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DFT: Density Functional Theory (Read 9811 times)
Gerrit-Jan Linker
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DFT: Density Functional Theory
07.02.08 at 14:44:22
 
DFT: Density Functional Theory
 
Basic idea of DFT: relate the total ground-state energy of a system to its ground-state density rather than to a (un-observable) wave function as is done in e.g. Hartree Fock theory.
 
Density Functional Theory gives for some properties superior accuracy compared to Hartree-Fock (HF) theory and semi-empirical approaches. In contrast to conventional ab initio methods (MP2, CI, CC) it enables accurate treatment of systems with several hundreds of atoms.
 
Standard DFT is a ground state theory.
 
See also:
Quantum chemical methods
http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1202388089
DFT Wiki
http://en.wikipedia.org/wiki/Density_functional_theory
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« Last Edit: 08.02.11 at 22:37:22 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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Re: DFT: Density Functional Theory
Reply #1 - 24.07.08 at 23:09:29
 
Exchange-correlation functionals
 
Different exchange-correlation functionals are used in density functional theory (DFT):
 

  • Correlation functionals

    • LYP: Lyy-Yang-Parr (GGA)
    • P86: Perdew 86 (LDA)
    • PBE: Perdew-Becke-Ernzerhof (GGA)
    • PBESOL: GGA. PBE functional revised for solids
    • PWGGA: Perdew-Wang 91 (GGA)
    • PWLSD: Perdew-Wang 92 (GGA)
    • PZ: Perdew-Zunger (LDA)
    • VBH: von Barth-Hedin (LDA)
    • WL: GGA- Wilson-Levy
    • VWN: Vosko-Wilk-Nusair (LDA)

  • Exchange functionals

    • Becke GGA: Generalised Gradient Approximation
      Improvement over LDA in that the exchange-correlation is also made a function of the gradient of the density.
    • LDA: Dirac-Slater: Local Density Approximation
      exc at some position r can be computed exclusively from a value of the density at that position, i.e. the 'local' value of the density.
    • LSDA: Local Spin Density Approximation
    • BPW91
    • PBE: Perdew-Becke-Ernzerhof (GGA)
    • PBESOL: GGA, PBE functional revised for solids
    • PWGGA: Perdew-Wang 91 (GGA)
    • SOGGA: second order GGA
    • VBH: von Barth-Hedin (LDA)
    • WCGGA: GGA Wu-Cohen

     
  • Hybrid functionals

    • B3PW
    • B3LYP
    • PBE0: Adamo and Barone


 
Source:
Crystal09 manual
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« Last Edit: 06.12.12 at 11:22:20 by Gerrit-Jan Linker »  

Gerrit-Jan Linker
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DFT: Energy expression
Reply #2 - 25.02.11 at 19:55:54
 
DFT: Energy expression
 
E0[ρ] = Ts[ρ] + J[ρ] + Eext[ρ] +Exc[ρ]
 
Ts[ρ] = ∑iNi|-½▼²|ψi< =  Kinetic energy of the electrons
J[ρ] = ∫(ρaρb/Rab)dτab  =Electron Repulsion
Eext[ρ] = Nuclear attraction
Exc[ρ] = Exchange Correlation Energy
 
Approximations Exc :
Local Density Approximation (LDA, ρ)
Generalized Gradient Approximations (GGA, ▼ρ)
meta-GGA (MGGA, ▼²ρ or kin.orbital energy)
hybrid (includes portion of exact exchange)
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« Last Edit: 25.02.11 at 20:14:01 by Gerrit-Jan Linker »  

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