Derivation of a simple coordination number model using a given equation of state and the effective pair potential function

In this work, a simple coordination number (C.N.) model for the (9, 3) Lennard-Jones (LJ) fluid is obtained. It is based on the comparison of the internal pressure derived from a given equation of state (EoS) with the internal pressure derived from the (9, 3) LJ fluid as an effective pair potential (EPP). This model reproduces well the thermodynamic properties of the fluid such as internal energy, and the C.N. which is comparable with the Monte Carlo simulation data for the C.N. in the high-density region. In addition, the obtained C.N. can predict the first shell radial distribution function, g(r), of the fluid as well.