DFT-D3: Difference between revisions
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In the | 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 | 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> | 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_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,6}</math> | ||
Alternatively, the Becke- | 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>s_6=1</math> and <math>a_1</math>, <math>a_2</math>, | 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 | 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_S8}}=[real] | *{{TAG|VDW_S8}}=[real] | ||
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*{{TAG|VDW_A2}}=[real] | *{{TAG|VDW_A2}}=[real] | ||
{{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.}} | |||
== Related tags and articles == | |||
{{TAG|VDW_RADIUS}}, | |||
{{TAG|VDW_CNRADIUS}}, | |||
{{TAG|VDW_S8}}, | |||
{{TAG|VDW_SR}}, | |||
{{TAG|VDW_A1}}, | |||
{{TAG|VDW_A2}}, | |||
{{TAG|IVDW}}, | {{TAG|IVDW}}, | ||
{{TAG|DFT-D2}} | |||
{{TAG|DFT-D2}} | |||
== References == | == References == | ||
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---- | ---- | ||
[[ | [[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]] | ||
[[Category:van der Waals]] |
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:
Unlike in the method DFT-D2, the dispersion coefficients are geometry-dependent as they are adjusted on the basis of the local geometry (coordination number) around atoms and . In the zero-damping variant of the DFT-D3 method (DFT-D3(zero)), the damping function reads:
where , the parameters , , and are fixed at values of 14, 16, 1, and 1, respectively, while and 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 ) for pair interactions considered in the equation of
- VDW_CNRADIUS=20.0 : cutoff radius (in ) for the calculation of the coordination numbers
- VDW_S8=[real] : damping function parameter
- VDW_SR=[real] : damping function parameter
Alternatively, the Becke-Johnson (BJ) damping can be used in the DFT-D3 method[2]:
with and , , and 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:
Mind:
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Related tags and articles
VDW_RADIUS, VDW_CNRADIUS, VDW_S8, VDW_SR, VDW_A1, VDW_A2, IVDW, DFT-D2