Free-energy calculations

Thermodynamic equilibria are evaluated by analysis of the free energy. When a thermodynamic system can exist in one of several distinct phases-differing perhaps in density, molecular composition, symmetry, and so on-the most stable of them is the one that minimizes the appropriate free energy for the choice of independent thermodynamic variables. The same criterion is invoked (directly or indirectly) when one attempts to analyze phase equilibria by molecular simulation. For molecular simulation to be broadly useful it is important then that it can be applied to the evaluation of free energies of model systems. Evaluating free-energies by simulation is not hard conceptually; evaluating them efficiently is difficult, however, and any advances that make free-energy calculations simpler can greatly expand the range of usefulness of molecular simulation

Molecular simulation never provides a direct measurement of the free energy, in the sense that it never performs a numerical quadrature of the partition function for the model system. Instead, simulation provides the difference in free energy between the system of interest (the target system) and a reference system, for which the free energy may be known. The reference system may differ from the target system in its thermodynamic state (e.g., temperature or density), or it may be represent an entirely different molecular model. The free energy of the reference may be known from a separate molecular simulation study, or it may form a system simple enough that its free-energy can be determined analytically. The free-energy difference may be an end in itself, since this difference is all that is needed to ascertain the relative stability of two candidate phases.