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

TL;DR

This paper extends the Einstein molecule approach to calculate free energies of molecular solids, demonstrating its accuracy and addressing key issues like simulation box shape, reference structure choice, and size dependence through applications to various complex systems.

Contribution

The study introduces an extended Einstein molecule method for molecular solids and analyzes critical factors affecting free energy calculations, validated on water ice phases and protein-mimicking models.

Findings

Both Einstein crystal and Einstein molecule methods agree within statistical uncertainty.

Using the equilibrium shape of the simulation box avoids artificial stress and free energy errors.

The calculated free energy is insensitive to the choice of reference structure if close to equilibrium.

Abstract

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-dumbbells 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 non-polarizable 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 non-cubic 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 of 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 not an 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.