Weighted-density approximation

In general, different approximations are invoked for the hard-core contribution and the attractive contribution to the free energy functional. For the hardcore contribution, two accurate approximations can be obtained from the fundamental measure theory [108] and the weighted density approximation... 

The other two approaches divide the excess functional into a hard-core and an attractive part with different approximations for the two. Rosinberg and coworkers [126-129] have derived a functional from Wertheim s first-order perturbation theory of polymerization [130] in the limit of complete association. Woodward, Yethiraj, and coworkers [39,131-137] have used the weighted density approximation for the hard-core contribution to the excess free energy functional, that is,... 

While the LSD exchange-correlation hole is accurate for small interelec-tronic separations (Sect. 2.3), it is less satisfactory at large separations, as discussed in Sect. 2.5. For example, consider the hole for an electron which has wandered out into the classically-forbidden tail region around an atom (or molecule). The exact hole remains localized around the nucleus, and in Sect. 2.5 we give explicit results for its limiting form as the electron moves far away [19]. The LSD hole, however, becomes more and more diffuse as the density at the electron s position gets smaller, and so is quite incorrect. The weighted density approximation (WDA) and the self-interaction correction (SIC) both yield more accurate (but not exact) descriptions of this phenomenon. 

Successful density functional approximations such as the PW91 GGA or the self-interaction correction (SIC) [57] to LSD recover [19] LSD values for the on-top hole density and cusp. The weighted density approximation (WDA) [41,42], which recovers the LSD exchange hole density but not the LSD correlation hole density [19] in the limit u -> 0, needs improvement in this respect. 

In summary, all exercises so far seem to lead nowhere simple-minded extensions based on the TF and vW functionals hit a dead end. A more innovative path has to be taken. Fortunately, there are such paths, mainly fueled by the advances in the design of the XCEDF s, namely the Average-Density Approximation (ADA) " " and the Weighted-Density Approximation (WDA). > 5 ... 

Wu Z, Cohen RE, Singh DJ (2004) Comparing die weighted density approximation with die LDA and GGA for ground-state properties of ferroelectric perovskites, Phys Rev B, 70 104112... 

Marzari N, Singh (2004) Dielectric response of oxides in die weighted density approximation,... 

Sadd M, Teter MP (1996) Weighted density approximation applied to diatomic molecules, Phys... 

An alternative approach under the heading of weighted density approximation (WDA) attempts to model the density dependence of the pair correlation function of inhomogeneous systems. 

To improve upon these defects, one has to go beyond the LDA The (modified) weighted density approximation [189] retains the correct asymptotic behaviour of and improves the response properties of metal clusters [162, 165]. A different route to improvement provides the self-interaction correction (SIC) of Perdew Zunger [37], where the spurious self-interaction of the LDA is compensated by additional terms in the ground-state potential [166] and in the effective perturbing potential as well [167] (Full-SIC[... 

Another kind of approach to expressing A[p] leads to what are referred to as weighted density approximations (WDAs). In the earliest of these approximations to be applied to SFE [122,123], Aex[p] is written in the form... 

The simulation results for coexistence properties are from Hoover and Ree [24] and the value of L is from the work of Ohnesorge et al. [135], The result from Barker s SCF theory [94] is from the leading term (order a ) in an expansion of the mean square displacement in powers of a = (p p/p) - 1 and may be an underestimate of the true value from that theory, SCF, self-consistent field LJD, Lennard-Jones and Devonshine MWDA, modified weighted-density approximation GELA, generalized effective liquid approximation FMF, fundamental measures functional. 

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