Self-referential method for calculation of the free energy of crystals by Monte Carlo simulation

We propose a Monte Carlo simulation method for the evaluation of free energies in crystalline systems. In principle, the method involves evaluating the free-energy difference between systems of N molecules and 2N molecules. This difference, coupled with the assumption that the free energy is extensive and thus proportional to N, provides sufficient information to obtain the absolute free energy of the crystal. The approach to doubling the system size does not involve insertion or removal of molecules in the system. Instead, the configurations of the molecules are expressed in terms of the normal-mode coordinates of a harmonic lattice. By decoupling certain of these coordinates from the molecule configurations, we obtain a transformation that in effect yields the system-size doubling. The method is examined via application to a system of hard rods in one dimension. This simple model is considered principally because of the availability of an analytic solution for its free energy, which permits accurate testing of the performance and correctness of the proposed method. In using the hard-rod model we also avoid other complications related to treatment of the temperature, and application of normal-mode coordinate decoupling in higher dimensions. The proposed method is shown to be able to provide good results for the free-energy calculation, but further development will be needed before it can be considered practical for general-purpose use.