SEMIANALYTICAL METHOD FOR 4-CENTER MOLECULAR INTEGRALS OVER SLATER-TYPE ORBITALS

A strategy for the evaluation of four-center molecular integrals over Slater-type orbitals is developed using the Lowdin in alpha-function approach in which displaced orbitals are expanded in spherical harmonics. The harmonic potentials are produced analytically and evaluated along a grid. The harmonic charge distributions are given an analytical formulation and are evaluated over the common grid, and numerical integrations are performed for each harmonic. Using an example with 1s orbitals, only nine harmonics are needed for good results. Computer algebra and integer arithmetic are used to generate C,E, and F matrices that are stored as part of the data base. One-dimensional T and X matrices are introduced as an aid in computation. The employment of look-up tables and vector and parallel processing promises to make this method, which can be generalized, practical.