Advanced

Gradient Corrections to Exchange Energies within Density Functional Theory

Svendsen, Per-Sverre (1996)
Abstract
The small-wavector expansions for the first- and second-order exchange energy kernels (second-and third-order functional density derivatives of the exchange energy) have been investigated. Expansion coefficients are found, both in the case of a statically screened Coulomb interaction and a 'bare' interaction. The ensuing series of gradient corrections to the local density approximation (LDA) is then given, with particular emphasis on the second-order and fourth-degree term. Exactly calculated exchange energies for model solids are compared to a truncated series of gradient terms. It is found that the first-principles gradient series can improve the LDA description of the exchange energy by two orders of magnitude for metallic s-p bonded... (More)
The small-wavector expansions for the first- and second-order exchange energy kernels (second-and third-order functional density derivatives of the exchange energy) have been investigated. Expansion coefficients are found, both in the case of a statically screened Coulomb interaction and a 'bare' interaction. The ensuing series of gradient corrections to the local density approximation (LDA) is then given, with particular emphasis on the second-order and fourth-degree term. Exactly calculated exchange energies for model solids are compared to a truncated series of gradient terms. It is found that the first-principles gradient series can improve the LDA description of the exchange energy by two orders of magnitude for metallic s-p bonded systems. In the case of semi-conductors the results are less accurate.



A scheme for obtaining exact Density-Functional orbitals and eigenvalues is tested on the Neon atom. These exact properties are compared to approximate ones within two so-called Generalized Gradient Approximation schemes. The schemes are found to give an accurate total energy, whereas the exchange-correlation potentials are of similar quality as within the LDA.



A method for obtaining total energies of solids from third-order perturbation theory is tried out in the case of impurities in the electron gas. The method turns out to work well for singly charged impurities. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Dr Gritsenko, Oleg
publishing date
type
Thesis
publication status
published
subject
keywords
thermodynamics, statistical physics, exchange energy, Density functional theory, gradient corrections, classical mechanics, Mathematical and general theoretical physics, response theory., quantum mechanics, gravitation, relativity, Matematisk och allmän teoretisk fysik, klassisk mekanik, kvantmekanik, relativitet, statistisk fysik, termodynamik, Fysicumarkivet A:1996:Svendsen
pages
6 pages
publisher
Per-Sverre Svendsen, Dept. of Theoretical Physics, Solvegata 14 A, 22362 LUND,
defense location
Lecture Hall B, Dept of Physics
defense date
1996-06-06 10:15
external identifiers
  • Other:ISRN: LUNFD 6/(TFME-1031)/1 - 110 (1996)
ISBN
91-628-2119-9
language
English
LU publication?
no
id
fff0a8ae-4a86-4f41-b5d9-c702fb65bc3b (old id 28538)
date added to LUP
2007-06-11 16:40:24
date last changed
2016-09-19 08:45:02
@misc{fff0a8ae-4a86-4f41-b5d9-c702fb65bc3b,
  abstract     = {The small-wavector expansions for the first- and second-order exchange energy kernels (second-and third-order functional density derivatives of the exchange energy) have been investigated. Expansion coefficients are found, both in the case of a statically screened Coulomb interaction and a 'bare' interaction. The ensuing series of gradient corrections to the local density approximation (LDA) is then given, with particular emphasis on the second-order and fourth-degree term. Exactly calculated exchange energies for model solids are compared to a truncated series of gradient terms. It is found that the first-principles gradient series can improve the LDA description of the exchange energy by two orders of magnitude for metallic s-p bonded systems. In the case of semi-conductors the results are less accurate.<br/><br>
<br/><br>
A scheme for obtaining exact Density-Functional orbitals and eigenvalues is tested on the Neon atom. These exact properties are compared to approximate ones within two so-called Generalized Gradient Approximation schemes. The schemes are found to give an accurate total energy, whereas the exchange-correlation potentials are of similar quality as within the LDA.<br/><br>
<br/><br>
A method for obtaining total energies of solids from third-order perturbation theory is tried out in the case of impurities in the electron gas. The method turns out to work well for singly charged impurities.},
  author       = {Svendsen, Per-Sverre},
  isbn         = {91-628-2119-9},
  keyword      = {thermodynamics,statistical physics,exchange energy,Density functional theory,gradient corrections,classical mechanics,Mathematical and general theoretical physics,response theory.,quantum mechanics,gravitation,relativity,Matematisk och allmän teoretisk fysik,klassisk mekanik,kvantmekanik,relativitet,statistisk fysik,termodynamik,Fysicumarkivet A:1996:Svendsen},
  language     = {eng},
  pages        = {6},
  publisher    = {ARRAY(0xb651050)},
  title        = {Gradient Corrections to Exchange Energies within Density Functional Theory},
  year         = {1996},
}