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An exact analytic form for the second virial coefficient, valid for theentire range of temperature, is presented for the Lennard-Jones fluid in thispaper. It is derived by making variable transformation that gives rise to theHamiltonian mimicking a harmonic oscillator-like dynamics for negative energy.It is given in terms of parabolic cylinder functions or confluenthypergeometric functions. Exact limiting laws for the second virial coefficientin the limits of low and high temperatuers are also deduced for theLennard-Jones fluid.

Exact Analytic Second Virial Coefficient for the Lennard-Jones Fluid