Category:Van der Waals functionals: Difference between revisions

Revision as of 15:27, 13 February 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:

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

There are essentially two types of dispersion terms $E_{\text{c,disp}}$ that have been proposed in the literature. The first type consists of a sum over the atom pairs $A$ - $B$ :

{\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 $C_{n}^{AB}$ are the dispersion coefficients, $R_{AB}$ is the distance between atoms $A$ and $B$ and $f_{n}^{\text{damp}}$ 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 $\Phi$ depends on the electronic density $n$ , its derivative $\nabla n$ , as well as on the distance $\left\vert\bf{r}-\bf{r}'\right\vert$ . 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.:
- DDsC dispersion correction^[12]^[13]
- DFT-ulg^[14]
Nonlocal vdW-DF functionals for van der Waals interactions: LUSE_VDW and IVDW_NL

References

Pages in category "Van der Waals functionals"

The following 58 pages are in this category, out of 58 total.

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GAMMA VDW

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HITOLER

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IVDW
IVDW NL

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Nonlocal vdW-DF functionals

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ZAB VDW

[romanperez:prl:09-1] G. Román-Pérez and J. M. Soler, Phys. Rev. Lett. 103, 096102 (2009).

[grimme:jcc:06-2] S. Grimme, J. Comput. Chem. 27, 1787 (2006).

[grimme:jcp:10-3] S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).

[grimme:jcc:11-4] S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).

[tkatchenko:prl:09-5] A. Tkatchenko and M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009).

[bucko:jctc:13-6] T. Bučko, S. Lebègue, J. Hafner, and J. G. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)

[bucko:jcp:14-7] T. Bučko, S. Lebègue, J. G. Ángyán, and J. Hafner, J. Chem. Phys. 141, 034114 (2014).

[tkatchenko:prl:12-8] A. Tkatchenko, R. A. DiStasio, Jr., R. Car, and M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012).

[ambrosetti:jcp:14-9] A. Ambrosetti, A. M. Reilly, and R. A. DiStasio Jr., J. Chem. Phys. 140, 018A508 (2014).

[gould:jctc:2016_a-10] 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).

[gould:jctc:2016_b-11] 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).

[steinmann:jcp:11-12] S. N. Steinmann and C. Corminboeuf, J. Chem. Phys. 134, 044117 (2011).

[steinmann:jctc:11-13] S. N. Steinmann and C. Corminboeuf, J. Chem. Theory Comput. 7, 3567 (2011).

[kim:jpcl:2012-14] H. Kim, J.-M. Choi, and W. A. Goddard, III, J. Phys. Chem. Lett. 3, 360 (2012).

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@@ Line 1: / Line 1: @@
-== 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''':
-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. This leads to the so-called van der Waals functionals:
 :<math>
 E_{\text{xc}} = E_{\text{xc}}^{\text{SL/hybrid}} + E_{\text{c,disp}}.
@@ Line 9: / Line 7: @@
 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). More details on the different types of van der Waals methods available in VASP and how to use them can be found in the pages listed below.
+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 other type of dispersion correction is of the following type:
 :<math>
-E_{\text{c,disp}} = \frac{1}{2}\int\int\rho(\textbf{r})
+E_{\text{c,disp}} = \frac{1}{2}\int\int n(\textbf{r})
-\Phi\left(\textbf{r},\textbf{r}'\right)\rho(\textbf{r}')
+\Phi\left(\textbf{r},\textbf{r}'\right) n(\textbf{r}')
-d^{3}rd^{3}r',
+d^{3}rd^{3}r'.
 </math>
-which requires a double spatial integration and is therefore of the nonlocal type. The kernel <math>\Phi</math> depends on the electron density <math>\rho</math>, its derivative <math>\nabla\rho</math> as well as on <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}}.
+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}}
+**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}}
+**[[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}}
+== References ==
+<references/>
-*Main tag for van der Waals algorithm: {{TAG|IVDW}}
-*{{TAG|DFT-D2}}.
-*{{TAG|DFT-D3}}.
-*{{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]]