The method decomposing the molecular electron charge, which facilitates the evaluation of electrostatic potential, is presented. The decomposition is based on the observation, that in a free atom the electron charge distribution in the vicinity of its nucleus does not change, when the atom is incorporated into the molecule. In the decomposed system, the cusp singularity is integrated analytically by the application of the Green's function of Laplace operator for spherically symmetric systems. It is shown, that the residual charge, which is not treated analytically, is a smooth function and is close to zero in the vicinity of the nuclei. In the second part of the paper, the adaptive numerical integration algorithm is applied to obtain the Dirichlet boundary condition, required to any real space solver of Poisson equation.

PACS numbers: 31.15.–p, 31.15.Ew, 71.15.–m, 71.15.Ap