Category:Exchange-correlation functionals: Difference between revisions

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

${\displaystyle E_{\rm tot}^{\rm KS}[\rho] = T_{\rm s}[\{\psi_{i}\}] + U_{\rm H}[\rho] + E_{\rm xc} + V_{\rm en}[\rho] + V_{\rm nn} }$

where ${\displaystyle T_{\rm s}}$ is the non-interacting kinetic energy of the electrons, ${\displaystyle J}$ the Hartree energy, the third term is the energy of the electrons-nuclei attraction interaction, and ${\displaystyle V_{\rm nn}}$ is the nuclei-nuclei repulsion energy.

${\displaystyle T_{\rm s}[\{\psi_{i}\}]=-\frac{1}{2}\sum_{i=1}^{N}\int \psi_{i}^{*}({\bf r})\nabla^{2}\psi_{i}({\bf r})d^{3}r }$

${\displaystyle V_{\rm en}[\rho] = \frac{1}{2}\int\int\frac{\rho({\bf r})\rho({\bf r'})} {\left\vert{\bf r}-{\bf r'}\right\vert}d^{3}rd^{3}r', }$

${\displaystyle U_{\rm H}[\rho] = \int v_{\rm ext}({\bf r})\rho({\bf r})d^{3}r }$

${\displaystyle \hat{V}_{\rm nn} = \sum_{A=1}^{M-1}\sum_{B=A+1}^{M} \frac{e^{2}}{4\pi\epsilon_{0}} \frac{Z_{A}Z_{B}}{\left\vert{\bf R}_{A}-{\bf R}_{B}\right\vert} }$

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.