Category:Van der Waals functionals: Difference between revisions

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== 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 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''':
:<math>
E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
</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>
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>
where <math>C_{n}^{AB}</math> are the dispersion coefficients, <math>R_{AB}</math> is the distance between atoms <math>A</math> and <math>B</math> and <math>f_{n}^{\text{damp}}</math> 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 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 term can be added to the semilocal or hybrid functional:
The other type of dispersion correction is of the following type:
:<math>
:<math>
E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}},
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'.
</math>
</math>
It requires a double spatial integration and is, therefore, of nonlocal. The kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the distance <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 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 {{TAG|IVDW}} tag):
**Methods from Grimme et al.:
***[[DFT-D2]]{{cite|grimme:jcc:06}}
***[[DFT-D3]]{{cite|grimme:jcp:10}}{{cite|grimme:jcc:11}}
***[[DFT-D4]]{{cite|caldeweyher:jcp:2019}} (available as of VASP.6.2 as [[Makefile.include#DFT-D4_.28optional.29|external package]])
**Methods from Tkatchenko, Scheffler et al.:
***[[Tkatchenko-Scheffler method]]{{cite|tkatchenko:prl:09}}
***[[Tkatchenko-Scheffler method with iterative Hirshfeld partitioning]]{{cite|bucko:jctc:13}}{{cite|bucko:jcp:14}}
***[[Self-consistent screening in Tkatchenko-Scheffler method]]{{cite|tkatchenko:prl:12}}
***[[Many-body dispersion energy]]{{cite|tkatchenko:prl:12}}{{cite|ambrosetti:jcp:14}}
***[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite|gould:jctc:2016_a}}{{cite|gould:jctc:2016_b}}
***[[LIBMBD_METHOD|Library libMBD of many-body dispersion methods]]{{cite|libmbd_1}}{{cite|libmbd_2}}{{cite|hermann:jcp:2023}}
**[[DDsC dispersion correction]]{{cite|steinmann:jcp:11}}{{cite|steinmann:jctc:11}}
**[[DFT-ulg]]{{cite|kim:jpcl:2012}}
*[[Nonlocal vdW-DF functionals]] for van der Waals interactions: {{TAG|LUSE_VDW}} and {{TAG|IVDW_NL}}


== van der Waals corrections ==  
== References ==
*{{TAG|DFT-D2}} method.
<references/>
*{{TAG|DFT-D3}} method.
*{{TAG|DDsC dispersion correction}}.
*{{TAG|Many-body dispersion energy}}.
*{{TAG|Tkatchenko-Scheffler method}}.
*{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}}.
*{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}}.
*{{TAG|VdW-DF functional of Langreth and Lundqvist et al.}}


== How to ==
*Main tag for van der Waals algorithm: {{TAG|IVDW}}
*{{TAG|DFT-D2}} method.
*{{TAG|DFT-D3}} method.
*{{TAG|DDsC dispersion correction}}.
*{{TAG|Many-body dispersion energy}}.
*{{TAG|Tkatchenko-Scheffler method}}.
*{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}}.
*{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}}.
*{{TAG|VdW-DF functional of Langreth and Lundqvist et al.}}
----
----


[[Category:VASP|van der Waals]][[Category:XC Functionals]]
[[Category:VASP|van der Waals]][[Category:Exchange-correlation functionals]]

Latest revision as of 14:47, 1 July 2024

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:

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:

It requires a double spatial integration and is, therefore, of nonlocal. The kernel depends on the electronic density , its derivative as well as on the distance . 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

References

  1. G. Román-Pérez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).
  2. S. Grimme, J. Comput. Chem. 27, 1787 (2006).
  3. S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).
  4. S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).
  5. E. Caldeweyher, S. Ehlert, A. Hansen, H. Neugebauer, S. Spicher, C. Bannwarth, and S. Grimme, J. Chem. Phys. 150, 154122 (2019).
  6. A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).
  7. T. Bučko, S. Lebègue, J. Hafner, and J. G. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)
  8. T. Bučko, S. Lebègue, J. G. Ángyán, and J. Hafner, J. Chem. Phys. 141, 034114 (2014).
  9. a b A. Tkatchenko, R. A. DiStasio, Jr., R. Car, and M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012).
  10. A. Ambrosetti, A. M. Reilly, and R. A. DiStasio Jr., J. Chem. Phys. 140, 018A508 (2014).
  11. T. Gould and T. Bučko, C6 Coefficients and Dipole Polarizabilities for All Atoms and Many Ions in Rows 1–6 of the Periodic Table, J. Chem. Theory Comput. 12, 3603 (2016).
  12. T. Gould, S. Lebègue, J. G. Ángyán, and T. Bučko, A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations, J. Chem. Theory Comput. 12, 5920 (2016).
  13. https://libmbd.github.io/
  14. https://github.com/libmbd/libmbd
  15. J. Hermann, M. Stöhr, S. Góger, S. Chaudhuri, B. Aradi, R. J. Maurer, and A. Tkatchenko, libMBD: A general-purpose package for scalable quantum many-body dispersion calculations, J. Chem. Phys. 159, 174802 (2023).
  16. S. N. Steinmann and C. Corminboeuf, J. Chem. Phys. 134, 044117 (2011).
  17. S. N. Steinmann and C. Corminboeuf, J. Chem. Theory Comput. 7, 3567 (2011).
  18. H. Kim, J.-M. Choi, and W. A. Goddard, III, J. Phys. Chem. Lett. 3, 360 (2012).