Cartesian-Spherical Transformation Formalism and the Theoretical Insight into Many-Body Long-Range Forces of the Electrostatic Origin in Multimolecular Systems

Abstract

Long-range many-body effects are responsible for the strong modification of the intermolecular pair potentials in condensed media (Piecuch 1987). They significantly affect the thermodynamical properties of pure liquids and solutions and are important for the proper understanding of solute-solute, solute-solvent and solvent-solvent interactions. In particular, inclusion of pairwise nonadditive long-range intermolecular forces considerably improves the theoretical description of liquid water and ionic hydrates. This wa’s, for example, observed in the Monte Carlo simulation studies performed by Clementi et al. (1980) and Clementi and Corongiu (1983). Taking into account the physical and formal necessity of considering the pairwise nonadditive molecular interactions, recently we have elaborated quite general, concise and uniform scheme of deriving the closed analytical anisotropic expressions for particular two- and many-body contributions to the long- range part of the interaction energy surface in an arbitrary multimolecular system which arise from the Rayleigh-Schrodinger perturbation theory (RSPT) at the multipole approximation level (Piecuch 1987). This scheme is based on the extensive use of the spherical tensor formalism and Racah-Wigner algebra as these mathematical methods assure considerable clarification of the formal considerations. Resulting intermolecular potentials possess numerous advantages because they are written in the spherical tensor forms. Unfortunately, the general procedure proposed by Piecuch (1987), although very clear, becomes lengthy and difficult when more complicated types of interactions are considered.