Category:Van der Waals functionals: Difference between revisions

Latest 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:

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 $A$ - $B$ :

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:

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 57 pages are in this category, out of 57 total.

D

G

GAMMA VDW

H

HITOLER

I

IVDW
IVDW NL

M

N

Nonlocal vdW-DF functionals

P

S

T

V

Z

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: @@
-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:
+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}}.
@@ Line 13: / Line 13: @@
 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',
+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>n</math>, its derivative <math>\nabla n</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 types methods available in VASP and how to use them can be found at the pages listed below.
+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 methods for van der Waals interactions: (selected with the {{TAG|IVDW}} tag):
+*Atom-pairwise and many-body methods for van der Waals interactions (selected with the {{TAG|IVDW}} tag):
 **Methods from Grimme et al.:
-***{{TAG|DFT-D2}}
+***[[DFT-D2]]{{cite|grimme:jcc:06}}
-***{{TAG|DFT-D3}}
+***[[DFT-D3]]{{cite|grimme:jcp:10}}{{cite|grimme:jcc:11}}
 **Methods from Tkatchenko, Scheffler et al.:
-***{{TAG|Tkatchenko-Scheffler method}}
+***[[Tkatchenko-Scheffler method]]{{cite|tkatchenko:prl:09}}
-***{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}}
+***[[Tkatchenko-Scheffler method with iterative Hirshfeld partitioning]]{{cite|bucko:jctc:13}}{{cite|bucko:jcp:14}}
-***{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}}
+***[[Self-consistent screening in Tkatchenko-Scheffler method]]{{cite|tkatchenko:prl:12}}
-***{{TAG|Many-body dispersion energy}}
+***[[Many-body dispersion energy]]{{cite|tkatchenko:prl:12}}{{cite|ambrosetti:jcp:14}}
-***{{TAG|Many-body_dispersion_energy_with_fractionally_ionic_model_for_polarizability}}
+***[[Many-body dispersion energy with fractionally ionic model for polarizability]]{{cite|gould:jctc:2016_a}}{{cite|gould:jctc:2016_b}}
-**{{TAG|DDsC dispersion correction}}
+**[[DDsC dispersion correction]]{{cite|steinmann:jcp:11}}{{cite|steinmann:jctc:11}}
-**{{TAG|DFT-ulg}}
+**[[DFT-ulg]]{{cite|kim:jpcl:2012}}
-*{{TAG|Nonlocal vdW-DF functionals}} for van der Waals interactions: {{TAG|LUSE_VDW}}
+*[[Nonlocal vdW-DF functionals]] for van der Waals interactions: {{TAG|LUSE_VDW}} and {{TAG|IVDW_NL}}
 == References ==