Density Functional for Hard Sphere Crystals: A Fundamental Measure Approach

Abstract

A new free energy density functional for hard spheres is presented, along the lines of the fundamental measure theory, which reproduces the Percus-Yevick equation of state and direct correlation function for the fluid, with a tensor weighted density. The functional, based on the zero-dimension limit, is exact for any one-dimensional density distribution of the spheres. The application to the hard sphere crystals gives excellent results, solving all of the qualitative problems of previous density functional approximations, including the unit cell anisotropy in the fcc lattice and the description of the metastable bcc lattice.

Density functional theory for hard-sphere mixtures: the White Bear version mark II

“…There are several other developments in FMT that were mainly concerned with improving the performance of FMT in highly confined geometries. These studies suggest to change the dependency of Φ on n 2 and n 2 [20,21] or to introduce new tensorial weighted densities [22]. It is worth pointing out that these improvements concerning the description of hard-sphere fluids in highly confined geometries are straightforwardly combined with the improvements on thermodynamics presented here.…”

“…This deficiency can be resolved empirically by modifying the third term in Eq. (12) [20,21], or more systematically by the recipe of Tarazona [22] who introduced an additional tensorial weighted density in the last term of Φ RF . There remains another factor which limits the accuracy of Φ RF , namely the equation of state obtained from Eq.…”

Density functional theory for a model colloid polymer mixture: bulk fluid phases

“…For HS the importance of this limit was demonstrated by Rosenfeld et al [19,20]. Later it was shown that the original Rosenfeld functional [18], as well as improved versions, can be obtained from a systematic treatment of superpositions of (up to three) such density peaks [21,22].…”

“…A strong guide for the general structure of the functional is provided by Percus's exact one-dimensional functional for hard rods [34]. In the case of HS knowledge of the exact zero-dimensional free energy was sufficient to derive a working theory [21], and was subsequently exploited to derive improved versions [22]. The same methodology was used to tackle other systems including penetrable spheres, which interact with a constant pair potential if they overlap [25], the Widom-Rowlinson model [26] and a needle-sphere mixture [28], as well as models for an amphiphilic [29] and a ternary mixture [30].…”

“…In the absence of polymer, 1 and 2 are equivalent to the free-energy densities for HS introduced in [18], and 3 is equivalent to the tensor treatment for pure HS in [22].…”