Second virial coefficient for the Lennard–Jones potential

The second virial coefficient for the (12−6) Lennard–Jones potential and its first and second temperature derivatives are explicitely derived. All coefficients can be explicitly written as a linear combination of four modified Bessel functions which can be evaluated for every temperature with high degree of numerical accuracy. Detailed comparisons with the classical series expansion for the coefficient and its temperature derivatives are made. The use of these analytical, simple and closed formulae can be very valuable when using experimental p–V–T data to fit a Lennard–Jones potential.