The virial theorem and stress calculation in molecular dynamics

In molecular dynamics, the pressure in a homogeneous system in equilibrium may be calculated by two different methods. The first is based on the virial theorem of Clausius and gives the pressure at the boundary of the system. The second is based on the notion of stress, which is the sum of the appropriate components of the interatomic forces intercepted by an area, and of the components of momentum flux across the area, averaged over the area and over time. We show by means of a detailed comparison of the forces involved that the two methods are equivalent in the thermodynamic limit. In a small system with arbitrary boundary conditions, the neglect of a part of the interactions between the system and the wall results in some error in the pressure calculated by the virial method. In the special case of a system with periodic boundaries, there is no external ’’wall,’’ and the internal pressures calculated by the two methods are the same. However, with comparable effort in computation, the stress method makes more efficient use of the data and yields a result of greater precision than does the virial method. In a system not in equilibrium or not homogeneous, the stress method remains valid but the virial method leads to ambiguous results. These considerations indicate that the method of stress calculation is more general than the virial method.