Development of a model that contains both multipole moments and gaussians for the calculation of molecular electrostatic potentials

Abstract

The electrostatic interaction is a critical component of intermolecular interactions in biological processes. Rapid methods for the computation and characterization of the molecular electrostatic potential (MEP) that segment the molecular charge distribution and replace this continuous function by a series of multipole moments for each segment have been described. There are two sources of error in these techniques: 1( The truncation of the expansion after just a few terms, and 2) the charge in the segmental distribution that is more distant from the expansion center than the observation point. The first may be eliminated by finite expansion methods where truncation is unnecessary or performed in a manner that gives errors that are acceptably small. The second is inherent in the multipole expansion and results from the assumption in performing the expansion that the distance to the observation point is larger than the distance to all points inside the charge distribution. As the basis functions used in molecular wave functions have infinite extent, this will never be the case and the multipole expansion is never strictly valid. In practice this inherent error limits the range of usefulness of all multipole expansion techniques. To expand this range we have introduced a method that uses exact techniques to compute the MEP for the part of the molecular charge distribution described by the gaussians on each atom with the smallest exponential parameter and uses segmental multipole methods for the remainder of the charge. Using pyrrole with an STO-3G wave function as an example, this method significantly improves the potential in the range 1.4–2.0 A from atoms with only a small increase in computational effort. If other basis sets are used with more diffuse gaussians the convergence of the multipole expansion will be at greater distances from the atoms and this type of correction will be more important.