dorsal/arxiv
View SchemaThe locality hypothesis in density-functional theory: An exact theorem
| Authors | Ingvar Lindgren, Sten Salomonson |
|---|---|
| Categories | |
| ArXiv ID | physics/0402029 |
| URL | https://arxiv.org/abs/physics/0402029 |
Abstract
The locality hypothesis in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A \bf{58}, R12 (1998); \it{ibid.} A \bf{65}, 010502 (2001); Adv. Quant. Chem, \bf{43}, 1 (2003)] claimed that this hypothesis is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have in a Comment to the Physical Review [Phys. Rev. A \bf{67}, 056501 (2003)] commented upon these works and recently extended the arguments [Adv. Quant. Chem. \bf{43}, 95 (2003)]. We have shown that there is no such conflict and that the locality hypothesis is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the $1s2s ^3S$ state of helium that generates the many-body electron density and shown that the corresponding $2s$ Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. In addition to verifying the locality hypothesis, this confirms the theorem regarding the Kohn-Sham eigenvalue of the highest occupied orbital.
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"abstract": "The locality hypothesis in density-functional theory (DFT) states that the\nfunctional derivative of the Hohenberg-Kohn universal functional can be\nexpressed as a local multiplicative potential function, and this is the basis\nof DFT and of the successful Kohn-Sham model. Nesbet has in several papers\n[Phys. Rev. A \\bf{58}, R12 (1998); \\it{ibid.} A \\bf{65}, 010502 (2001); Adv.\nQuant. Chem, \\bf{43}, 1 (2003)] claimed that this hypothesis is in conflict\nwith fundamental quantum physics, and as a consequence that the Hohenberg-Kohn\ntheory cannot be generally valid. We have in a Comment to the Physical Review\n[Phys. Rev. A \\bf{67}, 056501 (2003)] commented upon these works and recently\nextended the arguments [Adv. Quant. Chem. \\bf{43}, 95 (2003)]. We have shown\nthat there is no such conflict and that the locality hypothesis is inherently\nexact. In the present work we have furthermore verified this numerically by\nconstructing a local Kohn-Sham potential for the $1s2s ^3S$ state of helium\nthat generates the many-body electron density and shown that the corresponding\n$2s$ Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine\ndigits. Similar result is obtained with the Hartree-Fock density. In addition\nto verifying the locality hypothesis, this confirms the theorem regarding the\nKohn-Sham eigenvalue of the highest occupied orbital.",
"arxiv_id": "physics/0402029",
"authors": [
"Ingvar Lindgren",
"Sten Salomonson"
],
"categories": [
"physics.atom-ph"
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"title": "The locality hypothesis in density-functional theory: An exact theorem",
"url": "https://arxiv.org/abs/physics/0402029"
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