A reference hypernetted-chain equation for soft potentials. Atomic and molecular Lennard-Jones systems

Abstract

A recently proposed reference hypernetted-chain equation based on a semiphenomenological bridge function due to Verlet is reformulated for atomic and molecular Lennard-Jones liquids. In this new approximation we treat the size of the reference-system hard particles as a function of density and temperature through a functional relationship presented herein. The theory yields excellent results for the structure and thermodynamics of atomic Lennard-Jones liquids over a wide range of temperature and density and is quite satisfactory for Lennard-Jones homonuclear diatomics.

Structure and thermodynamics of heteronuclear two-centre Lennard-Jones fluids from Monte Carlo simulation and a reference hypernetted chain equation

“…where (9) with a = 1.62 • 10 -3 (see [2]) and 7 = ab/a,. This expression reduces to equation (12) of [2] whenever a, = ab( 7 = 1), i.e.…”

“…However, this has to be complemented by a criterion to determine the hard sphere diameters d, and db. In previous works [2,3] we proposed an expression for this purpose in the context of homonuclear fluids, which led to good results for two classes of molecular fluid system: pure 2CLJ, and 2CLJQ. There, we found an almost optimum relation between the hard sphere diameters and the thermodynamic parameters (T and p) of the system studied.…”

“…In recent works [1][2][3], we formulated a reference hypernetted chain approximation, denoted by RHNC-VM, that furnished remarkably good results for centrosymmetric linear molecules, such as homonuclear two-centre Lennard-Jones (2CLJ) [2] and quadrupole two-centre Lennard-Jones (2CLJQ) [3]. In these instances, the reference system is taken to be a homonuclear hard diatomic fluid in which the atomic (or site) diameter depends explicitly on temperature and density and on the Lennard-Jones parameters (e and a) of the system of interest.…”

“…This is done by a straightforward generalization of the scheme proposed in [1][2][3] in such a way that the original expressions are recovered when the system is homonuclear. Nonetheless, an accurate treatment requires the introduction of a new adjustable parameter to determine the different atomic diameters of the reference system.…”

“…Nonetheless, an accurate treatment requires the introduction of a new adjustable parameter to determine the different atomic diameters of the reference system. This, and the parameter ~ for the homonuclear system (see [2]), are treated on the same footing.…”