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

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. 78, 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.