Electron Correlation in Closed Shell Systems. I. Perturbation Theory Using Gaussian-Type Geminals

The calculation of electron correlation energy in closed‐shell atoms and molecules is approached using Rayleigh‐Schroedinger perturbation theory with the symmetric sum of Hartree‐Fock operators for H⁰. The alleged advantages of using a V^N−1 potential are questioned. Variational equations for first‐order pair correlation functions are computed for He, Be, $\mathrm{B}+$ and Ne by expansion in linear combinations of correlated Gaussian‐type geminal basis functions containing $r_{12}^2$ in the exponent. Such functions form mathematically complete sets, have convenient symmetry properties, and are integrable in closed form. An extensive search for optimum exponential parameters yielded trial functions for each of the ss orbital pairs giving better than 99% of the limiting second‐order pair energy using only five basis functions per pair. Similar but less thorough studies of sp and pp pairs in neon are also reported. Careful attention is paid to computational accuracy. An upper bound of $\text{−0.3428\hspace{0.17em}}\mathrm{a.u.}$ is established on the second‐order contribution to the correlation energy in neon.