A generating equation for mixing rules and assessment of their effect on the second virial coefficient

In this work, a generating equation for the mixing rules of interatomic potential energy parameters is proposed. It is demonstrated that this equation can indeed reproduce many popular mixing rules. A systematic framework is given for devising new mixing rules and/or comparing them. Two new mixing rules, which are more accurate than the available rules in the literature, are proposed. These rules are capable of reproducing the collision diameter and well depth parameters for the binary values of noble gases to within their experimental uncertainties.; The second virial coefficient is directly related to intermolecular forces. It is used to assess the effect of mixing rules on the second virial coefficients determined for the noble gases and compared to experimental data. The second virial coefficient is determined using a fast algorithm featuring a combination of multi-interval Gauss-Legendre and Gauss-Laguerre quadrature formulas combined with an Aitken's extrapolation formula to increase the accuracy of the determined second virial coefficients. The parameters of this algorithm were extensively studied and optimized. This algorithm is recommended to be implemented with 128 Legendre points and 16 Laguerre points, single interval, and a splitting distance of 20 Å.; Many forms of mixing rules were investigated for their effect on the determination of second virial coefficients. It appears that the Lorentz-Berthelot and Halgren HHG rules are inadequate. The Tang-Toennies is a slightly less accurate than the Waldman-Hagler, and the Functional and Fit forms proposed in this work. The Fit form is a slightly more accurate than the other two models. However, this comes at the expense of two extra adjustable parameters.