DFT-D3: Difference between revisions

Revision as of 15:05, 12 October 2023

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

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 ).

Unlike in the method DFT-D2, the dispersion coefficients $C_{6ij}$ are geometry-dependent as they are adjusted on the basis of the local geometry (coordination number) around atoms $i$ and $j$ . In the zero-damping variant of the DFT-D3 method (DFT-D3(zero)), the damping function reads:

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

where $R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}$ , the parameters $\alpha_6$ , $\alpha_8$ , $s_{R,8}$ and $s_{6}$ are fixed at values of 14, 16, 1, and 1, respectively, while $s_{8}$ and $s_{R,6}$ are adjustable parameters whose values depend on the choice of the exchange-correlation functional. The DFT-D3(zero) method is invoked by setting IVDW=11. Optionally, the following parameters can be user-defined (the given values are the default ones):

VDW_RADIUS=50.2 : cutoff radius (in $\AA$ ) for pair interactions considered in the equation of $E_{\mathrm{disp}}$
VDW_CNRADIUS=20.0 : cutoff radius (in $\AA$ ) for the calculation of the coordination numbers
VDW_S8=[real] : damping function parameter $s_8$
VDW_SR=[real] : damping function parameter $s_{R,6}$

Alternatively, the Becke-Johnson (BJ) damping can be used in the DFT-D3 method^[2]:

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

with $s_6=1$ and $a_1$ , $a_2$ , and $s_8$ being adjustable parameters. This variant of DFT-D3 method (DFT-D3(BJ)) is invoked by setting IVDW=12. As before, the parameters VDW_RADIUS and VDW_CNRADIUS can be used to change the default values for the cutoff radii. The parameters of the damping function can be controlled using the following tags:

VDW_S8=[real]
VDW_A1=[real]
VDW_A2=[real]

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.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.
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.

References

[grimme:jcp:10-1] S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).

[grimme:jcc:11-2] S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).

[1]

[2]

@@ Line 1: / Line 1: @@
-In the {{TAG|DFT-D3}} correction method of Grimme et al.<ref name="grimme2010"/>, the following vdW-energy expression 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 local geometry (coordination number) around atoms <math>i</math> and <math>j</math>. In the zero damping {{TAG|DFT-D3}} method (DFT-D3(zero)), damping of the following form is used:
+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:
-<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> are fixed at values of 14., 16., and 1., respectively, and <math>s_{6}</math>, <math>s_{8}</math>, and <math>s_{R,6}</math> are adjustable parameters whose values depend on the choice of 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>, the parameters <math>\alpha_6</math>, <math>\alpha_8</math>, <math>s_{R,8}</math> and <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 ones):
-*{{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_RADIUS}}=50.2 : cutoff radius (in <math>\AA</math>) for pair interactions considered in the equation of <math> E_{\mathrm{disp}}</math>
-*{{TAG|VDW_CNRADIUS}}=20.0 cutoff radius (in <math>\AA</math>) for the calculation of the coordination numbers\\
+*{{TAG|VDW_CNRADIUS}}=20.0 : cutoff radius (in <math>\AA</math>) for the calculation of the coordination numbers
-*{{TAG|VDW_S6}}=[real] damping function parameter <math>s_6</math>
+*{{TAG|VDW_S8}}=[real] : damping function parameter <math>s_8</math>
-*{{TAG|VDW_S8}}=[real] damping function parameter <math>s_8</math>
+*{{TAG|VDW_SR}}=[real] : damping function parameter <math>s_{R,6}</math>
-*{{TAG|VDW_SR}}=[real] damping function parameter <math>s_R</math>
-Alternatively, the Becke-Jonson (BJ) damping can be used in the {{TAG|DFT-D3}} method<ref name="grimme2011"/>:
+Alternatively, the Becke-Johnson (BJ) damping can be used in the DFT-D3 method{{cite|grimme:jcc:11}}:
-<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>a_1</math>, <math>a_2</math>, <math>s_6</math>, and <math>s_8</math> being the adjustable parameters.
+with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being adjustable parameters.
-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:
+This variant of 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 the default values for the cutoff radii. The parameters of the damping function can be controlled using the following tags:
-*{{TAG|VDW_S6}}=[real]
 *{{TAG|VDW_S8}}=[real]
 *{{TAG|VDW_A1}}=[real]
 *{{TAG|VDW_A2}}=[real]
-== IMPORTANT NOTES ==
+{{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.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/dft-d3.
+*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.}}
-The default values for damping function parameters are available for the following functionals: PBE ({{TAG|GGA}}=''PE''), RPBE ({{TAG|GGA}}=''RE''), revPBE ({{TAG|GGA}}=''RP'') and PBEsol ({{TAG|GGA}}=''PS''). 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
+== Related tags and articles ==
-on the webpage http://www.thch.uni-bonn.de/tc/dftd3.
+{{TAG|VDW_RADIUS}},
+{{TAG|VDW_CNRADIUS}},
-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 <ref name="grimme2010"/>. When using DFT-D3(BJ) references <ref name="grimme2010"/> and <ref name="grimme2011"/> should be cited.
+{{TAG|VDW_S8}},
+{{TAG|VDW_SR}},
-== Related Tags and Sections ==
+{{TAG|VDW_A1}},
+{{TAG|VDW_A2}},
 {{TAG|IVDW}},
-{{TAG|IALGO}},
+{{TAG|DFT-D2}}
-{{TAG|DFT-D2}},
-{{TAG|Tkatchenko-Scheffler method}},
-{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},
-{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}},
-{{TAG|Many-body dispersion energy}},
-{{TAG|dDsC dispersion correction}}
 == References ==
-<references>
+<references/>
-<ref name="grimme2010">[http://aip.scitation.org/doi/full/10.1063/1.3382344 S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).]</ref>
-<ref name="grimme2011">[http://onlinelibrary.wiley.com/doi/10.1002/jcc.21759/abstract S. Grimme, S. Ehrlich, and L. Goerigk, J. Comp. Chem. 32, 1456 (2011).]</ref>
-</references>
 ----
-[[The_VASP_Manual|Contents]]
+[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
-[[Category:INCAR]]