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DFT-D3 method

In the D3 correction method of Grimme et al. [128], the following vdW-energy expression is used:

$\displaystyle E_{\rm disp} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at...
...{6ij}} {r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}} {r_{ij,L}^8} \right ),$ (6.91)

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

$\displaystyle f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}},$ (6.92)

where $ R_{0ij} = \sqrt{\frac{C_{8ij}}{C_{6ij}}}$, the parameters $ \alpha_6$, $ \alpha_8$, $ s_{R,8}$ are fixed at values of 14., 16., and 1., respectively, and $ s_6$, $ s_8$, and $ s_{R,6}$ are adjustable parameters whose values depend on the choice of exchange-correlation functional. The D3(zero) method is invoked by setting IVDW= 11. Optionally, the following parameters can be user-defined (cf. eq. 6.92):

VDW_RADIUS = 50.2 cutoff radius (Å) for pair interactions considered in eq. 6.91
VDW_CNRADIUS = 20.0 cutoff radius (Å) for calculating the coordination number
VDW_S6 = [real] damping function parameter $ s_6$
VDW_S8 = [real] damping function parameter $ s_8$
VDW_SR = [real] damping function parameter $ s_R$

Alternatively, Becke-Jonson (BJ) damping can be used in the D3 method [129]:

$\displaystyle f_{d,n}(r_{ij}) = \frac{s_n\,r_{ij}^n}{r_{ij}^n + (a_1\,R_{0ij}+a_2)^n},$ (6.93)

with $ a_1$, $ a_2$, $ s_6$, and $ s_8$ being the adjustable parameters. This variant of 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 damping function can be controlled using the following tags (cf. eq. 6.93):

VDW_S6 = [real]  
VDW_S8 = [real]  
VDW_A1 = [real]  
VDW_A2 = [real]  


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