Approximate Evaluation of the Second-Order Term in the Perturbation Theory of Fluids

The second-order term in the free energy, A2, as given by the Barker–Henderson perturbation theory is considered for the square-well and 6:12 potentials. The second-order term is written in terms of integrals of the distribution functions of the unperturbed hard-sphere system. If the superposition approximation is used for the third- and fourth-order distribution functions, these integrals may be evaluated fairly easily and values for A2 may be obtained. Comparison of these values with either the exact second-order term Monte Carlo calculations of the exact second-order term gives exact agreement for the lattice gas, fairly good agreement for the square-well potential, and good agreement for the 6:12 potential.