This talk presents a practical method for calculating the two,
three, and four-center integrals that arise in molecular
calculations, with a special focus on the difficult electron
repulsion integrals.

With the help of Fock's relationships and the theory of
hyperspherical harmonics, we are able to evaluate molecular
integrals based on Coulomb Sturmians both rapidly and
accurately. The method is then extended to Slater-Type Orbitals by
using a closed-form expression for the expansion coefficients of
STO’s in terms of Coulomb Sturmians, allowing most of the work to be
relegated to a precalculation step.

A prototype software library has been implemented for calculating
molecular Coulomb Sturmian integrals, and preliminary benchmarks
have been performed, indicating good performance properties.
Timings for four-center electron repulsion integrals ranged from
tens to about a hundred nanoseconds, making molecular Coulomb
Sturmians competitive with Gaussian type orbitals in terms of
speed. Programs for Slater-Type orbitals are still at a rudimentary
stage.

Invited speaker (See http://mes14.amasya.edu.tr/?page_id=710)