Category:Van der Waals functionals

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 for 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:

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

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:

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

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

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

How to

• Atom-pairwise and many-body methods for van der Waals interactions (selected with the IVDW tag):
  • Methods from Grimme et al.:
    • DFT-D2^[2]
    • DFT-D3^[3][4]
  • Methods from Tkatchenko, Scheffler et al.:
    • Tkatchenko-Scheffler method^[5]
    • Tkatchenko-Scheffler method with iterative Hirshfeld partitioning^[6][7]
    • Self-consistent screening in Tkatchenko-Scheffler method^[8]
    • Many-body dispersion energy^[8][9]
    • Many-body dispersion energy with fractionally ionic model for polarizability^[10][11]
  • DDsC dispersion correction^[12][13]
  • DFT-ulg^[14]
• Nonlocal vdW-DF functionals for van der Waals interactions: LUSE_VDW and IVDW_NL

References