Total energy assessment of the quality of localized basis sets: ${\mathrm{O}}_2$ molecule

The quality of localized basis sets in molecular calculations is assessed using the total energy as a measure of variational freedom. Basis sets which also include a set of on-site functions obtained from positive ions are found to be far better variationally than those which include virtual (unoccupied) atomic levels: In particular, the inclusion of higher virtual states in the standard LCAO (linear combination of atomic orbitals) basis does not prove convergence. These efficient and accurate basis set results for ${\mathrm{O}}_2$ are in very good agreement with previously published full-potential linearized—augmented—plane-wave results and LCAO results using off-site functions.