Determining Force Field Parameters Using a Physically Based Equation of State

Abstract

Force field parameters used in classical molecular simulations can be estimated from quantum mechanical calculations or spectroscopic measurements. This especially applies to bonded interactions such as bond-stretching, bond-bending, and torsional interactions. However, it is difficult and computational expensive to obtain accurate parameters describing the nonbonded van der Waals interactions from quantum mechanics. In many studies, these parameters are adjusted to reproduce experimental data, such as vapor-liquid equilibria (VLE) data. Adjusting these force field parameters to VLE data is currently a cumbersome and computationally expensive task. The reason is that the result of a calculation of the vapor-liquid equilibria depends on the van der Waals interactions of all atom types in the system, therefore requiring many time-consuming iterations. In this work, we use an analytical equation of state, the perturbed chain statistical associating fluid theory (PC-SAFT), to predict the results of molecular simulations for VLE. The analytical PC-SAFT equation of state is used to approximate the objective function f(p) as a function of the array of force field parameters p. The objective function is here for example defined as the deviations of vapor pressure, enthalpy of vaporization and liquid density data, with respect to experimental data. The parameters are optimized using the analytical PC-SAFT equation of state, which is orders of magnitude quicker to calculate than molecular simulation. The solution is an excellent approximation of the real objective function, so that the resulting method requires only very few molecular simulation runs to converge. The method is here illustrated by optimizing transferable Lennard-Jones parameters for the n-alkane series. Optimizing four force field parameters p = (ε(CH(2))(CH(2)), ε(CH(3))(CH(3)), σ(CH(2))(CH(2)), σ(CH(3))(CH(3))) we obtain excellent agreement of coexisting densities, vapor pressure and caloric properties within only 2 -3 molecular simulation runs.