Electrostatic interaction energies from a generalized Gaussian quadrature

When used in conjunction with a properly chosen curvilinear coordinate system, a generalized Gaussian quadrature affords a new versatile approach to the computation of energies of electrostatic interaction between two non-overlapping, continuous charge distributions. Compared with the conventional discretization of distributions, this approach offers a vast reduction in computational effort without a concomitant loss of accuracy. Although potentially slower than the fast multipole method, the present formalism is more general and less prone to discretization errors due to finite grid sizes. Results of test calculations on the energies of classical electrostatic interaction between AIMs demonstrate the power of the new method.