A partitioned density functional theory of freezing: application to soft spheres

Structure of a soft-sphere fluid at a soft repulsive wall: A comparison of weighted density-functional theories

“…To remedy this, Kol and Laird [13] have demonstrated that if the excess free energy functional is partitioned into long and short range parts and only the short range part of the free energy is approximated by a MWDA scheme, the prediction of a stable bcc structure for the inverse sixth-power potential is realized. Motivated by these results, we have reformulated this partitioned WDA of Kol and Laird (KL WDA) within the context of CA WDA in order to apply it to current inhomogeneous fluid problem.…”

“…In partitioned WDA [13], the partitioning given in Eq. (15) is not exactly followed because the function, g ͑2͒ ͑r 1 , r 2 ; ͓͔͒, is not known, thus making the construction of an explicit expression for the free energy functional difficult.…”

“…In this work we compare three different weighted density-functional theories: the weighted density approximation of Curtin and Ashcroft (CA WDA) [12], a simplified version of the CA WDA by Denton and Ashcroft (DA WDA) [4,14], and the partitioned weighted density approximation of Kol and Laird (KL WDA) [13]. All of these methods require as input the excess Helmholtz free energy per particle f͑͒ and the two-body direct correlation function of the homogeneous fluid c͑r ; ͒, both of which can be obtained from experiment, simulation, or integral equation theory [22].…”

“…However, the application of WDA methods to inhomogeneous fluids with longer range repulsive cores, on the other hand, have not received much attention. In this study, we examine the structure of a simple model soft-sphere fluid at a soft wall as calculated by three different weighted density approximation schemes, namely, that of Curtin and Ashcroft (CA WDA) [12], a simplified WDA of Denton and Ashcroft (DA WDA) [14], and the partitioned WDA of Kol and Laird (KL WDA) [13]. The specific model system we study is an inverse-sixth power repulsive fluid against a stationary, structureless wall defined by a repulsive inverse twelth-power external potential.…”

“…Most classical DFT's fall into three classes: (a) perturbative methods based on functional Taylor-series expansions about some reference state [8,9]-usually the homogeneous phase, (b) nonperturbative methods based on weighted density-functional theories (WDFT) [11][12][13][14], or (c) methods based on the fundamental measure theory (FMT) of Rosenfeld [15]. For predicting the structure and thermodynamics of hard-sphere inhomogeous fluids, the highest accuracy theories are those based on fundamental measure theory.…”