The mean spherical approximation and effective pair potentials in liquids

Abstract

The mean spherical approximation (MSA) generalized for direct application to fluids with continuous intermolecular potentials. It is shown that, if the intermolecular potential is separated into a purely repulsive core and a weak tail as suggested by Weeks et al., then the generalized MSA includes the strengths of the Percus–Yevick (PY) and hypernetted‐chain (HNC) approximations with few of their weaknesses. At liquid state densities and temperatures the MSA pair correlation function is much more accurate than the corresponding PY and HNC pair correlation functions for the Lennard‐Jones (12–6) potential. The MSA equation may be inverted to give a semiempirical theory for deriving the pair potential from experimental x‐ray diffraction data. It is argued that the resulting pair potentials for liquid Na and liquid K are substantially more reliable than others previously obtained from x‐ray data.