A hybrid method for the evaluation of the matrix elements of the Coulomb potential

An analysis of the method of obtaining matrix elements of the Coulomb potential by numerical integration of the ‘exact’ potential, a strategy proposed by Termath and Handy, reveals that this method will be inaccurate in large systems because of the long-range nature of the Coulomb forces. The results can be improved substantially if one integrates the long-range part of the potential analytically. This has been achieved — at virtually no extra cost — by introducing a simple model density whose electrostatic potential has the correct long-range behaviour and whose Coulomb matrix elements can easily be evaluated analytically. The model density can be designed to reduce errors which arise in the fully numerical method due to the electrostatic potential in the cores of heavy atoms.