The pairwise correlated generalized valence bond model of electronic structure. IV. Low lying S states of two-electron atoms and ions

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Abstract
Quantitative tests for theories of electron correlation are rare, since exact nonrelativistic energies are generally unknown. An important exception to this dilemma is found in the case of two‐electron atoms. Accurate nonrelativistic energies are available for ground and excited states of two‐electron atoms and ions. Comparison with these exact results provides an ideal testing ground for a theory of electron correlation. We have, therefore, carried out SCF calculations on the (1s,1s)1S ground state and on the (1s,2s)1S and (1s,2s)3S excited states of two‐electron atoms for a wide range of nuclear charges. The resulting correlation energies (i.e., EEXACT−ESCF) are then compared to the overlap approximation we developed in an earlier paper. The observed correlation energies agree with the overlap approximation to within 2% for the singlet states. Hence, combining the overlap approximation for the correlation energy with the calculated SCF energy (i.e., the pairwise correlated generalized valence bond method) gives total energies two orders of magnitude more accurate than the SCF calculations, with only a trivial increase in computing effort. The agreement for triplet states is equally good for the pair of orbitals for which the 2s eigenvalue equals the ionization potential. However, discrepancies of 10% are found for the pair of orbitals for which the one‐electron Hamiltonian is diagonal.