Analytical treatment of second virial coefficient over Lennard-Jones (2n − n) potential and its application to molecular systems

•Established the general analytical formulae for the second virial coefficient.•The formulae are expressed through the well-known Gamma functions.•Formulae are especially useful in the calculation of various properties for molecules.

We have given analytical formulae for computing the second virial coefficient depending on the intermolecular potential energy. Computationally simple and useful formulas are derived for the second virial coefficient using the Lennard-Jones (2n − n) potential. As an example of the effectiveness of the method we present the calculation results of the second virial coefficients of the molecules He, Ne, Ar, Kr, Xe, N2, CH4, CF4, H2, CO2, C2H4, C6H6, O2, CO, C2H6, C3H8, C(CH3)4, C6H6–CH4O, C6H6–C2H6O, C6H6–C3H6O and C6H6–C4H10O. The results of the calculations are in good agreement with the data available in the literature.

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