Category:Van der Waals functionals: Difference between revisions

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The semilocal and hybrid exchange-correlation 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''':
The semilocal (SL) and hybrid exchange-correlation 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>
:<math>
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}}.
Line 11: Line 11:
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 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, listed below, are available in VASP and are selected with the {{TAG|IVDW}} tag.
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. Several variants of such atom-pair corrections exist and the most popular of them, listed below, are available in VASP and are selected with the {{TAG|IVDW}} tag.
*{{TAG|IVDW}}
*[[DFT-D2]]{{cite|grimme:jcc:06}}
*[[DFT-D2]]{{cite|grimme:jcc:06}}
*[[DFT-D3]]{{cite|grimme:jcp:10}}{{cite|grimme:jcc:11}}
*[[DFT-D3]]{{cite|grimme:jcp:10}}{{cite|grimme:jcc:11}}
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</math>
</math>
These methods, listed below, are selected with the {{TAG|IVDW}} tag.
These methods, listed below, are selected with the {{TAG|IVDW}} tag.
*{{TAG|IVDW}}
*[[Many-body dispersion energy]]{{cite|tkatchenko:prl:12}}{{cite|ambrosetti:jcp:14}}
*[[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}}
*[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite|gould:jctc:2016_a}}{{cite|gould:jctc:2016_b}}
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</math>
</math>
where the kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the interelectronic 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}}. These methods are selected with the {{TAG|LUSE_VDW}} and {{TAG|IVDW_NL}} tags.
where the kernel <math>\Phi</math> depends on the electronic density <math>n</math>, its derivative <math>\nabla n</math> as well as on the interelectronic 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}}. These methods are selected with the {{TAG|LUSE_VDW}} and {{TAG|IVDW_NL}} tags.
*{{TAG|LUSE_VDW}}
*{{TAG|IVDW_NL}}
*[[Nonlocal vdW-DF functionals]]
*[[Nonlocal vdW-DF functionals]]


Latest revision as of 15:57, 25 February 2025

The semilocal (SL) and hybrid exchange-correlation 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 three types of dispersion terms that are available in VASP, and a brief sketch of them is given below along with links to pages that provide more detail. Note that libMBD is an external package that provides the Tkatchenko-Scheffler atom-pairwise methods and their many-body dispersion extensions.

Approximations

Atom-pairwise methods

They consist of a sum over the atoms pairs -:

where are the dispersion coefficients, is the distance between atoms and , and is a damping function. Several variants of such atom-pair corrections exist and the most popular of them, listed below, are available in VASP and are selected with the IVDW tag.

Many-body dispersion methods

These methods are based on the random-phase expression for the correlation energy, which is expressed as an integral over the frequency involving the frequency-dependent polarizability :

These methods, listed below, are selected with the IVDW tag.

Nonlocal vdW-DF functionals

These are density functionals that require a double spatial integration and are, therefore, nonlocal:

where the kernel depends on the electronic density , its derivative as well as on the interelectronic distance . The nonlocal functionals are more expensive to calculate than semilocal functionals, however, they are efficiently implemented by using FFTs [18]. These methods are selected with the LUSE_VDW and IVDW_NL tags.

References

  1. ↑ S. Grimme, J. Comput. Chem. 27, 1787 (2006).
  2. ↑ S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).
  3. ↑ S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).
  4. ↑ E. Caldeweyher, S. Ehlert, A. Hansen, H. Neugebauer, S. Spicher, C. Bannwarth, and S. Grimme, J. Chem. Phys. 150, 154122 (2019).
  5. ↑ A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).
  6. ↑ T. Bučko, S. Lebègue, J. Hafner, and J. G. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)
  7. ↑ T. Bučko, S. Lebègue, J. G. Ángyán, and J. Hafner, J. Chem. Phys. 141, 034114 (2014).
  8. ↑ a b A. Tkatchenko, R. A. DiStasio, Jr., R. Car, and M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012).
  9. ↑ a b https://libmbd.github.io/
  10. ↑ a b https://github.com/libmbd/libmbd
  11. ↑ a b 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).
  12. ↑ S. N. Steinmann and C. Corminboeuf, J. Chem. Phys. 134, 044117 (2011).
  13. ↑ S. N. Steinmann and C. Corminboeuf, J. Chem. Theory Comput. 7, 3567 (2011).
  14. ↑ H. Kim, J.-M. Choi, and W. A. Goddard, III, J. Phys. Chem. Lett. 3, 360 (2012).
  15. ↑ A. Ambrosetti, A. M. Reilly, and R. A. DiStasio Jr., J. Chem. Phys. 140, 018A508 (2014).
  16. ↑ 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).
  17. ↑ 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).
  18. ↑ G. Román-Pérez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).
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