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In the DFT-D3 method of Grimme et al.{{cite|grimme:jcp:10}}, the following expression for the vdW-dispersion energy-correction term is used:
In the DFT-D3 method of Grimme et al.{{cite|grimme:jcp:10}}, the following expression for the vdW dispersion energy-correction term is used:


:<math> E_{\mathrm{disp}} = -\frac{1}{2}  \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>
:<math> E_{\mathrm{disp}} = -\frac{1}{2}  \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ).</math>


Unlike in the method {{TAG|DFT-D2}}, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are adjusted on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. In the zero-damping variant of the DFT-D3 method (DFT-D3(zero)), the damping function reads:
Unlike in the older {{TAG|DFT-D2}} method, the dispersion coefficients <math>C_{6ij}</math> are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. Two variants of DFT-D3, that differ in the mathematical form  of the damping functions <math>f_{d,n}</math>, are available. More variants of the damping function are available via the [[simple-DFT-D3]] external package ({{TAG|IVDW}}=15).
 
=== DFT-D3(zero) ===
In the zero-damping variant of DFT-D3,{{cite|grimme:jcp:10}} invoked by setting {{TAG|IVDW}}=11, the damping function reads


:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>
:<math>f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}}</math>


where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, the parameters <math>\alpha_6</math>, <math>\alpha_8</math>, <math>s_{R,8}</math>, <math>s_{6}</math> are fixed at values of 14, 16, 1, and 1, respectively, while <math>s_{8}</math> and <math>s_{R,6}</math> are adjustable parameters whose values depend on the choice of the exchange-correlation functional. The DFT-D3(zero) method is invoked by setting {{TAG|IVDW}}=11. Optionally, the following parameters can be user-defined (the given values are the default values):
where <math>R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}</math>, <math>\alpha_6=14</math> and <math>\alpha_8=16</math> are fixed (there is no tag to change their values), and the others parameters, whose default values depend on the choice of the exchange-correlation functional, can be modified as follows:
 
*{{TAG|VDW_S6}}=[real] : scaling <math>s_6</math> of the dipole-dipole dispersion. '''Available since VASP.6.6.0'''.
*{{TAG|VDW_RADIUS}}=50.2 cutoff radius (in <math>\AA</math>) for pair interactions considered in the equation of <math> E_{\mathrm{disp}}</math>
*{{TAG|VDW_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion
*{{TAG|VDW_CNRADIUS}}=20.0 cutoff radius (in <math>\AA</math>) for the calculation of the coordination numbers
*{{TAG|VDW_SR}}=[real] : radii scaling <math>s_{r,6}</math> in the dipole-dipole damping function
*{{TAG|VDW_S8}}=[real] damping function parameter <math>s_8</math>
*{{TAG|VDW_SR8}}=[real] : radii scaling <math>s_{r,8}</math> in the dipole-quadrupole damping function. '''Available since VASP.6.6.0'''.
*{{TAG|VDW_SR}}=[real] damping function parameter <math>s_{R,6}</math>
*{{TAG|VDW_RADIUS}}=[real] : two-body interaction cutoff (in Å)
*{{TAG|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å)


Alternatively, the Becke-Jonson (BJ) damping can be used in the {{TAG|DFT-D3}} method{{cite|grimme:jcc:11}}:
=== DFT-D3(BJ) ===
In the rational Becke-Johnson (BJ) damping variant of DFT-D3,{{cite|grimme:jcc:11}}, invoked by setting {{TAG|IVDW}}=12, the damping function is given by


:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>
:<math>f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} </math>


with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being the adjustable parameters.
where <math>s_6</math>, <math>s_8</math>, <math>a_1</math>, and <math>a_2</math> are parameters whose default values depend on the choice of the exchange-correlation functional, but can also be modified as follows:
This variant of {{TAG|DFT-D3}} method (DFT-D3(BJ)) is invoked by setting {{TAG|IVDW}}=12. As before, the parameters {{TAG|VDW_RADIUS}} and {{TAG|VDW_CNRADIUS}} can be used to change default values for cutoff radii. The parameters of the damping function can be controlled using the following tags:
*{{TAG|VDW_S6}}=[real] : scaling <math>s_6</math> of the dipole-dipole dispersion. '''Available since VASP.6.6.0'''.
 
*{{TAG|VDW_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion
*{{TAG|VDW_S8}}=[real]
*{{TAG|VDW_A1}}=[real] : scaling <math>a_{1}</math> of the critical radii
*{{TAG|VDW_A1}}=[real]
*{{TAG|VDW_A2}}=[real] : offset <math>a_{2}</math> of the critical radii
*{{TAG|VDW_A2}}=[real]
*{{TAG|VDW_RADIUS}}=[real] : two-body interaction cutoff (in Å)
 
*{{TAG|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å)
{{NB|mind|The default values for damping function parameters are available for the following functionals: PBE ({{TAG|GGA}}), RPBE ({{TAG|GGA}}), revPBE ({{TAG|GGA}}) and PBEsol ({{TAG|GGA}}). If another functional is used, the user must define these parameters via corresponding tags in the {{TAG|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found
on the webpage http://www.thch.uni-bonn.de/tc/dftd3.}}
{{NB|mind|The D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the {{TAG|DFT-D3}} method, please cite reference {{cite|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite|grimme:jcp:10}} and {{cite|grimme:jcc:11}} should be cited.}}


{{NB|mind|
*The default values for the damping function parameters are available for several {{TAG|GGA}} (PBE, RPBE, revPBE and PBEsol), {{TAG|METAGGA}} (TPSS, M06L and SCAN) and [[list_of_hybrid_functionals|hybrid]] (B3LYP and PBEh/PBE0) functionals, as well as [[list_of_hybrid_functionals|Hartree-Fock]]. If another functional is used, the user has to define these parameters via the corresponding tags in the {{TAG|INCAR}} file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals".
*The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference {{cite|grimme:jcp:10}}. When using DFT-D3(BJ) references {{cite|grimme:jcp:10}} and {{cite|grimme:jcc:11}} should also be cited. Also carefully check the more extensive list of references found on  https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.}}


== Related tags and articles ==
== Related tags and articles ==
{{TAG|IVDW}},
{{TAG|IVDW}},
{{TAG|IALGO}},
{{TAG|VDW_S6}},
{{TAG|DFT-D2}},
{{TAG|VDW_S8}},
{{TAG|Tkatchenko-Scheffler method}},
{{TAG|VDW_SR}},
{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},
{{TAG|VDW_SR8}},
{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}},
{{TAG|VDW_A1}},
{{TAG|Many-body dispersion energy}},
{{TAG|VDW_A2}},
{{TAG|dDsC dispersion correction}}
{{TAG|VDW_RADIUS}},
{{TAG|VDW_CNRADIUS}},
[[DFT-D2]],
[[simple-DFT-D3]],
[[DFT-D4]],
[[DFT-ulg]]


== References ==
== References ==
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----
----
[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]][[Category:Howto]]

Latest revision as of 11:19, 2 March 2026

In the DFT-D3 method of Grimme et al.[1], the following expression for the vdW dispersion energy-correction term is used:

[math]\displaystyle{ E_{\mathrm{disp}} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}}{}^\prime \left ( f_{d,6}(r_{ij,L})\,\frac{C_{6ij}}{r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}}{r_{ij,L}^8} \right ). }[/math]

Unlike in the older DFT-D2 method, the dispersion coefficients [math]\displaystyle{ C_{6ij} }[/math] are geometry-dependent as they are calculated on the basis of the local geometry (coordination number) around atoms [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math]. Two variants of DFT-D3, that differ in the mathematical form of the damping functions [math]\displaystyle{ f_{d,n} }[/math], are available. More variants of the damping function are available via the simple-DFT-D3 external package (IVDW=15).

DFT-D3(zero)

In the zero-damping variant of DFT-D3,[1] invoked by setting IVDW=11, the damping function reads

[math]\displaystyle{ f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}} }[/math]

where [math]\displaystyle{ R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}} }[/math], [math]\displaystyle{ \alpha_6=14 }[/math] and [math]\displaystyle{ \alpha_8=16 }[/math] are fixed (there is no tag to change their values), and the others parameters, whose default values depend on the choice of the exchange-correlation functional, can be modified as follows:

  • VDW_S6=[real] : scaling [math]\displaystyle{ s_6 }[/math] of the dipole-dipole dispersion. Available since VASP.6.6.0.
  • VDW_S8=[real] : scaling [math]\displaystyle{ s_8 }[/math] of the dipole-quadrupole dispersion
  • VDW_SR=[real] : radii scaling [math]\displaystyle{ s_{r,6} }[/math] in the dipole-dipole damping function
  • VDW_SR8=[real] : radii scaling [math]\displaystyle{ s_{r,8} }[/math] in the dipole-quadrupole damping function. Available since VASP.6.6.0.
  • VDW_RADIUS=[real] : two-body interaction cutoff (in Å)
  • VDW_CNRADIUS=[real] : coordination number cutoff (in Å)

DFT-D3(BJ)

In the rational Becke-Johnson (BJ) damping variant of DFT-D3,[2], invoked by setting IVDW=12, the damping function is given by

[math]\displaystyle{ f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} }[/math]

where [math]\displaystyle{ s_6 }[/math], [math]\displaystyle{ s_8 }[/math], [math]\displaystyle{ a_1 }[/math], and [math]\displaystyle{ a_2 }[/math] are parameters whose default values depend on the choice of the exchange-correlation functional, but can also be modified as follows:

  • VDW_S6=[real] : scaling [math]\displaystyle{ s_6 }[/math] of the dipole-dipole dispersion. Available since VASP.6.6.0.
  • VDW_S8=[real] : scaling [math]\displaystyle{ s_8 }[/math] of the dipole-quadrupole dispersion
  • VDW_A1=[real] : scaling [math]\displaystyle{ a_{1} }[/math] of the critical radii
  • VDW_A2=[real] : offset [math]\displaystyle{ a_{2} }[/math] of the critical radii
  • VDW_RADIUS=[real] : two-body interaction cutoff (in Å)
  • VDW_CNRADIUS=[real] : coordination number cutoff (in Å)


Mind:
  • The default values for the damping function parameters are available for several GGA (PBE, RPBE, revPBE and PBEsol), METAGGA (TPSS, M06L and SCAN) and hybrid (B3LYP and PBEh/PBE0) functionals, as well as Hartree-Fock. If another functional is used, the user has to define these parameters via the corresponding tags in the INCAR file. The up-to-date list of parametrized DFT functionals with recommended values of damping function parameters can be found on the webpage https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/ and follow the link "List of parametrized functionals".
  • The DFT-D3 method has been implemented in VASP by Jonas Moellmann based on the dftd3 program written by Stefan Grimme, Stephan Ehrlich and Helge Krieg. If you make use of the DFT-D3 method, please cite reference [1]. When using DFT-D3(BJ) references [1] and [2] should also be cited. Also carefully check the more extensive list of references found on https://www.chemie.uni-bonn.de/grimme/de/software/dft-d3/.

Related tags and articles

IVDW, VDW_S6, VDW_S8, VDW_SR, VDW_SR8, VDW_A1, VDW_A2, VDW_RADIUS, VDW_CNRADIUS, DFT-D2, simple-DFT-D3, DFT-D4, DFT-ulg

References

  1. ↑ a b c d S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).
  2. ↑ a b S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).
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