Theory and simulation of central force model potentials:
Application to homonuclear diatomic molecules
Fernando Bresme, Jose L.F. Abascal, and Enrique Lomba
ABSTRACT
Structure and thermodynamics of fluids made of particles that interact
via a central force model potential are studied by means of Monte Carlo
simulations and integral equation theories.
The hamiltonian has two terms, an intramolecular component represented by
a harmonic oscillator-like potential and an intermolecular interaction of the
Lennard-Jones type.
The potential does not fulfill the steric saturation condition so it leads to
a polydisperse system.
Firstly, we investigate the association (clustering) and thermodynamic
properties as a function of the potential parameters such as the intramolecular
potential depth, force constant and bond length.
It is shown that the atomic HNC integral equation provides a correct description
of the model as compared with simulation results.
The calculation of the HNC pseudospinodal curve indicates that the stability
boundaries between the vapor and liquid phases are strongly dependent on the
bond length and suggests that there might be a direct gas-solid transition for
certain elongations.
On the other hand we have assessed the ability of the model to describe the
thermodynamics and structure of diatomic liquids such as N_2 and halogens.
To this end we have devised a procedure to model the intramolecular
potential depth to reproduce the complete association limit (i.e., an
average number of bonds per particle equal to one).
This constraint is imposed on the Ornstein-Zernike (OZ) integral equation
in a straightforward numerical way.
The structure of the resulting fluid is compared with results from molecular
theories.
An excellent agreement between the HNC results for the associating fluid and
the RISM-HNC computations for the atom-atom model of the same fluid is
obtained.
There is also a remarkable coincidence between the simulation results for the
molecular and the associating liquids despite the polydisperse character of the
latter.
The stability boundaries in the complete association limit as predicted by
the HNC integral equation have been computed for different bond lengths
corresponding to real molecular liquids.
These boundaries appear close to the experimental liquid branch of the
vapor-liquid coexistence line of the molecular systems under consideration.