Density of states and free energy landscapes from equations of state and from molecular simulation

The connection between molecular force fields and equations of state (EoS) is typically established by comparing simulation data and EoS data. This work demonstrates how the density of states (O) and the probability density of macrostates (H) can be extracted from empirical and semi-empirical equations of state, thus allowing a useful connection between molecular models and widely used classical thermodynamic models. The approach is based on the fact that the configurational O is related to residual thermodynamic properties that could be found from an EoS. The key relation used is Boltzmann's entropy equation. Expressions for O and H are derived from several equations of state for several types of single-component model systems. It is shown how such an EoS O can be used to aid multi-canonical (MUCA) Monte Carlo simulation methods designed to map out O. Furthermore, Massieu's formalism is used to derive generalized expressions for O and H valid for multi-component systems with any EoS and in any isothermal ensemble. This work also focuses on developing of MUCA methods for mapping out O and free energy profiles. Results for O and H obtained by MUCA simulations are compared to ones obtained by using suitable equations of state. It also extends and applies to more complex systems the method introduced by M. Fenwick and F. Escobedo [J. Chem. Phys. 120, 3066 (2004)] that uses Bennett's acceptance ratio method of free energy estimation. The focus is on efficient mapping of multi-phase regions of multi-component systems. For mixtures, the macrospace to be mapped is multi-dimensional, simulations times become very large, and the issue of devising efficient mapping schemes becomes of paramount importance. Again, Massieu's formalism is used to derive general MUCA expressions valid for any number of components for any type of mapping space and simulations in any isothermal ensemble. Free energy profiles obtained from MUCA simulations are used to determine phase-coexisting conditions.