Second order of perturbation theory correction to the radial distribution function of a liquid with the interaction potential of hard spheres plus a square-well

A liquid with the interaction potential of hard spheres plus a square-well is analyzed using the Monte-Carlo technique. Numerical results for the perturbation theory series over a square-well potential are obtained in the form of the Barker and Henderson discrete representation. Approximating expressions for the correction to a liquid radial distribution function in the second order of perturbation theory are presented. The obtained results allow us to define this correction with a root-mean-square deviation of about 0.007. It is shown that the given approach provides a complete calculation in the second order of perturbation theory, and also the determination of the third order correction to the free energy for a liquid interacting with the potential of the Lennard-Jones type.