Category:Van der Waals functionals: Difference between revisions

From VASP Wiki
No edit summary
No edit summary
Line 13: Line 13:
The other type of dispersion correction is of the following type:
The other type of dispersion correction is of the following type:
:<math>
:<math>
E_{\text{c,disp}} = \frac{1}{2}\int\int\rho(\textbf{r})
E_{\text{c,disp}} = \frac{1}{2}\int\int n(\textbf{r})
\Phi\left(\textbf{r},\textbf{r}'\right)\rho(\textbf{r}')
\Phi\left(\textbf{r},\textbf{r}'\right) n(\textbf{r}')
d^{3}rd^{3}r',
d^{3}rd^{3}r',
</math>
</math>
which requires a double spatial integration and is therefore of the nonlocal type. The kernel <math>\Phi</math> depends on the electron density <math>\rho</math>, its derivative <math>\nabla\rho</math> as well as on <math>\left\vert\bf{r}-\bf{r}'\right\vert</math>. The nonlocal functionals are more expensive to calculate than semilocal functionals, however they are efficiently implemented by using FFTs {{cite|romanperez:prl:09}}.
which requires a double spatial integration and is therefore of the nonlocal type. The kernel <math>\Phi</math> depends on the electron density <math>n</math>, its derivative <math>\nabla n</math> as well as on <math>\left\vert\bf{r}-\bf{r}'\right\vert</math>. The nonlocal functionals are more expensive to calculate than semilocal functionals, however they are efficiently implemented by using FFTs {{cite|romanperez:prl:09}}.


More details on the various van der Waals types methods available in VASP and how to use them can be found in the pages listed below.  
More details on the various van der Waals types methods available in VASP and how to use them can be found in the pages listed below.  

Revision as of 14:43, 6 April 2022

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. This leads to the so-called van der Waals functionals:

There are essentially two types of dispersion terms that have been proposed in the literature. The first type consists of a sum over the atom pairs -:

where are the dispersion coefficients, is the distance between atoms and and 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:

which requires a double spatial integration and is therefore of the nonlocal type. The kernel depends on the electron density , its derivative as well as on . The nonlocal functionals are more expensive to calculate than semilocal functionals, however they are efficiently implemented by using FFTs [1].

More details on the various van der Waals types methods available in VASP and how to use them can be found in the pages listed below.

How to