Weighted density approximation scheme

Other non-local density functional schemes have also been used to solve the problem of the LDA in relation to the electron affinity of atoms and clusters. One of those non-local schemes is the weighted-density-approximation (WDA), briefly mentioned in Sects. 2.2 and 2.3 above. In this scheme the large-r behavior of V,c(f) is given correctly (see Ref. [48] for details) and, as a consequence, electron affinity levels are bound. Figure 7 gives the calculated affinities of Aluminium clusters [49]. The spherical jellium model was used in this calculation and the affinities were obtained from the total energies of neutral and... 

Figure 16. The counterion density near a charged wall for the DFT scheme. Conditions as in Fig. 14. DFT denotes the density functional theory based on the fundamental measure theory [78], and WDA denotes the weighted density approximation based on the generalized Carnahan-Starling equation [75].

Introduction of the AWF within the ADA and the SADA allows for an extra degree of freedom so that the correct LR behavior can be exactly obeyed. Then, the explicit enforcement of the idempotency property on the DM 1 should in principle determine an unique functional form for the TBFWV of the AWE We have started to work on this idea numerical results will be published elsewhere. For later reference, we call this scheme the Weighted-Average-Density Approximation (WADA)... 

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