DDsC dispersion correction

The expression for dispersion energy within the dDsC dispersion correction^[1]^[2] (DFT-dDsC) is very similar to that of the DFT-D2 method (see the equation for 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_{{disp}} for the DFT-D2 method). The important difference is, however, that the dispersion coefficients and damping function are charge-density dependent. The dDsC method is therefore able to take into account variations in the vdW contributions of atoms due to their local chemical environment. In this method, polarizability, dispersion coefficients, charge and charge-overlap of an atom in a molecule or solid are computed in the basis of a simplified exchange-hole dipole moment formalism^[1] pioneered by Becke and Johnson^[3].

The dDsC dispersion energy is expressed as follows

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}}}}}=-\sum \limits _{{i=2}}^{{{{N}_{{\mathrm {at}}}}}}{\sum \limits _{{j=1}}^{{i-1}}\sum \limits _{{n=3}}^{{n=5}}{{{f}_{{2n}}}(b{{R}_{{ij}}}){\frac {C_{{2n}}^{{ij}}}{R_{{ij}}^{{2n}}}}}}{{E}_{{{\mathrm {disp}}}}}=-\sum \limits _{{i=2}}^{{{{N}_{{{\mathrm {at}}}}}}}{\sum \limits _{{j=1}}^{{i-1}}{{{f}_{{6}}}(b{{R}_{{ij}}}){\frac {C_{{6,ij}}}{R_{{ij}}^{{6}}}}}}

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/":): N_{{{\mathrm {at}}}} is the number of atoms in the system 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/":): b is the Tang and Toennies (TT) damping factor. The damping function 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_{{6}}(bR_{{ij}}) is defined as follows

$f_{6}(x)=1-\exp(-x)\sum _{k=0}^{6}{\frac {x^{k}}{k!}}$

and its role is to attenuate the correction at short internuclear distances. A key component of the dDsC method is the damping factor 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/":): b :

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/":): b(x)={\frac {2b_{{ij,{\mathrm {asym}}}}}{{{e}^{{{{a}_{{0}}}\cdot x}}}+1}}

where the fitted 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/":): a_{{0}} controls the short-range behaviour 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/":): x is the damping argument for the TT-damping factor associated with two separated 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/":): b_{{ij,{\mathrm {asym}}}} ). The term 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/":): b_{{ij,{\mathrm {asym}}}} is computed according to the combination rule:

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/":): b_{{ij,{\mathrm {asym}}}}=2{\frac {b_{{ii,{\mathrm {asym}}}}\cdot b_{{jj,{\mathrm {asym}}}}}{b_{{ii,{\mathrm {asym}}}}+b_{{jj,{\mathrm {asym}}}}}}

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/":): b_{{ii,{\mathrm {asym}}}} being estimated from effective atomic polarizabilities:

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/":): {b}_{{ii,{\mathrm {asym}}}}={b}_{{0}}\cdot {\sqrt[ {3}]{{\frac {1}{\alpha _{{i}}}}}}

The effective atom-in-molecule polarizabilities 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 _{{i}} are computed from the tabulated free-atomic polarizabilities (available for the elements of the first six rows of the periodic table except of lanthanides) in the same way as in the Tkatchenko-Scheffler method and Tkatchenko-Scheffler method with iterative Hirshfeld partitioning but the Hirshfeld-dominant instead of the conventional Hirshfeld partitioning is used. The last element of the correction is the damping argument 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/":): x

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/":): x=\left(2{{q}_{{ij}}}+{\frac {|({{Z}_{{i}}}-N_{{i}}^{{D}})\cdot ({{Z}_{{j}}}-N_{{j}}^{{D}})|}{{{r}_{{ij}}}}}\right){\frac {N_{{i}}^{{D}}+N_{{j}}^{{D}}}{N_{{i}}^{{D}}\cdot N_{{j}}^{{D}}}}

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/":): Z_{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/":): N_{i}^{D} are the nuclear charge and Hirshfeld dominant population of atom 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 , respectively. The term 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/":): 2q_{{ij}}=q_{{ij}}+q_{{ji}} is a covalent bond index based on the overlap of conventional Hirshfeld populations 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/":): q_{{ij}}=\int w_{i}({{\mathbf {r}}})w_{j}({{\mathbf {r}}})\rho ({{\mathbf {r}}})d{{\mathbf {r}}} , and the fractional term in the parentheses is a distance-dependent ionic bond index.

The DFT-dDsC calculation is invoked by setting IVDW=4. The default values for damping function parameters are available for the functionals PBE (GGA=PE}) and revPBE (GGA=RP). If another functional is used, the user must define these parameters via corresponding tags in the INCAR file (parameters for common DFT functionals can be found in reference ^[2]. The following parameters can be optionally defined in the INCAR file (the shown values are the default valeus):

VDW_RADIUS=50.0 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 pair interactions
VDW_S6=13.96 scaling factor 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}_{{0}}
VDW_SR=1.32 scaling factor 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/":): {b}_{{0}}

The Performance of PBE-dDsC in the description of the adsorption of hydrocarbons on Pt(111) has been examined in reference ^[4].\\

IMPORTANT NOTES

The dDsC method has been implemented into VASP by Stephan N. Steinmann.
This method requires the use of POTCAR files from the PAW dataset version 52 or later
The input reference polarizabilities for non-interacting atoms are available only for elements of the first six rows of periodic table except of the lanthanides.
It is essential that a sufficiently dense FFT grid (controlled via NGFX(Y,Z)) is used in the DFT-dDsC, especially for accurate gradients. We strongly recommend to use PREC=Accurate for this type of calculations (in any case, avoid using PREC=Low).
The charge-density dependence of gradients is neglected. This approximation has been thoroughly investigated and validated in reference ^[5].

Related Tags and Sections

IVDW, IALGO, DFT-D2, DFT-D3, Tkatchenko-Scheffler method, Tkatchenko-Scheffler method with iterative Hirshfeld partitioning, Many-body dispersion energy method

Examples that use this tag

References

Contents

[steinmann2011-1] S. N. Steinmann, and C. Corminboeuf, J. Chem. Phys. 134, 044117 (2011).

[steinmann2011b-2] S. N. Steinmann, and C. Corminboeuf, J. Chem. Theory Comput. 7, 3567 (2011).

[becke2007-3] A. D. Becke, and E. R. Johnson, ``Exchange-hole dipole moment and the dispersion interaction, J. Chem. Phys. 122, 154104 (2005).

[gautier2015-4] S. Gautier, S. N. Steinmann, C. Michel, P. Fleurat-Lessard, and P. Sautet, Phys. Chem. Chem. Phys. 17, 28921 (2015).

[bremond2014-5] E. Bremond, N. Golubev, S. N. Steinmann, and C. Corminboeuf, J. Chem. Phys. 140, 18A516 (2014).

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