DFT-D3

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

[math]\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 ). }[/math]

Unlike in the method DFT-D2, the dispersion coefficients [math]\displaystyle{ C_{6ij} }[/math] are geometry-dependent as they are adjusted on the basis of the local geometry (coordination number) around atoms [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math]. In the zero-damping variant of the DFT-D3 method (DFT-D3(zero)), the damping function reads:

[math]\displaystyle{ f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}} }[/math]

where [math]\displaystyle{ R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}} }[/math], the parameters [math]\displaystyle{ \alpha_6 }[/math], [math]\displaystyle{ \alpha_8 }[/math], [math]\displaystyle{ s_{R,8} }[/math] and [math]\displaystyle{ s_{6} }[/math] are fixed at values of 14, 16, 1, and 1, respectively, while [math]\displaystyle{ s_{8} }[/math] and [math]\displaystyle{ s_{R,6} }[/math] 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 [math]\displaystyle{ \AA }[/math]) for pair interactions considered in the equation of [math]\displaystyle{ E_{\mathrm{disp}} }[/math]
• VDW_CNRADIUS=20.0 : cutoff radius (in [math]\displaystyle{ \AA }[/math]) for the calculation of the coordination numbers
• VDW_S8=[real] : damping function parameter [math]\displaystyle{ s_8 }[/math]
• VDW_SR=[real] : damping function parameter [math]\displaystyle{ s_{R,6} }[/math]

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

[math]\displaystyle{ f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n} }[/math]

with [math]\displaystyle{ s_6=1 }[/math] and [math]\displaystyle{ a_1 }[/math], [math]\displaystyle{ a_2 }[/math], and [math]\displaystyle{ s_8 }[/math] 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 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.chemiebn.uni-bonn.de/pctc/mulliken-center/software/dft-d3/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

VDW_RADIUS, VDW_CNRADIUS, VDW_S8, VDW_SR, VDW_A1, VDW_A2, 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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