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17.5 Empirical damped dispersion correction

Empirical damped dispersion corrections can be calculated in addition to Kohn-Sham calculations. This is particularly important in cases where long-range correlation effects become dominant.

The dispersion correction can be added to the DFT energy by using

 ks,<func>; disp

The total energy will then be calculated as

$$E_\mathrm{DFT-D}=E_\mathrm{DFT}+E_\mathrm{disp}$$ (30)

Currently the default dispersion correction added to the DFT energy is the D3 dispersion correction developed by Grimme et al., see Ref. [1]. The disp keyword can have the following additional options:

FUNC

Functional name (default: FUNC='pbe').

VERSION

Can have values 2 and 3 according to parametrisations from Refs. [2] and [3] (default: VERSION=3)

ANAL

Performs a detailed analysis of pair contributions.

GRAD

Cartesian gradients are computed. (note that geometry optimisations with DFT+dispcorr3 are currently not yet possible).

TZ

Use special parameters for calculations with triple-zeta basis sets. Preliminary results in the SI of Ref. [3] indicate that results are slightly worse than with the default parameters and QZVP type basis sets. This option should be carfully tested for future use in very large computations.

(see also http://toc.uni-muenster.de/DFTD3/index.html for further documentation).

Alternatively, the D3 dispersion correction can also be calculated separately from the DFT calculation using the following template:

 ks,<func>
 eks=energy
 dispcorr3
 eks_plus_disp=eks+edisp

The older DFT-D1 [2] or DFT-D2 [3] methods by Grimme can still be used invoking

 ks,<func>
 eks=energy
 dispcorr
 eks_plus_disp=eks+edisp

with the following options to dispcorr:

MODE

Adjusts the parametrisation used: MODE=1 uses parameters from Ref. [1] and MODE=2 uses parameters from Ref. [2] (default: MODE=1)

SCALE

Overall scaling parameter $s_6$ (see Eq. (33) and Refs. [2,3] for optimised values).

ALPHA

Damping function parameter (see Eq. (36)). Smaller values lead to larger corrections for intermediate distances.

In the DFT-D1 and DFT-D2 method the dispersion energy is calculated as

$$E_\mathrm{disp}=-s_6\sum_{i,j<i}^{N_\mathrm{atoms}}f_\mathrm{damp}(R_{ij}) \frac{C_6^{ij}}{R_{ij}^6}~.$$ (31)

where $N_\mathrm{atoms}$ is the total number of atoms, $R_{ij}$ is the interatomic distance of atoms $i$ and $j$, $s_6$ is a global scaling parameter depending on the choice of the functional used and the $C_6^{ij}$ values are calculated from atomic dispersion coefficients $C_6^i$ and $C_6^j$ in the following way:

$$C_6^{ij} = 2\frac{C_6^i C_6^j}{C_6^i + C_6^j} ~~~~~\mathrm{(Ref.\ [1])}$$ (32)

$$C_6^{ij} = \sqrt{C_6^i C_6^j} ~~~~~~~~~\mathrm{(Ref.\ [2])}$$ (33)

The function $f_\mathrm{damp}$ damps the dispersion correction for shorter interatomic distances and is given by:

$$f_\mathrm{damp}(R_{ij})=\frac{1}{1+\exp{[-\alpha(R_{ij}/ (R_\mathrm{vdW}^i+R_\mathrm{vdW}^j)-1)]}}$$ (34)

whith $R_\mathrm{vdW}^i$ being the van-der-Waals radius for atom $i$ and $\alpha$ is a parameter that is usually set to 23 (Ref. [1]) or 20 (Ref. [2]).

References:

$[1]$ S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys. 132, 154104 (2010)
$[2]$ S. Grimme, J. Comp. Chem. 25, 1463 (2004).
$[3]$ S. Grimme, J. Comp. Chem. 27, 1787 (2006).

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