Numerical solution of Poisson’s equation in polyatomic molecules

We have developed a completely numerical scheme for solution of Poisson’s equation in multicenter systems. We are thus able to numerically calculate the Coulomb potential of arbitrary charge distributions in polyatomic molecules. The method is based on a decomposition of the multicenter Poisson problem into independent single-center problems, each of which is solvable in standard spherical coordinates. In combination with our multicenter numerical integration scheme reported previously, completely numerical evaluation of arbitrary two-electron Coulomb integrals is possible. Test calculations on the classic two-electron Coulomb and exchange integrals of H2 and the Coulomb interaction energies of several model polyatomic systems indicate that the scheme is both practical and accurate.