Tarazona weighted density

The Kierhk-Rosinberg [264] theory is formally similar to the treatment of Tarazona. They use four weight functions, which are chosen such that this theory exactly reproduced the Percus-Yevick result for the direct correlation function in the uniform hard-sphere fluid. However, these functions are independent of the density. In consequence, the calculation of the weighted density... 

When the smoothed or nonlocal density approximation (or NL-DFT model) is used, the weighting function is chosen so that the hard-sphere direct pair-correlation function is well described for the uniform fluid over a wide range of densities. One example of such a weighting function is the model proposed by Tarazona [69], which uses the Percus-Yevick theory for approximating the correlation function over a wide range of density. In this case, the weighting function is expanded as a power series of the smoothed density. The use of a smoothed density in NL-DFT provides an oscillating density profile expected of a fluid adjacent to a sohd surface, the existence of which is corroborated by molecular simulation results [17,18]. 

The form of the function efr ( ) is different in different versions of the smoothed-density approximation proposed by Somo-za and Tarazona [71, 72] and by Poniwier-ski and Sluckin [69, 73]. The density functional model of Somoza and Tarazona is based on the reference system of parallel hard ellipsoids that can be mapped into hard spheres. In the Poniwierski and Sluckin theory the effective weight function is determined by the Maier function for hard sphe-rocylinders and the expression for Ayr (p) is obtained from the Carnahan-Starling ex-... 

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