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.

The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: An analytical equation of state

“…This model will be referred to as rod-coil fluid. 33,50,53 We employ a general m-m R notation to denote a rod-coil with a total number of m segments and a number of m R segments in the rigid block. A completely linear chain is referred to as a linear m-mer.…”

“…As a measure for the partial flexibility of a molecule, a dimensionless rigidity parameter is introduced, which, following our previous work, 33,50,53 is defined as the ratio of the total number of rigid bond-angles and the total number of bondangles in a molecule:…”

“…The rigidity parameter serves as an input for the excluded volume expression 50 and isotropic equation of state 53 used in this work. It varies conveniently from zero to unity between the completely flexible-and rigid chain limit, respectively.…”

“…In a previous work, 53 we extended the LH EoS 56, 57 to describe linear-and partially flexible tangent hard-sphere chain fluids and their mixtures. The extension was based on a refitting of one (a) of the three model constants (a, b, c) to the 2nd virial coefficient of linear and partially flexible chain fluids (as obtained analytically from Eq.…”

Liquid-crystal phase equilibria of Lennard-Jones chains

“…Simulations based on coarse-grained models can access longer time and length scales than their atomistic counterparts, allowing a bulk description of fluids. Coarse-grained models are commonly used to represent a simplified picture of large molecules, such as biomolecules [12][13][14][15][16], polymers [17][18][19][20][21][22], or liquid crystals [23][24][25][26][27][28]. Moreover, simulation results obtained from coarse-grained models can be directly compared with theoretical predictions that are based on a well-defined Hamiltonian, such as the family of perturbation theories developed from the statistical association fluid theory (SAFT) [29][30][31][32][33][34][35][36].…”