Category:Van der Waals functionals

Theoretical background

The semilocal and hybrid functionals do not include the London dispersion forces, therefore they can not be applied reliably on systems where the London dispersion forces play an important role. To account more properly of the London dispersion forces in DFT, a correlation dispersion term can be added to the semilocal or hybrid functional:

${\displaystyle E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}. }$

There are essentially two types of dispersion terms ${\displaystyle E_{\text{c,disp}}}$ that have been proposed in the literature. The first type consists of a sum over the atom pairs ${\displaystyle A}$-${\displaystyle B}$:

${\displaystyle E_{\text{c,disp}} = -\sum_{A<B}\sum_{n=6,8,10,\ldots}f_{n}^{\text{damp}}(R_{AB})\frac{C_{n}^{AB}}{R_{AB}^{n}}, }$

where ${\displaystyle C_{n}^{AB}}$ are the dispersion coefficients, ${\displaystyle R_{AB}}$ is the distance between atoms ${\displaystyle A}$ and ${\displaystyle B}$ and ${\displaystyle f_{n}^{\text{damp}}}$ is a damping function. Many variants of such atom-pair corrections exist and the most popular of them are available in VASP (see list below).

The other type of dispersion correction is of the following type:

${\displaystyle E_{\text{c,disp}} = \frac{1}{2}\int\int\rho(\textbf{r}) \Phi\left(\textbf{r},\textbf{r}'\right)\rho(\textbf{r}') d^{3}rd^{3}r', }$

which requires a double spatial integration and are therefore of the nonlocal type. The kernel ${\displaystyle \Phi}$ depends on the electron density ${\displaystyle \rho}$, its derivative ${\displaystyle \nabla\rho}$ as well as on ${\displaystyle \left\vert\bf{r}-\bf{r}'\right\vert}$. The nonlocal functionals are more expensive to calculate than semilocal functionals, however they are efficiently implemented by using FFTs ^[1].

How to

• 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.