O the Use of Core Polarization Potentials to Account for Core-Valence Correlation Effects in Quantum Chemical Valence-Only Electronic Structure Calculations: Evaluation of Molecular Integrals Over Gaussian Basis Functions.

Quantum chemical valence-only electronic structure calculations have been performed for 22 states of NaK using full-valence configuration interaction, effective core potentials to provide the core-valence orthogonality constraints, and independent-particle core polarization functions (W. J. Stevens, D. D. Konowalow, and L. B. Ratcliff, J. Chem. Phys. 80, 1215-1224 (1984); L. B. Ratcliff, D. D. Konowalow, and W. J. Stevens, J. Mol. Spectrosc. 110, 242-255 (1985)). The resultant wavefunctions yield potential energies, dipole moments, and transition dipole moments as functions of nuclear geometry. Characteristic spectroscopic state constants were obtained. Theoretically determined electronic transition dipole moments are presented (L. B. Ratcliff, J. L. Fish, and D. D. Konowalow, J. Mol. Spectrosc. 122, 293-312 (1987)) for dipole-allowed transitions among the 26 states of Li_2 treated by D. D. Konowalow and J. L. Fish (Chem. Phys. 77, 435-448 (1983); Chem. Phys. 84, 463-475 (1984)). Charge-transfer effects are prevalent in many of the moments. Comparisons are made with existing empirical and theoretical determinations of the 1 ^1Sigma_sp{rm u}{+ }-1^1Sigma_sp{ rm g}{+} and 1^1 Pi_{rm u}-1 ^1Sigma_sp{rm g}{+ } transition moments. We calculated the vibrational energy levels for all three possible isotopic species of the 2^1 Sigma_sp{rm g}{+} state of Li_2 and from them deduce a set of Dunham constants (D. D. Konowalow and L. B. Ratcliff, Chem. Phys. Lett. 111, 413-415 (1984)). Since the 2^1Sigma_sp{rm g}{+} state has substantial ionic character, its shape is unusual and so is the spacing of its vibrational energy levels. A method for incorporating core-valence correlation in valence-only electronic structure calculations by the use of core polarization potentials (CPP) is outlined. Formulae are presented for the evaluation of the necessary integrals over Gaussian basis functions of arbitrary angular momentum, and in such a manner that is easily extended to 2 ^lambda-pole CPP for any lambda . Computer routines have been incorporated into the ARGOS program, which enables the use of effective core potentials and both core-dipole and core-quadrupole CPP functions, for Gaussian basis functions with angular momentum quantum number l <=q 4.