DDsC dispersion correction: Difference between revisions

Revision as of 15:09, 20 January 2017

The expression for dispersion energy within thedDsC dispersion correction^[1]^[2] (DFT-dDsC) is very similar to that of the DFT-D2 method (see the equation for $E_{disp}$ for the {TAG|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

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

where $N_{\mathrm {at} }$ is the number of atoms in the system and $b$ 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://www.vasp.at/wiki/restbase/vasp.at/v1/":): f_{{6}}(bR_{{ij}}) is defined as follows

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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://www.vasp.at/wiki/restbase/vasp.at/v1/":): b :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/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://www.vasp.at/wiki/restbase/vasp.at/v1/":): {b}_{{ii,{\mathrm {asym}}}}={b}_{{0}}\cdot {\sqrt[ {3}]{{\frac {1}{\alpha _{{i}}}}}}

The effective atom-in-molecule polarizabilities $\alpha _{i}$ 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 $x$

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

where $Z_{i}$ and $N_{i}^{D}$ are the nuclear charge and Hirshfeld dominant population of atom $i$ , respectively. The term $2q_{ij}=q_{ij}+q_{ji}$ is a covalent bond index based on the overlap of conventional Hirshfeld populations $q_{ij}=\int w_{i}({\mathbf {r} })w_{j}({\mathbf {r} })\rho ({\mathbf {r} })d{\mathbf {r} }$ , 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 $\mathrm {\AA}$ ) for pair interactions
VDW_S6=13.96 scaling factor ${a}_{0}$
VDW_SR=1.32 scaling factor ${b}_{0}$

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

References

↑ ^a ^b S. N. Steinmann, and C. Corminboeuf, J. Chem. Phys. 134, 044117 (2011).
↑ ^a ^b S. N. Steinmann, and C. Corminboeuf, J. Chem. Theory Comput. 7, 3567 (2011).
↑ http://aip.scitation.org/doi/full/10.1063/1.2795701 A. D. Becke, and E. R. Johnson, ``Exchange-hole dipole moment and the dispersion interaction, J. Chem. Phys. 122, 154104 (2005). ]
↑ S. Gautier, S. N. Steinmann, C. Michel, P. Fleurat-Lessard, and P. Sautet, Phys. Chem. Chem. Phys. 17, 28921 (2015).
↑ E. Bremond, N. Golubev, S. N. Steinmann, and C. Corminboeuf, J. Chem. Phys. 140, 18A516 (2014).

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] ttp://aip.scitation.org/doi/full/10.1063/1.2795701 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).

[1]

[2]

[3]

[4]

[5]

@@ Line 24: / Line 24: @@
 <math>{b}_{ii,\mathrm{asym}}={b}_{0}\cdot \sqrt[3]{\frac{1}{\alpha_{i}}}</math>
-The effective atom-in-molecule polarizabilities ${\alpha }_{i}$ are
+The effective atom-in-molecule polarizabilities <math>\alpha_{i}</math> 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 {{TAG|Tkatchenko-Scheffler method}} and {{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}} but the Hirshfeld-dominant instead of the conventional Hirshfeld partitioning is used.
-computed from the tabulated free-atomic polarizabilities (available for the
+The last element of the correction is the damping argument <math>x</math>
-elements of the first six
-rows of the periodic table except of lanthanides) in the same way as in the method
-of Tkatchenko and Scheffler (see Sec.~\ref{sec:vdwTS})
-but the Hirshfeld-dominant instead of the conventional Hirshfeld partitioning is used.
-The last element of the correction is the damping argument $x$
-\
-\begin{equation}
+<math>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}}</math>
-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}}
-\label{eqn:dDsCx}
-\end{equation}
-where $Z_i$ and $N_i^D$ are the nuclear charge and Hirshfeld dominant population of atom $i$, respectively.
-The term $2q_{ij} = q_{ij} + q_{ji}$ is a covalent bond index based on the overlap of conventional
-Hirshfeld populations $q_{ij}=\int w_i({\mathbf{r}})w_j({\mathbf{r}})\rho({\mathbf{r}})d{\mathbf{r}}$,
-and the fractional term in the parentheses is a distance-dependent ionic bond index.
-\noindent The DFT-dDsC calculation is invoked by setting {\tt IVDW}=4.
+where <math>Z_i</math> and <math>N_i^D</math> are the nuclear charge and Hirshfeld dominant population of atom <math>i</math>, respectively.
-The default values for damping function parameters are available for
+The term <math>2q_{ij} = q_{ij} + q_{ji}</math> is a covalent bond index based on the overlap of conventional Hirshfeld populations <math>q_{ij}=\int w_i({\mathbf{r}})w_j({\mathbf{r}})\rho({\mathbf{r}})d{\mathbf{r}}</math>, and the fractional term in the parentheses is a distance-dependent ionic bond index.
-the  functionals
-PBE ({\tt GGA=PE}) and revPBE ({\tt GGA=RP}).
-If other functional is used, the user must
-define these parameters via corresponding tags in
-INCAR (parameters for common DFT functionals can be found in Ref.~\cite{Steinmann:11b})
-The following parameters can be optionally defined in {\tt INCAR}:\\
-\begin{tabular}{rll}
-{\tt VDW\_RADIUS}  &= 50.0      & cutoff radius ({\AA}) for pair interactions\\
-{\tt VDW\_S6} &= 13.96    & scaling factor ${a}_{0}$\\
-{\tt VDW\_SR} &= 1.32      & scaling factor ${b}_{0}$\\
-\end{tabular}
-\hspace{5mm}
-\noindent Performance of PBE-dDsC in description of the adsorption of
+The DFT-dDsC calculation is invoked by setting {{TAG|IVDW}}=4. The default values for damping function parameters are available for the  functionals PBE ({{TAG|GGA}}=''PE''}) and revPBE ({{TAG|GGA}}=''RP''). If another functional is used, the user must define these parameters via corresponding tags in the {{TAG|INCAR}} file (parameters for common DFT functionals can be found in reference <ref name="steinmann2011b"/>. The following parameters can be optionally defined in the {{TAG|INCAR}} file (the shown values are the default valeus):
-hydrocarbons on Pt(111)
+*{{TAG|VDW_RADIUS}}=50.0 cutoff radius (in <math>\AA</math>) for pair interactions
-has been examined in Ref.~\cite{Gautier:15} PCCP 17, 28921 (2015).\\
+*{{TAG|VDW_S6}}=13.96 scaling factor <math>{a}_{0}</math>
+*{{TAG|VDW_SR}}=1.32  scaling factor <math>{b}_{0}</math>
-\noindent IMPORTANT NOTES:
+The Performance of PBE-dDsC in the description of the adsorption of hydrocarbons on Pt(111) has been examined in reference <ref name="gautier2015"/>.\\
-\begin{itemize}
-\item
+== IMPORTANT NOTES ==
-the dDsC method has been implemented into VASP by Stephan N. Steinmann
-\item
+*The dDsC method has been implemented into VASP by Stephan N. Steinmann.
-this method requires the use of POTCAR files from the
+*This method requires the use of {{TAG|POTCAR}} files from the PAW dataset version 52 or later
-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.
-\item
+*It is essential that a sufficiently dense FFT grid (controlled via {{TAG|NGFX(Y,Z)}}) is used in the DFT-dDsC, especially for accurate gradients. We strongly recommend to use {{TAG|PREC}}=''Accurate'' for this type of calculations (in any case, avoid using {{TAG|PREC}}=''Low'').
-the input reference
+*The charge-density dependence of gradients is neglected. This approximation has been thoroughly investigated and validated in reference <ref name="bremond2014"/>.
-polarizabilities for non-interacting atoms are available only for elements
-of the first six rows of periodic table except of lanthanides
-\item
-it is essential that a sufficiently dense FFT grid (controlled via {\tt NGFX(Y,Z)}) is
-used in the DFT-dDsC, especially for accurate gradients - we strongly recommend
-to use {\tt PREC=Accurate} for this type of calculations
-(in any case, avoid using {\tt PREC=Low}).
-\item
-the charge-density dependence of gradients is neglected.
-This approximation has been thoroughly
-investigated and validated.\cite{Bremond:14}
-\end{itemize}
 == Related Tags and Sections ==
@@ Line 88: / Line 52: @@
 {{TAG|DFT-D2}},
 {{TAG|DFT-D3}},
-{{TAG|Tkatchenko-Scheffler method}}
+{{TAG|Tkatchenko-Scheffler method}},
+{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},
+{{TAG|Many-body dispersion energy method}}
 == References ==
@@ Line 95: / Line 61: @@
 <ref name="steinmann2011b">[http://pubs.acs.org/doi/abs/10.1021/ct200602x S. N. Steinmann, and C. Corminboeuf, J. Chem. Theory Comput. 7, 3567 (2011).]</ref>
 <ref name="becke2007">http://aip.scitation.org/doi/full/10.1063/1.2795701 A. D. Becke, and E. R. Johnson, ``Exchange-hole dipole moment and the dispersion interaction'', J. Chem. Phys. 122, 154104 (2005). ]</ref>
-<ref name="kerber">[http://onlinelibrary.wiley.com/doi/10.1002/jcc.21069/abstract Kerber and J. Sauer, J. Comp. Chem. 29, 2088 (2008).]</ref>
+<ref name="gautier2015">[http://pubs.rsc.org/en/Content/ArticleLanding/2015/CP/C5CP04534G#!divAbstract S. Gautier, S. N. Steinmann, C. Michel, P. Fleurat-Lessard, and P. Sautet, Phys. Chem. Chem. Phys. 17, 28921 (2015).]</ref>
+<ref name="bremond2014">[http://aip.scitation.org/doi/10.1063/1.4867195 E. Bremond, N. Golubev, S. N. Steinmann, and C. Corminboeuf, J. Chem. Phys. 140, 18A516 (2014).]</ref>
 </references>
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