Category:Exchange-correlation functionals

In the Kohn-Sham (KS) formulation of density functional theory (DFT)^[1][2], the total energy is given by

${\displaystyle E_{\rm tot}^{\rm KS} = -\frac{1}{2}\sum_{i}\int\psi_{i}^{*}({\bf r})\nabla^{2}\psi_{i}({\bf r})d^{3}r + \frac{1}{2}\int\int\frac{\rho({\bf r})\rho({\bf r'})}{\left\vert{\bf r}-{\bf r'}\right\vert}d^{3}rd^{3}r' + E_{\rm xc} + \int v_{\rm en}({\bf r})\rho({\bf r})d^{3}r + \frac{1}{2}\sum_{A\ne B}\frac{Z_{A}Z_{B}}{\left\vert{\bf R}_{A}-{\bf R}_{B}\right\vert} }$

where the terms on the left-hand side represent the non-interacting kinetic energy of the electrons, the Classical Coulomb Hartree term, the exchange-correlation energy, the electrons-nuclei attraction energy and the nuclei-nuclei repulsion energy. The orbitals <math>\psi_{i}<\math>

Theoretical Background

• Hybrid functionals: Hartree-Fock and HF/DFT hybrid functionals.
• L(S)DA (on-site interactions): LDAUTYPE.
• van der Waals:
  • DFT-D2 method.
  • DFT-D3 method.
  • DDsC dispersion correction.
  • Many-body dispersion energy.
  • Tkatchenko-Scheffler method.
  • Tkatchenko-Scheffler method with iterative Hirshfeld partitioning.
  • Self-consistent screening in Tkatchenko-Scheffler method.
  • VdW-DF functional of Langreth and Lundqvist et al.

How to

• Hybrid functionals: Specific hybrid functionals.
• Meta GGA's: METAGGA.
• L(S)DA (on-site interactions): LDAUTYPE.
• van der Waals:
  • Main tag for van der Waals algorithm: IVDW
  • DFT-D2 method.
  • DFT-D3 method.
  • DDsC dispersion correction.
  • Many-body dispersion energy.
  • Tkatchenko-Scheffler method.
  • Tkatchenko-Scheffler method with iterative Hirshfeld partitioning.
  • Self-consistent screening in Tkatchenko-Scheffler method.
  • VdW-DF functional of Langreth and Lundqvist et al.