DFT-D3
In the DFT-D3 correction method of Grimme et al.[1], the following vdW-energy expression 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 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 DFT-D3 method (DFT-D3(zero)), damping of the following form 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/":): 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}} , 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, 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}} , 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 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-Jonson (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:
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.
Related Tags and Sections
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