Gradient Corrections to Exchange Energies within Density Functional Theory
(1996) Abstract
 The smallwavector expansions for the first and secondorder exchange energy kernels (secondand thirdorder 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 secondorder and fourthdegree term. Exactly calculated exchange energies for model solids are compared to a truncated series of gradient terms. It is found that the firstprinciples gradient series can improve the LDA description of the exchange energy by two orders of magnitude for metallic sp bonded... (More)
 The smallwavector expansions for the first and secondorder exchange energy kernels (secondand thirdorder 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 secondorder and fourthdegree term. Exactly calculated exchange energies for model solids are compared to a truncated series of gradient terms. It is found that the firstprinciples gradient series can improve the LDA description of the exchange energy by two orders of magnitude for metallic sp bonded systems. In the case of semiconductors the results are less accurate.
A scheme for obtaining exact DensityFunctional orbitals and eigenvalues is tested on the Neon atom. These exact properties are compared to approximate ones within two socalled Generalized Gradient Approximation schemes. The schemes are found to give an accurate total energy, whereas the exchangecorrelation potentials are of similar quality as within the LDA.
A method for obtaining total energies of solids from thirdorder 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:
http://lup.lub.lu.se/record/28538
 author
 Svendsen, PerSverre
 supervisor
 opponent

 Dr Gritsenko, Oleg
 publishing date
 1996
 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
 PerSverre Svendsen, Dept. of Theoretical Physics, Solvegata 14 A, 22362 LUND,
 defense location
 Lecture Hall B, Dept of Physics
 defense date
 19960606 10:15
 external identifiers

 Other:ISRN: LUNFD 6/(TFME1031)/1  110 (1996)
 ISBN
 9162821199
 language
 English
 LU publication?
 no
 id
 fff0a8ae4a864f41b5d9c702fb65bc3b (old id 28538)
 date added to LUP
 20070611 16:40:24
 date last changed
 20160919 08:45:02
@phdthesis{fff0a8ae4a864f41b5d9c702fb65bc3b, abstract = {The smallwavector expansions for the first and secondorder exchange energy kernels (secondand thirdorder 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 secondorder and fourthdegree term. Exactly calculated exchange energies for model solids are compared to a truncated series of gradient terms. It is found that the firstprinciples gradient series can improve the LDA description of the exchange energy by two orders of magnitude for metallic sp bonded systems. In the case of semiconductors the results are less accurate.<br/><br> <br/><br> A scheme for obtaining exact DensityFunctional orbitals and eigenvalues is tested on the Neon atom. These exact properties are compared to approximate ones within two socalled Generalized Gradient Approximation schemes. The schemes are found to give an accurate total energy, whereas the exchangecorrelation potentials are of similar quality as within the LDA.<br/><br> <br/><br> A method for obtaining total energies of solids from thirdorder 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, PerSverre}, isbn = {9162821199}, 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 = {PerSverre Svendsen, Dept. of Theoretical Physics, Solvegata 14 A, 22362 LUND,}, title = {Gradient Corrections to Exchange Energies within Density Functional Theory}, year = {1996}, }