Nonlocal density approximation

Calculations on T4H4 with symmetry show it to be less stable per Si atom by 7.3 or lOkcalmoU, respectively, by DPT (nonlocal density approximation), or Hartree-Fock (HF at the 6-31G(d)//6-31G(d) level) than Oh symmetry TgHg. Similarly, calculations on C21, symmetry T4Mc4 show it to be 7.4 and 7.8 kcal moU less stable per Si atom, respectively, than Cj and C4J, symmetry TgMeg. ... 

Before introducing the Nonlocal Density Approximations (NLDA s) for the OF-KEDF,we would like to briefly outline the essence of the ADA and the WDA for the XCEDF to aid our imderstanding later. 

On the other hand, the double integration form in Eqs. (48)-(50) suggests the following Simplified Nonlocal Density Approximation (SNDA), ... 

The results presented here were obtained in the framework of DFT by using a modified version of deMon code [43], All calculations were performed within the nonlocal density approximation employing the gradient-corrected functional of Perdew [44] for correlation and that of Perdew and Wang [45] for exchange energy (PPW) respectively. For some species test calculations using the local potential [46] were carried out. 

The choice of the weighting function w depends on the version of density functional theory used. For highly inhomogeneous confined fluids, a smoothed or nonlocal density approximation is introduced, in which the weighting function is chosen to give a good description of the hard sphere direct pair correlation function for the uniform fluid over a... 

The weighting factor in the function is again chosen to ensure that the Lindhard response is recovered. Functionals like Equation 1.105 are called simplified nonlocal density approximations. - ... 

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]. 

To avoid the dependence on orbitals when computing ELF, Gadre et al. [50] proposed in 1993 to utilize an approximate constmction of the 1-matrix by the application of a nonlocal density approximation. At the l-determinantal level of theory, the pair density is recovered from the knowledge of the 1-matrix. This allows to follow the procedure of Becke and Edgecombe and finally arrive at purely electron density-based variant of ELF. The so-caUed DELF shows topology similar to the one of ELF. 

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