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# DFT-D3

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

${\displaystyle E_{{{\mathrm {disp}}}}=-{\frac {1}{2}}\sum _{{i=1}}^{{N_{{at}}}}\sum _{{j=1}}^{{N_{{at}}}}\sum _{{{\mathbf {L}}}}{}^{\prime }\left(f_{{d,6}}(r_{{ij,L}})\,{\frac {C_{{6ij}}}{r_{{ij,{L}}}^{6}}}+f_{{d,8}}(r_{{ij,L}})\,{\frac {C_{{8ij}}}{r_{{ij,L}}^{8}}}\right).}$

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

${\displaystyle f_{{d,n}}(r_{{ij}})={\frac {s_{n}}{1+6(r_{{ij}}/(s_{{R,n}}R_{{0ij}}))^{{-\alpha _{{n}}}}}}}$

where ${\displaystyle R_{{0ij}}={\sqrt {{\frac {C_{{8ij}}}{C_{{6ij}}}}}}}$, the parameters ${\displaystyle \alpha _{6}}$, ${\displaystyle \alpha _{8}}$, ${\displaystyle s_{{R,8}}}$, ${\displaystyle s_{{6}}}$ are fixed at values of 14., 16., 1., and 1., respectively, and ${\displaystyle s_{{8}}}$, and ${\displaystyle s_{{R,6}}}$ are adjustable parameters whose values depend on the choice of 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 values):

• VDW_RADIUS=50.2 cutoff radius (in ${\displaystyle \AA }$) for pair interactions considered in the equation of ${\displaystyle E_{{{\mathrm {disp}}}}}$
• VDW_CNRADIUS=20.0 cutoff radius (in ${\displaystyle \AA }$) for the calculation of the coordination numbers
• VDW_S8=[real] damping function parameter ${\displaystyle s_{8}}$
• VDW_SR=[real] damping function parameter ${\displaystyle s_{{R,6}}}$

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

${\displaystyle f_{{d,n}}(r_{{ij}})={\frac {s_{n}\,r_{{ij}}^{n}}{r_{{ij}}^{n}+(a_{1}\,R_{{0ij}}+a_{2})^{n}}}}$

with ${\displaystyle s_{6}=1}$ and ${\displaystyle a_{1}}$, ${\displaystyle a_{2}}$, and ${\displaystyle s_{8}}$ being the 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 default values for cutoff radii. The parameters of the damping function can be controlled using the following tags:

## IMPORTANT NOTES

The default values for damping function parameters are available for the following functionals: PBE (GGA=PE), RPBE (GGA=RP), revPBE (GGA=RE) and PBEsol (GGA=PS). If another functional is used, the user must define these parameters via 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 http://www.thch.uni-bonn.de/tc/dftd3.

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 DFT-D3 method, please cite reference [1]. When using DFT-D3(BJ) references [1] and [2] should be cited.