The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice. Discussions, including implications of the method, and a short conclusion follow the description of the method. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment.
These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT.
#DFO FLAUNCHER PHYATTACK OR STRENGTH OR INDEPENDENT TRIAL#
We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF).
We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it.
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