible for the electron correlation cusp, is included in the reference Hamiltonian. Accelerated convergence of orbital-based methods for this smooth reference Hamiltonian is shown by a detailed partial wave analysis. Contracted orbital basis sets constructed from atomic natural orbitals are shown to be significantly better for the new Hamiltonian than standard basis sets of the same size. The short-range component becomes the perturbation. The low-order perturbation equations are solved variationally using basis sets of correlated Gaussian geminals. Variational energies and low-order perturbation wave functions for the model system are shown to be in excellent agreement with highly accurate numerical solutions for that system. Approximations of the reference wave functions, described by fewer basis functions, are tested for use in the perturbation equations and shown to provide significant computational advantages with tolerable loss of accuracy. Lower bounds for the radius of convergence of the resulting perturbation expansions are estimated. The proposed method is capable of achieving sub-μHartree accuracy for all systems considered here.