Computing the free energy of molecular solids by the Einstein molecule approach: ices XIII and XIV, hard-dumbbells and a patchy model of proteins.

The recently proposed Einstein molecule approach is extended to compute the free energy of molecular solids. This method is a variant of the Einstein crystal method of Frenkel and Ladd [J. Chem. Phys. 81, 3188 (1984)]. In order to show its applicability, we have computed the free energy of a hard-dumbbell solid, of two recently discovered solid phases of water, namely, ice XIII and ice XIV, where the interactions between water molecules are described by the rigid nonpolarizable TIP4P/2005 model potential, and of several solid phases that are thermodynamically stable for an anisotropic patchy model with octahedral symmetry which mimics proteins. Our calculations show that both the Einstein crystal method and the Einstein molecule approach yield the same results within statistical uncertainty. In addition, we have studied in detail some subtle issues concerning the calculation of the free energy of molecular solids. First, for solids with noncubic symmetry, we have studied the effect of the shape of the simulation box on the free energy. Our results show that the equilibrium shape of the simulation box must be used to compute the free energy in order to avoid the appearance of artificial stress in the system that will result in an increase in the free energy. In complex solids, such as the solid phases of water, another difficulty is related to the choice of the reference structure. As in some cases there is no obvious orientation of the molecules; it is not clear how to generate the reference structure. Our results will show that, as long as the structure is not too far from the equilibrium structure, the calculated free energy is invariant to the reference structure used in the free energy calculations. Finally, the strong size dependence of the free energy of solids is also studied.