Cusped-gaussian molecular wave functions. Part 3.—Basis sets for the first-row atoms

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Abstract
SCF calculations using a variety of cusped-Gaussian basis sets have been performed for the first-row atoms B to F and for the nitrogen and water molecules. It is shown that the atomic s-type basis (c+ 4s), consisting of a cusp function and four Gaussians, is of double-zeta quality and provides a highly accurate description of the wave function at and near a nucleus. The error in the density at a nucleus, up to 5 % for an all-Gaussian basis of double-zeta quality, is almost entirely eliminated with the basis (c+ 4s), whilst the cusp condition at a nucleus, which cannot be satisfied at all by an all-Gaussian basis, is accurately reproduced by the basis (c+ 4s), with an error of ≈ 1%. The problem of the large number of functions normally used to describe the polarization effects in molecules is discussed. It is shown that polarization effects can be described economically by the use of a relatively small number of molecular bond and lone-pair functions.

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