The ellipsoidal gaussian basis in molecular orbital theory - I. Integral formulas and test calculations

New analytic integral formulas are presented for the potential energy integrals over ellipsoidal Gaussian basis functions [∼ exp (-αx² - βy² - γz²)] that enter into solving the conventional expansion self-consistent field equations. Near minimal atomic orbital bases combined from large nuclear-centered primitive Gaussian sets are used in test calculations on the HF and CO molecules. The ellipsoidal exponential parameters for the valence atomic orbitals are fully optimized using a single scale factor for each atomic orbital and nuclear coordinate. The results are compared with those obtained using an unoptimized nuclear centered double-zeta spherical Gaussian basis.