Molecular Simulation of Chemical Reaction Equilibrium by Computationally Efficient Free Energy Minimization

The molecular simulation of chemical reaction equilibrium (CRE) is a challenging and important problem of broad applicability in chemistry and chemical engineering. The primary molecular-based approach for solving this problem has been the reaction ensemble Monte Carlo (REMC) algorithm [Turner et al. Molec. Simulation2008, 34, (2), 119-146], based on classical force-field methodology. In spite of the vast improvements in computer hardware and software since its original development almost 25 years ago, its more widespread application is impeded by its computational inefficiency. A fundamental problem is that its MC basis inhibits the implementation of significant parallelization, and its successful implementation often requires system-specific tailoring and the incorporation of special MC approaches such as replica exchange, expanded ensemble, umbrella sampling, configurational bias, and continuous fractional component methodologies. We describe herein a novel CRE algorithm (reaction ensemble molecular dynamics, ReMD) that exploits modern computer hardware and software capabilities, and which can be straightforwardly implemented for systems of arbitrary size and complexity by exploiting the parallel computing methodology incorporated within many MD software packages (herein, we use GROMACS for illustrative purposes). The ReMD algorithm utilizes these features in the context of a macroscopically inspired and generally applicable free energy minimization approach based on the iterative approximation of the system Gibbs free energy function by a mathematically simple convex ideal solution model using the composition at each iteration as a reference state. Finally, we additionally describe a simple and computationally efficient a posteriori method to estimate the equilibrium concentrations of species present in very small amounts relative to others in the primary calculation. To demonstrate the algorithm, we show its application to two classic example systems considered previously in the literature: the N₂-O₂-NO system and the ammonia synthesis system.