Detailed examination of the calculation of the pressure in simulations of systems with discontinuous interactions from the mechanical and thermodynamic perspectives

We consider some fundamental aspects of the calculation of the pressure from simulations of systems characterized by discontinuous interactions. The usual approach to the computation of the pressure in such systems is based on the mechanical (or virial) expression, which in turn can be expressed in terms of the value of the radial distribution function at contact or the number of overlaps that would occur under a virtual compression of the system. A less widespread, and formally equivalent, approach invokes the thermodynamic definition of the pressure and involves the estimate of the change in free energy associated with a small volume perturbation. There are, however, important differences in the way the virial and thermodynamic evaluations of the pressure are implemented, and, as a consequence, in the corresponding errors associated with each technique. The bulk pressure is determined with the virial and the thermodynamic routes for the hard-sphere system in the fluid and solid states. Good agreement is found between the two approaches, though the virial route is generally found to provide a greater accuracy. This is also borne out from simulations of hard non-spherical particles characterized by the hard Gaussian overlap potential in isotropic and anisotropic (nematic) fluid states. We show that the tensorial components of the pressure can be determined by a simple extension of the approaches developed for the bulk pressure. The diagonal components evaluated in this way for the hard-sphere solid are found to be equivalent and equal to the bulk pressure within the accuracy of the calculation. The most stringent test of the virial and thermodynamic approaches is the computation of the normal and tangential components (and hence the interfacial tension) of a hard-sphere fluid confined between two structureless hard walls.