dorsal/arxiv
View SchemaDensity Functional Theory -- an introduction
| Authors | Nathan Argaman, Guy Makov |
|---|---|
| Categories | |
| ArXiv ID | physics/9806013 |
| URL | https://arxiv.org/abs/physics/9806013 |
| DOI | 10.1119/1.19375 |
| Journal | American Journal of Physics 68 (2000), 69-79 |
Abstract
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often considered too lengthy to be included in various curricula. An alternative introduction to DFT is presented here, drawing on ideas which are well-known from thermodynamics, especially the idea of switching between different independent variables. The central theme of DFT, i.e. the notion that it is possible and beneficial to replace the dependence on the external potential v(r) by a dependence on the density distribution n(r), is presented as a straightforward generalization of the familiar Legendre transform from the chemical potential (\mu) to the number of particles (N). This approach is used here to introduce the Hohenberg-Kohn energy functional and to obtain the corresponding theorems, using classical nonuniform fluids as simple examples. The energy functional for electronic systems is considered next, and the Kohn-Sham equations are derived. The exchange-correlation part of this functional is discussed, including both the local density approximation to it, and its formally exact expression in terms of the exchange-correlation hole. A very brief survey of various applications and extensions is included.
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"abstract": "Density Functional Theory (DFT) is one of the most widely used methods for\n\"ab initio\" calculations of the structure of atoms, molecules, crystals,\nsurfaces, and their interactions. Unfortunately, the customary introduction to\nDFT is often considered too lengthy to be included in various curricula. An\nalternative introduction to DFT is presented here, drawing on ideas which are\nwell-known from thermodynamics, especially the idea of switching between\ndifferent independent variables. The central theme of DFT, i.e. the notion that\nit is possible and beneficial to replace the dependence on the external\npotential v(r) by a dependence on the density distribution n(r), is presented\nas a straightforward generalization of the familiar Legendre transform from the\nchemical potential (\\mu) to the number of particles (N). This approach is used\nhere to introduce the Hohenberg-Kohn energy functional and to obtain the\ncorresponding theorems, using classical nonuniform fluids as simple examples.\nThe energy functional for electronic systems is considered next, and the\nKohn-Sham equations are derived. The exchange-correlation part of this\nfunctional is discussed, including both the local density approximation to it,\nand its formally exact expression in terms of the exchange-correlation hole. A\nvery brief survey of various applications and extensions is included.",
"arxiv_id": "physics/9806013",
"authors": [
"Nathan Argaman",
"Guy Makov"
],
"categories": [
"physics.ed-ph",
"cond-mat",
"physics.chem-ph",
"physics.comp-ph"
],
"doi": "10.1119/1.19375",
"journal_ref": "American Journal of Physics 68 (2000), 69-79",
"title": "Density Functional Theory -- an introduction",
"url": "https://arxiv.org/abs/physics/9806013"
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