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

Following Barker, Pople and Gubbins &amp; Gray, the <i>u</i>-expansion of the perturbation theory, used for developing equations of state for fluids, requires sets of <i>J</i>-, <i>K</i>-, <i>L</i>-, <i>M</i>-, and <i>N</i>-integrals as a function of <i>ρ</i> and <i>T</i>. These integrals are calculated here from pair and triplet correlation functions, which were derived in a previous communication, using particle configurations from extensive <i>Monte-Carlo</i> simulations of a <i>Lennard-Jones</i> 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 <i>M</i>- and <i>N</i>-integrals, were calculated using the <i>trans-superposition</i> approximation, using pair and triplet correlation functions. A total of 597 <i>J</i>, 90 <i>K</i>, 256 <i>L</i>, 4 <i>M</i>, and 4 <i>N</i> 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 <i>J-</i>, and in the range of 6999–7053, 6789–7055, 6440–6587, 6544–6751 for the <i>K-</i>, <i>L-</i>, <i>M-</i>, and <i>N-</i>integrals, respectively. The integrals are formulated and fitted over the whole available range of the ρ∗-T∗-space.