General contraction of Gaussian atomic orbitals: Core, valence, polarization, and diffuse basis sets; Molecular integral evaluation

Generally contracted Gaussian basis functions are defined as those for which each contracted function may have a nonzero contribution from each primitive Gaussian. Alternatives for choice of such bases are tested and guidelines proposed. The basis is compared with standard methods in current use and is shown to be superior in terms of energy lowering obtained per additional basis function beyond a minimal number. A new program for computation of the required multicentered integrals is described.