Thermodynamic significance to correct the location of first rising region in radial distribution function approximately estimated from Ornstein–Zernike integral equation theory for Lennard–Jones fluids

Abstract

We have calculated the excess internal energy, Uex, pressure through the virial route, pv, and excess chemical potential, μex, for one-component Lennard–Jones (LJ) fluids by using hypernetted chain (HNC), Kovalenko–Hirata (KH), Percus–Yevick (PY) and Verlet modified (VM) approximations in an Ornstein–Zernike (OZ) integral equation theory. The results have been compared with molecular dynamics simulation to examine the accuracy of each approximation at relatively high density region. HNC and KH approximations significantly overestimate the above three thermodynamic quantities, whereas PY and VM approximations give relatively accurate results. The analysis upon the integrand to evaluate Uex, pv and μex has revealed that the precise location of the first rising (FR) region in radial distribution function is the most important for the accurate evaluation of these quantities. We have applied an approximate bridge function pretending to adjust σ parameter in the LJ potential both to HNC and KH approximations, to obtain satisfactorily corrected results regarding Uex, pv and μex. Thus, we propose one of the necessary conditions for accurately evaluating thermodynamic quantities by using some approximated OZ theories: it is the proper location of the FR region in radial distribution functions.