Subtleties in the calculation of the pressure and pressure tensor of anisotropic particles from volume-perturbation methods and the apparent asymmetry of the compressive and expansive contributions

Abstract

An efficient and versatile method to calculate the components of the pressure tensor for hard-body fluids of generic shape from the perspective of molecular simulation is presented. After due consideration of all the possible repulsive contributions exerted by molecules upon their surroundings during an anisotropic system expansion, it is observed that such a volume change can, for non-spherical molecules, give rise to configurations where overlaps occur. This feature of anisotropic molecules has to be taken into account rigorously as it can lead to discrepancies in the calculation of tensorial contributions to the pressure. Using the condition of detailed balance as a basis, a perturbation method developed for spherical molecules has been extended so that it is applicable to non-spherical and non-convex molecules. From a series of ‘ghost’ anisotropic volume perturbations the residual contribution to the components of the pressure tensor may be accurately calculated. Comparisons are made with prior methods and, where relevant, results are evaluated against existing data. For inhomogeneous systems this method provides a particularly convenient route to the calculation of the interfacial tension (surface free energy) from molecular simulations.

Keywords:

• Monte Carlo
• pressure tensor
• perturbation
• surface tension
• hard-core particles
• non-convex particles
• detailed balance

Acknowledgements

PEB would like to thank Felipe Blas and Elvira Martín del Río for their kind hospitality while he visited Universidad de Huelva to continue our collaboration with EdM. PEB is grateful to the Engineering and Physical Sciences Research Council (EPSRC) of the UK for funding a doctoral training award (DTA), and for support to the Molecular Systems Engineering Group (Grant No. EP/E016340). EdM also acknowledges additional funding from the DGI (Grant No. FIS200766079C0202) and the Junta de Andalucia (Grant No. P07FQM02884) of Spain. The computations reported in this work were performed on the High Performance Cluster (HPC) at Imperial College London. PEB would like to thank Simon Burbidge in particular for assistance his with the smooth running of our simulations.