DFT-D3

In the DFT-D3 method of Grimme et al., 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 adjusted on the basis of the local geometry (coordination number) around atoms $i$ and $j$. In the zero-damping variant of the DFT-D3 method (DFT-D3(zero)), the damping function reads:

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

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

Alternatively, the Becke-Johnson (BJ) damping can be used in the DFT-D3 method:

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

with $s_{6}=1$ and $a_{1}$, $a_{2}$, and $s_{8}$ being adjustable parameters. 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:

• VDW_S8=[real]
• VDW_A1=[real]
• VDW_A2=[real]

Mind: The default values for the 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 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/pctc/mulliken-center/software/dft-d3/.

Mind: 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 . When using DFT-D3(BJ) references and should also be cited.

Related tags and articles

IVDW, DFT-D2, Tkatchenko-Scheffler method, Tkatchenko-Scheffler method with iterative Hirshfeld partitioning, Self-consistent screening in Tkatchenko-Scheffler method, Many-body dispersion energy, dDsC dispersion correction

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