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 Gaussianexpansion method, this method has an advantage in the ease of combination with 0(N) density functional calculations. Additional mathematical derivations are also presented including theanalytic derivatives of the integrals with respect to atomic positions and spatial damping of theCoulomb interaction due to the screening effect. In the numerical test for a simple molecule, theconvergence up to 10-5 hartree in energy is successfully obtained with a feasible cost ofcomputation.
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