Abstract
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.
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