A multipole approximation of the electrostatic potential of molecules

The problem of approximating three-dimensional spatial distributions of quantum-mechanical electrostatic potentials of molecules by analytic potentials on the basis of atomic charges, real dipoles, and atomic multipoles up to quadrupoles inclusive was considered. Real dipole potentials are created by pairs of point charges of opposite signs, and the search for their arrangement in the volume of a molecule is part of the approximation problem. A FitMEP program was developed for the optimization of the parameters of models of the types specified taking into account molecular symmetry. It was shown for the example of several molecules (HF, CO, H₂O, NH₃, CH₄, formaldehyde, methanol, formamide, ethane, cyclopropane, cyclobutane, cyclohexane, tetrahedrane, cubane, adamantane, ethylene, and benzene) that the real dipole and atomic multipole models gave errors in approximated quantum-mechanical electrostatic potential values smaller by one or two orders of magnitude compared with the atomic charge model. The atomic charge model was shown to be virtually inoperative as applied to saturated hydrocarbons. Real dipole models were slightly inferior to atomic multipole models in quality but had all the advantages of the potential of point charges as concerned simplicity and compactness, and their use in potential energy calculations did not require changes in the existing program codes.