Reproduction of correct electrostatic field by charges and dipoles on a closed surface

A general algorithm based on the Green function theorem has been developed to correctly reproduce electrostatic fields inside a closed space by point charges and point dipoles on the surface surrounding the space. For actual computations, limited numbers of point charges, including charge pairs replacing point dipoles, are enough to approximate the inner fields. As examples, reaction fields were reproduced by the current surface charges and dipoles for the dielectric models, where a monopole, dipole, or quadrupole was individually set at the center in a vacuum sphere surrounded by high dielectric continuum. The potentials due to those reaction fields agree well with the analytical ones. As an application of this method to the analysis of the electronic structure of the active site of a protein, a combination of the continuum dielectric model and ab initio molecular orbital calculation was carried out. Other applications to molecular dynamics and quantum mechanical calculations are also discussed.