Fast evaluation of the Coulomb energy for electron densities

The evaluation of the Coulomb interaction of the electron density with itself dominates the cost of a density-functional theory calculation, due to its quadratic scaling with the size of the system. A similar problem is found in simulations of systems of particles, where the cost is dominated by the particle–particle interactions. Recently, we have presented a simple method for the particle–particle problem [J. M. Pérez-Jordá and W. Yang, Chem. Phys. Lett. 247, 484 (1995)]. In this paper, our scheme is generalized to densities, in particular for calculations with Gaussian basis functions. Near linear scaling is observed for molecules with about 400 first-row atoms. CPU time savings of up to one order of magnitude are observed for these molecules. The method distinguishes between localized and diffuse distributions in a much simpler way than in other proposed approaches.