Evaluation of numerous J-, K-, L-, M-, and N-integrals used in perturbation theory

Following Barker, Pople and Gubbins & Gray, the u-expansion of the perturbation theory, used for developing equations of state for fluids, requires sets of J-, K-, L-, M-, and N-integrals as a function of ρ and T. These integrals are calculated here from pair and triplet correlation functions, which were derived in a previous communication, using particle configurations from extensive Monte-Carlo simulations of a Lennard-Jones fluid. The pair and triplet correlation functions are based on 27,615 state points covering a ρ∗-T∗ space from 0.002−1.41 and 0.45−25 in reduced variables, respectively, which are also the range of the calculated integral functions. Quadruplet correlation functions, required by the M- and N-integrals, were calculated using the trans-superposition approximation, using pair and triplet correlation functions. A total of 597 J, 90 K, 256 L, 4 M, and 4 N ρ∗-T∗ functions are reported describing those integrals. The number of available values for each individual integral at different ρ∗-T∗ state points are 27,615 for the J-, and in the range of 6999–7053, 6789–7055, 6440–6587, 6544–6751 for the K-, L-, M-, and N-integrals, respectively. The integrals are formulated and fitted over the whole available range of the ρ∗-T∗-space.