Structural properties pair direct correlation function

The difference between the two calculation is displayed more dramatically in Figure 2, where the short-range direct correlation functions arising from the two calculations are plotted. They differ markedly. As show below, a convenient theory of the wall - solution interface uses moments of these functions as input into the calculation of the structure and properties of the inhomogeneous system. Not shown in Figures 1 and 2 are the predictions of the well-known HNC approximation, which yields unacceptable CFl pair correlation functions. 

In this section, we review some of the important formal results in the statistical mechanics of interaction site fluids. These results provide the basis for many of the approximate theories that will be described in Section III, and the calculation of correlation functions to describe the microscopic structure of fluids. We begin with a short review of the theory of the pair correlation function based upon cluster expansions. Although this material is featured in a number of other review articles, we have chosen to include a short account here so that the present article can be reasonably self-contained. Cluster expansion techniques have played an important part in the development of theories of interaction site fluids, and in order to fully grasp the significance of these developments, it is necessary to make contact with the results derived earlier for simple fluids. We will first describe the general cluster expansion theory for fluids, which is directly applicable to rigid nonspherical molecules by a simple addition of orientational coordinates. Next we will focus on the site-site correlation functions and describe the interaction site cluster expansion. After this, we review the calculation of thermodynamic properties from the correlation functions, and then we consider the calculation of the dielectric constant and the Kirkwood orientational correlation parameters. 

Closely related to the QHS fluid is the QHSY fluid. In this regard, one notes that while QHS state points can be characterized with two parameters, that is, (Ag, pI ), QHSY state points need two additional parameters, which are the de Boer quantumness /C=hl(me(T and the inverse range of the attraction k = kdifferent ranges of conditions within (0.2 < A < 0.6 0.27 pi 0.5). Use of direct correlation functions (BDH) was also made, and its reliability to identify the onset of critical behavior was clearly stated [108]. These QHSY studies covered the following issues mechanical and pair structural properties [108] the asymptotic behavior of the pair radial correlations, with a view to the existence of FW lines [159] and the features of triplet correlations in Fourier space [161]. 

This could be achieved with rigor if the statistical mechanical theory of the liquid state were quantitatively accurate. The difficulty is that complete description of the liquid structure involves specification of not only the two-body correlations, but three-body and higher correlations as well. Some properties of the three-body correlation function g R, R2,Ri) are available experimentally from the density derivative of S Q) or g R) (Egelstaff, 1992), but the experiments in general yield a direct measure of only the pair correlation function. Therefore essentially all the existing liquid state theories invoke an assumed form for the three-particle correlation function (see, e.g., Hansen and McDonald, 1976 Egelstaff, 1992) and theoretical models. 

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