Virial pressure
From SklogWiki
The virial pressure is commonly used to obtain the pressure from a general simulation. It is particularly well suited to molecular dynamics, since forces are evaluated and readily available. For pair interactions, one has:
where p is the pressure, T is the temperature, V is the volume and kBis the Boltzmann constant.
In this equation one can recognize an ideal gas contribution, and a second term due to the virial. The overline is an average, which would be a time average in molecular dynamics, or an ensemble average in Monte Carlo; d is the dimension of the system (3 in the "real" world). 
is the force on particle i exerted by particle j, and 
is the vector going from i to j: 
.
This relationship is readily obtained by writing the partition function in "reduced coordinates", i.e. x * = x / L, etc, then considering a "blow-up" of the system by changing the value of L. This would apply to a simple cubic system, but the same ideas can also be applied to obtain expressions for the stress tensor and the surface tension, and are also used in constant-pressure Monte Carlo.
If the interaction is central, the force is given by
where f(r) the force corresponding to the intermolecular potential Φ(r):
For example, for the Lennard-Jones potential, f(r) = 24ε(2(σ / r)12 − (σ / r)6) / r. Hence, the expression reduces to
Notice that most realistic potentials are attractive at long ranges, hence the first correction to the ideal pressure will be a negative contribution: the second virial coefficient. On the other hand, contributions from purely repulsive potentials, such as hard spheres, are always positive.
