Gradient Corrections to Exchange Energies within Density Functional Theory

Research output: ThesisDoctoral Thesis (compilation)


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.


  • Per-Sverre Svendsen
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Condensed Matter Physics


  • 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
Original languageEnglish
Awarding Institution
Supervisors/Assistant supervisor
Award date1996 Jun 6
  • Per-Sverre Svendsen, Dept. of Theoretical Physics, Solvegata 14 A, 22362 LUND,
Print ISBNs91-628-2119-9
Publication statusPublished - 1996
Publication categoryResearch
Externally publishedYes

Bibliographic note

Defence details Date: 1996-06-06 Time: 10:15 Place: Lecture Hall B, Dept of Physics External reviewer(s) Name: Gritsenko, Oleg Title: Dr Affiliation: [unknown] ---

Related research output

Svendsen, P-S., 1997, In : Physica Scripta. 55, 4, p. 459-463

Research output: Contribution to journalArticle

Springer, M., Svendsen, P-S. & Ulf von Barth, 1996, In : Physical Review B. 54, p. 17392

Research output: Contribution to journalArticle

Svendsen, P. S. & Ulf von Barth, 1996, In : Physical Review B. 54, 17402.

Research output: Contribution to journalArticle

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