REPRESENTATION OF VANDERWAALS (VDW) INTERACTIONS IN MOLECULAR MECHANICS FORCE-FIELDS - POTENTIAL FORM, COMBINATION RULES, AND VDW PARAMETERS

This paper explores the premise that insights gained from studying the well-characterized van der Waals (vdW) interactions of rare-gas atoms can be used advantageously in formulating the representation of vdW nonbonded interactions in molecular mechanics force fields, a subject to which little attention has been given to date. We first show that the commonly used Lennard-Jones and Exp-6 potentials fail to account for the high quality rare-gas data but that a relatively simple distance-buffered potential (Buf-14-7, eq 10) accurately reproduces the reduced rare-gas potentials over the range of interatomic separations of primary interest in molecular mechanics calculations. We also show that the standard arithmetic- and geometric-mean combination rules used in molecular mechanics force fields perform poorly, and we propose alternative "cubic-mean" and "HHG" combination rules for minimum-energy separations R*ij and well depths epsilon(ij) (eqs 12, 14) which perform significantly better. We then make further use of the known behavior of the rare gases by developing a formalism for relating epsilon and R* to experimentally derived data on atomic polarizabilities and on the Slater-Kirkwood "effective number of electrons" for the interacting atoms (eqs 27, 35). This formalism yields the vdW parameters (Table XIII) which we propose to use in the Merck Molecular Force Field (MMFF) being developed in our laboratories. Comparisons to other force fields such as MM2, our laboratory's MM2-based MM2X, AMBER, VFF, CHARMM, and MM3 demonstrate wide variations in vdW parameters from force field to force field but reflect broad agreement with the calculated MMFF values apart from a tendency of the MMFF formalism (i) to yield slightly larger minimum-energy separations and (ii) essentially in agreement with MM2 and MM3 but contrary to AMBER, VFF, and CHARMM to give vdW well depths which do not depend on the chemical environment.