Correlation functions LMBW equation

This is our new equation for the single-site density distributions which generalizes the LMBW equation (2) to polyatomic fluids, below called a site-site LMBW (SS-LMBW) equation [47]. As distinct from the site-site DFT approaches [20-24], the SS-LMBW equation properly treats the short- and long-range correlations coupled in the site-site direct correlation function Cy (r2, rs). The SS-LMBW theory also differs from the RISM approach to inhomogeneous polyatomic fluids derived within the density functional formalism by Chandler et al. [25,26]. In Equations (3.7) and (3.13) of Ref. [26] for the site density profiles p (r), the orientational averaging with the intramolecular matrix (r 12)... 

Since the approximation (19)-(20) to the inhomogeneous direct correlation function < ay(ri, F2) spans it between the homogeneous ones of the bulk phases c y(r p ), a suitable way to ensure the existence of solutions to the SS-LMBW equation (18) is to optimize the expansion coefficients >, (p). First we span the vector of site densities... 

For a planar interface the interpolation (19)-(20) of the inhomogeneous site-site direct correlation function in terms of the homogeneous ones simplifies the SS-LMBW equation (18) to the form... 

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