DFT-D3: Difference between revisions

Revision as of 15:01, 24 February 2025

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 calculated on the basis of the local geometry (coordination number) around atoms $i$ and $j$ . Two variants of DFT-D3, that differ in the damping functions $f_{d,n}$ , are available.

DFT-D3(zero)

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

Optionally, the following parameters can be defined in the INCAR file (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 $s_{R,6}$

DFT-D3(BJ)

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

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. As before, the parameters VDW_RADIUS and VDW_CNRADIUS can be used to change the default values for the cutoff radii.

Optionally, the parameters of the damping function can be controlled using the following INCAR 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.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/.

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 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>
-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 method {{TAG|DFT-D2}}, 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 damping functions <math>f_{d,n}</math>, are available.
+=== 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>
-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):
+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.
+Optionally, the following parameters can be defined in the {{FILE|INCAR}} file (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>
@@ Line 14: / Line 19: @@
 *{{TAG|VDW_SR}}=[real] : damping function parameter <math>s_{R,6}</math>
-Alternatively, the Becke-Johnson (BJ) damping can be used in the DFT-D3 method{{cite|grimme:jcc:11}}:
+=== DFT-D3(BJ) ===
+In the 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>
-with <math>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, and <math>s_8</math> being 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. As before, the parameters {{TAG|VDW_RADIUS}} and {{TAG|VDW_CNRADIUS}} can be used to change the default values for the cutoff radii.
-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:
+Optionally, the parameters of the damping function can be controlled using the following {{FILE|INCAR}} tags:
 *{{TAG|VDW_S8}}=[real]
@@ Line 26: / Line 33: @@
 {{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 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/.}}

Revision as of 15:01, 24 February 2025

DFT-D3(zero)

DFT-D3(BJ)

Related tags and articles

References