Category:Van der Waals functionals: Difference between revisions

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d^{3}rd^{3}r',
d^{3}rd^{3}r',
</math>
</math>
which requires a double spatial integration. The kernel <math>\Phi</math> depends on the electron density <math>\rho</math>, it's derivative <math>\nabla\rho</math> as well as on <math>\left\vert\bf{r}_{1}-\bf{r}_{2}\right\vert</math>.
which requires a double spatial integration. The kernel <math>\Phi</math> depends on the electron density <math>\rho</math>, it's derivative <math>\nabla\rho</math> as well as on <math>\left\vert\bf{r}-\bf{r}_{2}'\right\vert</math>.





Revision as of 20:14, 10 March 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:

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. The kernel depends on the electron density , it's derivative as well as on .


How to