(685c) Predicting the Free Energy Landscape of Multicomponent Fluids

We derive a statistical mechanical framework for predicting the grand canonical free energy landscape of multicomponent fluids obtained from flat-histogram Monte Carlo simulations at chemical potentials and temperatures other than those used during a simulation itself. This is accomplished by expanding the landscape in a multidimensional Taylor series at each macrostate on the surface defined by the sampling order parameter; we illustrate how all equations necessary to precisely obtain the coefficients in these series may be obtained using classical statistical mechanics, and may be computed using data trivially available during the simulation. While each individual series may be relatively simplistic, when used in concert they are capable of producing feature-rich landscapes out of relatively simple ones. This approach allows us to obtain the thermodynamic behavior of multicomponent fluid systems, for instance, at low temperatures using only a single simulation at a much higher one. For multicomponent systems, we illustrate how a small number of different simulations may be rationally combined in a self-consistent fashion that yields a continuous thermodynamic phase phase for the fluid. This enables the equation of state for multicomponent fluid systems to be easily computed, and phase diagrams to be obtained over a broad range of conditions. After surveying a variety of different fluid systems, we identify a range of temperature and chemical potential differences over which the extrapolation of simulations tends to quantitatively predict various thermodynamic properties accurately. Beyond this range, extrapolation still provides a reasonable estimate of the free energy landscape; this requires less computational effort to refine via additional simulation(s) at the desired conditions than construction of the surface without any initially informed estimate. In either case, this method significantly increases the computational efficiency of flat-histogram Monte Carlo simulations when investigating thermodynamic properties of multicomponent fluids over a wide range of conditions.