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).](https://www.vasp.at/wiki/restbase/vasp.at/v1/media/math/render/svg/115aad1369355f7a4a2807b41de039fdb607d655)
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:
![f_{{d,n}}(r_{{ij}})={\frac {s_{n}}{1+6(r_{{ij}}/(s_{{R,n}}R_{{0ij}}))^{{-\alpha _{{n}}}}}}](https://www.vasp.at/wiki/restbase/vasp.at/v1/media/math/render/svg/554dd4daa3bc630004ad7fa2a8b9ece7eff11ce9)
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 ![E_{{{\mathrm {disp}}}}](https://www.vasp.at/wiki/restbase/vasp.at/v1/media/math/render/svg/619c66ce92be8a7bc3867a53f1413ab353fccb7e)
- VDW_CNRADIUS=20.0 : cutoff radius (in
) for the calculation of the coordination numbers
- VDW_S8=[real] : damping function parameter
![s_{8}](https://www.vasp.at/wiki/restbase/vasp.at/v1/media/math/render/svg/d1a1e1ac30255dbe2081cfaa2ba3d0921d21305e)
- VDW_SR=[real] : damping function parameter
![s_{{R,6}}](https://www.vasp.at/wiki/restbase/vasp.at/v1/media/math/render/svg/07696dde259c9ee309eb3fafaa00aa74fc34ae18)
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}}}](https://www.vasp.at/wiki/restbase/vasp.at/v1/media/math/render/svg/9d10b1fcfa1d24f377f433c980a9c166f1568edc)
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:
- 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/.
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Related tags and articles
VDW_RADIUS,
VDW_CNRADIUS,
VDW_S8,
VDW_SR,
VDW_A1,
VDW_A2,
IVDW,
DFT-D2,
DFT-D4
References