DFT-D3

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C_{{6ij}} are geometry-dependent as they are adjusted on the basis of the local geometry (coordination number) around atoms Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): i and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): j . In the zero-damping variant of the DFT-D3 method (DFT-D3(zero)), the damping function reads:

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): f_{{d,n}}(r_{{ij}})={\frac {s_{n}}{1+6(r_{{ij}}/(s_{{R,n}}R_{{0ij}}))^{{-\alpha _{{n}}}}}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): R_{{0ij}}={\sqrt {{\frac {C_{{8ij}}}{C_{{6ij}}}}}} , the parameters Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): \alpha _{6} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): \alpha _{8} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): s_{{R,8}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): s_{{6}} are fixed at values of 14, 16, 1, and 1, respectively, while Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): s_{{8}} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): 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 values):

  • VDW_RADIUS=50.2 : cutoff radius (in Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): \AA ) for pair interactions considered in the equation of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): E_{{{\mathrm {disp}}}}
  • VDW_CNRADIUS=20.0 : cutoff radius (in Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): \AA ) for the calculation of the coordination numbers
  • VDW_S8=[real] : damping function parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): s_{8}
  • VDW_SR=[real] : damping function parameter Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): s_{{R,6}}

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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): f_{{d,n}}(r_{{ij}})={\frac {s_{n}\,r_{{ij}}^{n}}{r_{{ij}}^{n}+(a_{1}\,R_{{0ij}}+a_{2})^{n}}}

with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): s_{6}=1 and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): a_{1} , Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): a_{2} , and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): 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:


Mind: The default values for damping function parameters are available for the following functionals: PBE (GGA), RPBE (GGA), revPBE (GGA) and PBEsol (GGA). 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.

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 [1]. When using DFT-D3(BJ) references [1] and [2] should also be cited.


Related tags and articles

IVDW, IALGO, 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

References

  1. ↑ a b c S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).
  2. ↑ a b S. Grimme, S. Ehrlich, and L. Goerigk, J. Comput. Chem. 32, 1456 (2011).
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