Numerical evaluation of electron repulsion integrals for pseudoatomic orbitals and their derivatives.

A numerical method to calculate the four-center electron-repulsion integrals for strictly localized pseudoatomic orbital basis sets has been developed. Compared to the conventional Gaussian expansion method, this method has an advantage in the ease of combination with O(N) density functional calculations. Additional mathematical derivations are also presented including the analytic derivatives of the integrals with respect to atomic positions and spatial damping of the Coulomb interaction due to the screening effect. In the numerical test for a simple molecule, the convergence up to 10(-5) hartree in energy is successfully obtained with a feasible cost of computation.