Potential Functions for Anisotropic Molecules

Perhaps the most significant difficulty in the computer simulation of polyatomic fluids is the formulation of the intermolecular potential function. Extremely little is known about the details of anisotropic molecular interactions, and the possibilities for modeling are restricted by considerations of practicality for computer applications. In this section we shall discuss several approaches that have been used to model the interactions of anisotropic molecules. 

The interactions of diatomic molecules have been treated in two fashions. In one case, orientation-dependent dipolar and quadrupolar interactions are superimposed on a spherically symmetric potential. Computer simulations of N2 and CO have been carried out using the Stockmayer potential, which is a sum of a center-to-center Lennard-Jones potential and a number of multipole interaction terms. Alternately, the N2 molecule can be envisioned as two bound force centers, each of which interacts isotropically with force centers on other molecules. The total potential of two nitrogen molecules is thus the sum of four terms. 

Corner has generalized the force center concept to include all moderately elongated molecules with approximate cylindrical symmetry (e.g., normal butane)/ In Corner s scheme, each molecule is represented by four force centers arranged on a line. The force centers are equally spaced by a distance determined by the overall length ratio of the molecule. The interaction of two molecules is then taken to be the sum of sixteen Lennard-Jones terms between the force centers on distinct molecules. In order to simplify the complicated superposition of potentials, Corner numerically fit the sum of Lennard-Jones terms to a single Lennard-Jones potential for the two molecules. The Lennard-Jones parameters a and e that appear in the resultant potential are no longer constant, but are functions of the relative orientation of the two molecules. 

x is determined by the anisotropy of the ellipsoids. Given the axial ratio a = then 

the Gaussian overlap model generates a strength parameter e and a range parameter a that are determined by the relative orientation of the two molecules. These two parameters may now be used in any of a variety of two-parameter potentials that have been proposed to describe atomic interactions. For example, we may use e(ui, U2) and o-(Ui, O2, r) in the Lennard-Jones (12-6) potential 

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