Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

Overview of Computer Simulation Methods 51

exactly true in computer simulations, because of the limited number of particles

used. On the other hand, the temperature is not fixed in this ensemble, so that

it must be calculated from averaging the instantaneous temperature as defined in

Equation 3.33.

In any case, we must correct for the truncation of the potential at r

c

. This may be

achieved by approximating the RDF beyond the cutoff distance by that corresponding

to the ideal gas, namely, g(r) = 1forr > r

c

. Then, the pressure equation (2.36) gives

for the correction term Z

c

the expression

Z

c

=−

2

3

π

ρ

k

B

T

∞



r

c

du(r)

dr

r

3

dr. (3.62)

Obviously, this correction is ...