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

The second‐order term in the free energy, $A_2$ , 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 $A_2$ 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.