DFT-D3: Difference between revisions
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In the DFT-D3 method of Grimme et al.{{cite|grimme:jcp:10}}, the following expression for the vdW | 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 | 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>, | 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_S8}}=[real] : scaling <math>s_8</math> of the dipole-quadrupole dispersion | |||
*{{TAG|VDW_SR}}=[real] : radii scaling <math>s_{r,6}</math> in the dipole-dipole damping function | |||
*{{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_RADIUS}}=[real] : two-body interaction cutoff (in Å) | |||
*{{TAG|VDW_CNRADIUS}}=[real] : coordination number cutoff (in Å) | |||
=== 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> | ||
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: | |||
*{{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_A1}}=[real] : scaling <math>a_{1}</math> of the critical radii | |||
*{{TAG|VDW_A2}}=[real] : offset <math>a_{2}</math> of the critical radii | |||
*{{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 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| | {{TAG|IVDW}}, | ||
{{TAG| | {{TAG|VDW_S6}}, | ||
{{TAG|VDW_S8}}, | {{TAG|VDW_S8}}, | ||
{{TAG|VDW_SR}}, | {{TAG|VDW_SR}}, | ||
{{TAG|VDW_SR8}}, | |||
{{TAG|VDW_A1}}, | {{TAG|VDW_A1}}, | ||
{{TAG|VDW_A2}}, | {{TAG|VDW_A2}}, | ||
{{TAG| | {{TAG|VDW_RADIUS}}, | ||
{{TAG| | {{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:
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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