New Combining Rules for Rare Gas van der Waals Parameters Marvin Waldman and A.T. Hagler* zyxwvut Biosym Technologies, zyxwvutsrqp Inc., San Diego, Cali,fornia 92121 Receiued zyxwvutsrqpo 23 October 1992; accepted 26 March 1993 zyxwvut New combining rules are proposed for the well depth, E, and interaction distance, a, describing nonbonded interatomic forces for rare gas pair interactions. Concepts underlying current combining rules applied in simulations of macromolecular and polymer systems are shown to be incompatible with experimental data on the rare gases. The current combining rules are compared with the new results using the experimental data. Mathematical properties of combining rules are considered, and it is shown how to reduce combining rule formulas from a two-parameter to a single-parameter problem. It is also shown how to graphically analyze combining rules against experimental data. We demonstrate using this analysis technique that the rare gas potentials do not obey a single combining rule for the E parameter but do follow a single combining rule for the zyxwvutsr v parameter. Finally, we demonstrate that a combining rule using both E and zyxw (T can be used to predict the zyxwvutsrq F parameters for the mixed rare gas pairs. 0 1993 by John zyxwvu Wiley & Sons, Inc. INTRODUCTION Understanding the nature of intermolecular forces is central to predicting both the microscopic and bulk properties of molecular systems. Molecular sim- ulations involving molecular mechanics and dynam- ics calculations are often used to predict properties of interest such as structure, conformation, energy, transport coefficients, etc. of molecules ranging from peptide hormones and proteins to po1ymers.l.l These calculations rely on the use of force-field approxi- mations for the quantitative description of the intra- and intermolecular forces. In most of the popular force fields in use, the description of the intermo- lecular component is broken down into contribu- tions from electrostatic energy and a contribution from nonbond or van der Waal’s interactions.’>-” Due to the problem of overabundance of parameters, the nonbond interactions for unlike systems are gener- ally approximated from knowledge of the interac- tions for like systems by the use of combining rules involving the nonbond parameters of the atom-atom pair potentials. The combining rules in common use with most available force fields are: (1) a geometric mean rule for the well depth parameter, E, of the nonbond potential; and (2) a geometric or arithmetic mean rule for the well depth position, R,,l, of the nonbond p~tential.~ In recent years, as experimental data provided more accurate information on nonbond potentials for rare gas interactions, it has become clear that *Author to whom all correspondence should be addressed. these simple combining rules lead to large errors in predicting the potential parameters of mixed rare gas atom pairs, especially with regard to the well depth parameter, F. As a result, more elaborate com- bination rules have been proposed that significantly improve the fit of the rare gas data, zy as well as other simple molecular systems.12-’” However, none of these more elaborate rules have yet been incorpo- rated into the more popular molecular mechanics force fields. In part, this may be due to the perception that the force fields are not sensitive to the specific form of the combining rules. However, another key factor is that the newer combination rules generally involve additional parameters such as polarizability, ionization potentials, or dispersion force coeffi- cients. Therefore, these combination rules are less easily incorporated into molecular force fields be- cause they lead, again, to an excess of parameters that are not easily determined for systems other than rare gases, and the original goal in employing com- bination rules was to reduce, rather than increase, the number of force-field parameters. In this article, we propose new combination rules for the well depth and position parameters for non- bond potentials. These combination rules require no new parameters other than the values of the well depth and position themselves. We show how the new combining rules provide excellent fits to the well depths and interaction distances of the mixed rare gas pairs. Because of the specific data analyzed for the rare gas systems and for ease of comparison with prior work, we have actually chosen to use CT, the point at which the potential curve crosses zero, rather than R,, the minimum of the curve, to for- Journal of Computational Chemistry, Vol. 14, No. 9, 1077-1084 (1993) zyxwvu 0 1993 by John Wiley & Sons, Inc. CCC 0192-8651 /93/091077-08