Atomic and molecular correlation energies with explicitly correlated Gaussian geminals. II. Perturbation treatment through third order for He, Be, H2, and LiH

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Abstract
Third‐order correlation energies for He, Be, H2, and LiH were calculated using highly accurate first‐order pair functions obtained recently by us [J. Chem. Phys. 7 8, 1420 (1983)] with a novel second‐order energy functional and a large basis set of explicitly correlated Gaussian geminals. Since these strong orthogonality projection, no new types of integrals appear as compared to the second‐order treatment. Consequently, the third‐order calculation does not require much more time than the second‐order one. For He and Be atoms, the calculated third‐order energies agree very well with the most accurate results obtained using the partial‐wave expansion and extrapolation techniques. We estimate that our third‐order energies are accurate up to within a fraction of 1%. The sum of the calculated values of the second‐ and third‐order energies represents 97.5%, 90.4%, 94.4%, and 95.0% of the experimental correlation energy for He, Be, H2, and LiH, respectively.