Characterizing Molecular Rotations using Monte Carlo Simulations

Abstract

The Monte Carlo (MC) simulation technique is a powerful method for calculating thermodynamic averages of physical quantities of many-body systems. The physical property we focus on in this Chapter is molecular rotational motion. The rotational degrees of freedom in molecular crystals give rise to temperatureand/or pressure-driven transitions between phases with freely rotating, quasi-freely rotating, or orientationally ordered molecules. Orientationally disordered crystals represent a state of matter between the liquid and the purely crystalline state, and can be compared to liquid crystals. In liquid crystals, however, translational order is destroyed and orientational order is preserved, while in molecular crystals translational order persists while molecules are (partially) orientationally disordered. For a review on molecular crystals we refer to Lynden-Bell & Michel (1994). The molecular crystals we envisage can be as simple as solid hydrogen, but as complex as protein crystals. Also, we do not restrict ourselves to crystals containing only one type of molecule, or to three-dimensional (3D) molecular arrangements. An example of a heterogeneous molecular crystal is fullerene-cubane, C60.C8H8, while fullerene molecules like C60 or C70 packed inside a carbon nanotube (CNT) provide an instance of a one-dimensional (1D) molecular chain. MC simulations provide an excellent tool for the computational study of the different phases, and the transitions between them, of molecular crystals. First, molecular crystals typically consist of molecules interacting via van der Waals interactions, which can be relatively easy modeled using phenomenological potential models. Secondly, the main advantage of MC simulations is the possibility to directly change pressure and temperature, and to examine how the crystal’s structure (from the point of view of molecular order/disorder) changes accordingly. While the actual implementation of molecular rotations in (MC) simulations is typically covered in textbooks, e.g. Allen & Tildesley (1987) and Frenkel & Smit (2002), the actual characterization of molecular rotations and orientations has received much less attention. In this Chapter, we present a method to assess molecular rotational motion within molecular crystals based on the concept of orientational mean-squared displacements (OMSDs). The technique provides an efficient way for describing different rotational regimes of individual molecules and of the molecular crystal as a whole. From a computational point of view, the method has the advantage that only a limited number of parameters has to be sampled and stored to obtain the necessary information on molecular motion and ordering. We consider rigidmolecules, so that each molecule has three translational and three rotational degrees of freedom. The context of the present Chapter assumes a fully set-up MC simulation of a system of molecules, in any ensemble, with all the usual ingredients like interaction 17