Electron Correlation and Separated-Pair Approximation. An Application to Berylliumlike Atomic Systems

A method is developed for determining, with the help of the variation principle, the best antisymmetrized product of separated geminals for a polyatomic system. The strongly orthogonal geminals are determined directly in natural form and the natural orbitals are expressed in terms of Slater‐type atomic orbitals. An application to the berylliumlike atomic systems uniformly recovers 90% of the correlation energy. Correction for defects in the $K$ shell of the calculated wavefunctions gives an estimate of 91% for the correlation energy recovered by the best possible separated‐pair approximation, corresponding to an absolute error of about 5 kcal in beryllium. The correlation energy recovered is analyzed by partitioning the energy expression into intra‐ and intergeminal contributions, and both are further resolved into natural orbital contributions. The analysis makes it possible to assess the roles played by the various natural orbitals in lowering the energy and shows certain types of intergeminal as well as intrageminal interactions to be negligible. It also permits the comparison with calculations by other methods. The introduction of additional terms containing interelectronic distances is found to be less efficient than the further addition of natural orbitals.