Category:Van der Waals functionals: Difference between revisions

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E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
</math>
</math>
There are essentially two types of dispersion terms <math>E_{\text{c,disp}}</math> that have been proposed in the literature. The first type consists of a sum over the atom pairs <math>A-B</math>:
There are essentially two types of dispersion terms <math>E_{\text{c,disp}}</math> that have been proposed in the literature. The first type consists of a sum over the atom pairs <math>A</math>-<math>B</math>:
:<math>
:<math>
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}},
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}},
</math>
</math>
where <math>C_{n}^{AB}</math> are the dispersion coefficientsted by the distance $R_{AB}$ and $f_{n}^{\text{damp}}$ is a damping
where <math>C_{n}^{AB}</math> are the dispersion coefficientst, $R_{AB}$ is the distance between atoms <math>A</math> and <math>B</math> and $f_{n}^{\text{damp}}$ is a damping function.
function preventing Eq.~(\ref{Ecdisp1}) to become too large for small $R_{AB}$





Revision as of 14:55, 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 coefficientst, $R_{AB}$ is the distance between atoms and and $f_{n}^{\text{damp}}$ is a damping function.


van der Waals corrections

How to