Manoj K Harbola
Articles written in Bulletin of Materials Science
Volume 26 Issue 1 January 2003 pp 63-67
Many electron effects in semiconductor quantum dots
R K Pandey Manoj K Harbola V Ranjan Vijay A Singh
Semiconductor quantum dots (QDs) exhibit shell structures, very similar to atoms. Termed as ‘artificial atoms’ by some, they are much larger (1 100 nm) than real atoms. One can study a variety of manyelectron effects in them, which are otherwise difficult to observe in a real atom. We have treated these effects within the local density approximation (LDA) and the Harbola–Sahni (HS) scheme. HS is free of the selfinteraction error of the LDA. Our calculations have been performed in a three-dimensional quantum dot. We have carried out a study of the size and shape dependence of the level spacing. Scaling laws for the Hubbard ‘𝑈’ are established.
Volume 26 Issue 1 January 2003 pp 69-74
Obtaining Kohn–Sham potential without taking the functional derivative
Over the past decade and a half, many new accurate density functionals, based on the generalized gradient approximation, have been proposed, and they give energies close to chemical accuracy. However, accuracy of the energy functional does not guarantee that its functional derivative, which gives the corresponding potential, is also accurate all over space. For example, although the Becke88 exchange–energy functional gives very good exchange energies, its functional derivative goes as $-\frac{1}{r^2}$ in comparison to the correct $-\frac{1}{r}$ for $r \rightarrow \infty$, where 𝑟 is the distance of the electron from a finite system. On the other hand, accuracy of the potential is of prime importance if one is interested in properties other than the total energy; properties such as optical response depend crucially on the potential in the outer regions of a system. In this paper we present a different approach, based on the ideas of Harbola and Sahni, to obtain the potential directly from the energy density of a given approximation, without taking recourse to the functional derivative route. This leads to a potential that is as accurate as the functional itself. We demonstrate the accuracy of our approach by presenting some results obtained from the Becke88 functional.
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