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In the D2 method of Grimme<ref name="grimme"/>, the correction term takes the form:
In the DFT-D2 method of Grimme{{cite|grimme:jcc:06}}, the correction term takes the form:


<math>E_{\mathrm{disp}} = -\frac{1}{2}  \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}}  \sum_{\mathbf{L}} ^{\prime}  \frac{C_{6ij}}{r_{ij,L}^{6}}  f_{d,6}({r}_{ij,L}) </math>
:<math>E_{\mathrm{disp}} = -\frac{1}{2}  \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}}  \sum_{\mathbf{L}} {}^{\prime}  \frac{C_{6ij}}{r_{ij,L}^{6}}  f_{d,6}({r}_{ij,\mathbf{L}}) </math>


where the summations are over all atoms $N_{at}$ and all
where the first two summations are over all <math>N_{at}</math> atoms in the unit cell and the third summation is over all translations of the unit cell <math>{\mathbf{L}}=(l_1,l_2,l_3)</math> where the prime indicates that <math>i\not=j</math> for <math>{\mathbf{L}}=0</math>. <math>C_{6ij}</math> denotes the dispersion coefficient for the atom pair <math>ij</math>, <math>{r}_{ij,\mathbf{L}}</math> is the distance between atom <math>i</math> located in the reference cell <math>\mathbf{L}=0</math> and atom <math>j</math> in the cell <math>L</math> and the term <math>f(r_{ij})</math> is a damping function whose role is to scale the force field such as to minimize the contributions from interactions within typical bonding distances. In practice, the terms in the equation for <math>E_{\mathrm{disp}}</math> corresponding to interactions over distances longer than a certain suitably chosen cutoff radius ({{TAG|VDW_RADIUS}}, see below) contribute only negligibly to  <math>E_{\mathrm{disp}}</math> and can be ignored. Parameters <math>C_{6ij}</math> and <math>R_{0ij}</math> are computed using the following combination rules:
translations of the unit cell ${L}=(l_1,l_2,l_3)$,
the prime indicates that $i\not=j$ for ${L}=0$,
$C_{6ij}$ denotes the dispersion
coefficient for the atom pair $ij$,
${r}_{ij,{L}}$ is distance between atom $i$ located
in the reference cell $L$=0 and atom $j$ in the cell ${L}$,
and the term $f(r_{ij})$ is a damping function
whose role is to scale the force field such as to minimize
contributions from interactions within typical bonding
distances. In practice, the terms in eq.~\ref{eq:VDWenergy}
corresponding to interactions over distances
longer than a certain suitably chosen cutoff radius contribute
only negligibly to  $E_{\rm disp}$ and can be ignored.
Parameters $C_{6ij}$ and $R_{0ij}$ are computed using the
following combination rules:
\begin{equation}
    C_{6ij} = \sqrt{C_{6ii} C_{6jj}},
\end{equation}
\begin{equation}
    R_{0ij} = R_{0i}+ R_{0j},
\end{equation}
the values of $C_{6ii}$ and $R_{0i}$ are tabulated for
each element and are insensitive to the particular
chemical situation (for instance,
$C_6$ for carbon in methane takes exactly the same value
as that for C in benzene within this approximation).
In the original method of Grimme~\cite{Grimme:06}, Fermi-type
damping function is used:
\begin{equation}\label{eq_damping}
f_{d,6}(r_{ij}) = \frac{s_6}{1+e^{-d(r_{ij}/(s_R\,R_{0ij})-1)}},
\end{equation}
whereby the global scaling parameter $s_6$
has been optimized for several different DFT functionals such as
PBE ($s_6=0.75$), BLYP ($s_6=1.2$), and B3LYP ($s_6=1.05$).
The parameter $s_R$ is usually fixed at 1.00.
The DFT-D2 method can be activated by setting {\tt IVDW}=1$|$10 or
by specifying {\tt LVDW}=.TRUE. (this parameter is obsolete as of VASP.5.3.3).
Optionally, the damping function and the vdW parameters can be controlled using the following flags
(the default values are listed):\\


\begin{tabular}{rll}
:<math>C_{6ij} = \sqrt{C_{6ii} C_{6jj}}</math>
{\tt VDW\_RADIUS} &= 50.0     & cutoff radius ({\AA}) for pair interactions\\
 
{\tt VDW\_S6} &= 0.75     & global scaling factor $s_6$\\
and
                & & (available in VASP.5.3.4 and later)\\
 
{\tt VDW\_SR} &= 1.00     & scaling factor $s_R$\\
:<math>R_{0ij} = R_{0i}+ R_{0j}. </math>
& & (available in VASP.5.3.4 and later)\\
 
{\tt VDW\_SCALING} & =0.75 & the same as {\tt VDW\_S6}\\
The values for <math>C_{6ii}</math> and <math>R_{0i}</math> are tabulated for each element and are insensitive to the particular chemical situation (for instance, <math>C_6</math> for carbon in methane takes exactly the same value as that for C in benzene within this approximation). In the DFT-D2 method, a Fermi-type damping function is used:
  & & (obsolete as of VASP.5.3.4)\\
 
{\tt VDW\_D}       &= 20.0     & damping parameter $d$\\
:<math>f_{d,6}(r_{ij}) = \frac{s_6}{1+e^{-d(r_{ij}/(s_R\,R_{0ij})-1)}}</math>
{\tt VDW\_C6}     &= [real array] & $C_6$ parameters ($Jnm^6mol^{-1}$) for each species\\
 
            & &  defined in POSCAR\\
whereby the global scaling parameter <math>s_6</math> has been optimized for several different DFT functionals such as PBE (<math>s_6=0.75</math>), BLYP (<math>s_6=1.2</math>) or B3LYP (<math>s_6=1.05</math>). The parameter <math>s_R</math> is usually fixed at 1.00. The DFT-D2 method can be activated by setting {{TAG|IVDW}}=''1|10'' or by specifying {{TAG|LVDW}}=''.TRUE.'' (this parameter is obsolete as of VASP.5.3.3). Optionally, the damping function and the vdW parameters can be controlled using the following flags (the given values are the default ones):
{\tt VDW\_R0}     &= [real array] & $R_0$ parameters ({\AA}) for each species \\
 
          & & defined in POSCAR\\
*{{TAG|VDW_RADIUS}}=50.0 : cutoff radius (in <math>\AA</math>) for pair interactions
{\tt LVDW\_EWALD}     &= .FALSE.$|$.TRUE. & compute lattice summation in $E_{disp}$ expression\\
*{{TAG|VDW_S6}}=0.75 : global scaling factor <math>s_6</math> (available in VASP.5.3.4 and later)
& & by means of Ewald's summation - no$|$yes\\
*{{TAG|VDW_SR}}=1.00 : scaling factor <math>s_R</math> (available in VASP.5.3.4 and later)
  & & (available in VASP.5.3.4 and later)\\
*{{TAG|VDW_SCALING}}=0.75 : the same as {{TAG|VDW_S6}} (obsolete as of VASP.5.3.4)
\end{tabular}
*{{TAG|VDW_D}}=20.0 : damping parameter <math>d</math>
\\
*{{TAG|VDW_C6}}=[real array] : <math>C_6</math> parameters (<math>\mathrm{Jnm}^{6}\mathrm{mol}^{-1}</math>) for each species defined in the {{TAG|POSCAR}} file
\\
*{{TAG|VDW_R0}}=[real array] : <math>R_0</math> parameters (<math>\AA</math>) for each species defined in the {{TAG|POSCAR}} file
\noindent The performance of PBE-D2 method in optimization of
*{{TAG|LVDW_EWALD}}=''.FALSE.'' : the lattice summation in <math>E_{\mathrm{disp}}</math> expression is computed by means of Ewald's summation (''.TRUE.'' ) or via a real space summation over all atomic pairs within cutoff radius {{TAG|VDW_RADIUS}} (''.FALSE.''). (available in VASP.5.3.4 and later)
various crystalline systems has been tested systematically in J. Phys. Chem. A 114, 11814 (2010).\\
 
\vspace{5mm}
The performance of PBE-D2 method in optimization of various crystalline systems has been tested systematically in reference {{cite|bucko:jpca:10}}.
\\
 
\noindent IMPORTANT NOTES:
{{NB|important|It is recommended to use the more advanced and more accurate method {{TAG|DFT-D3}}.{{cite|grimme:jcp:10}}}}
\begin{itemize}
 
\item
{{NB|mind|
the defaults for {\tt VDW\_C6} and {\tt VDW\_R0} are defined
*The defaults for {{TAG|VDW_C6}} and {{TAG|VDW_R0}} are defined only for elements in the first five rows of the periodic table (i.e. H-Xe). If the system contains other elements the user has to define these parameters in {{TAG|INCAR}}.
only for elements in the first five rows of periodic table (i.e. H-Xe)
*The defaults for parameters controlling the damping function ({{TAG|VDW_S6}}, {{TAG|VDW_SR}}, {{TAG|VDW_D}}) are available for the PBE ({{TAG|GGA}}{{=}}PE), BP, revPBE, PBE0, TPSS, and B3LYP functionals. If any other functional is used in a DFT-D2 calculation, the value of {{TAG|VDW_S6}}  (or {{TAG|VDW_SCALING}} in versions before VASP.5.3.4) has to be defined in {{TAG|INCAR}}.
- if the system contains other elements the user must define these parameters in INCAR.
*As of VASP.5.3.4, the default value for {{TAG|VDW_RADIUS}} has been increased from 30 to 50 <math>\AA</math>.
\item
*Ewald's summation in the calculation of <math>E_{\mathrm{disp}}</math> calculation (controlled via {{TAG|LVDW_EWALD}}) is implemented according to reference {{cite|kerber:jcc:08}} and is available as of VASP.5.3.4.}}
the defaults for parameters controlling damping function ({\tt VDW\_S6}, {\tt VDW\_SR}, {\tt VDW\_D})
 
are available only for the PBE functional. If functional other than PBE is
== Related tags and articles ==
used in DFT+D2 calculation, the value of {\tt VDW\_S6}  (or {\tt VDW\_SCALING} in versions before VASP.5.3.4)
{{TAG|VDW_RADIUS}},
must be defined in INCAR.
{{TAG|VDW_S6}},
\item
{{TAG|VDW_SR}},
as of VASP.5.3.4, the default value for {\tt VDW\_RADIUS} has been increased from
{{TAG|VDW_SCALING}},
30 to 50 {\AA}.
{{TAG|VDW_D}},
\item
{{TAG|VDW_C6}},
Ewald's summation in $E_{disp}$ calculation (controlled via {\tt LVDW\_EWALD})
{{TAG|VDW_R0}},
implemented according to Ref.~\cite{Kerber:08}
{{TAG|LVDW_EWALD}},
is available as of VASP.5.3.4
{{TAG|IVDW}},
\end{itemize}
{{TAG|DFT-ulg}},
{{TAG|DFT-D3}},
[[DFT-D4]]


== References ==
== References ==
<references>
<references/>
<ref name="grimme">[http://onlinelibrary.wiley.com/doi/10.1002/jcc.20495/abstract S. Grimme., J. Comp. Chem. 27, 1787 (2006).]</ref>
 
</references>
----
----
[[The_VASP_Manual|Contents]]
[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
 
[[Category:INCAR]]

Latest revision as of 20:14, 13 June 2024

In the DFT-D2 method of Grimme[1], the correction term takes the form:

where the first two summations are over all atoms in the unit cell and the third summation is over all translations of the unit cell where the prime indicates that for . denotes the dispersion coefficient for the atom pair , is the distance between atom located in the reference cell and atom in the cell and the term is a damping function whose role is to scale the force field such as to minimize the contributions from interactions within typical bonding distances. In practice, the terms in the equation for corresponding to interactions over distances longer than a certain suitably chosen cutoff radius (VDW_RADIUS, see below) contribute only negligibly to and can be ignored. Parameters and are computed using the following combination rules:

and

The values for and are tabulated for each element and are insensitive to the particular chemical situation (for instance, for carbon in methane takes exactly the same value as that for C in benzene within this approximation). In the DFT-D2 method, a Fermi-type damping function is used:

whereby the global scaling parameter has been optimized for several different DFT functionals such as PBE (), BLYP () or B3LYP (). The parameter is usually fixed at 1.00. The DFT-D2 method can be activated by setting IVDW=1|10 or by specifying LVDW=.TRUE. (this parameter is obsolete as of VASP.5.3.3). Optionally, the damping function and the vdW parameters can be controlled using the following flags (the given values are the default ones):

  • VDW_RADIUS=50.0 : cutoff radius (in ) for pair interactions
  • VDW_S6=0.75 : global scaling factor (available in VASP.5.3.4 and later)
  • VDW_SR=1.00 : scaling factor (available in VASP.5.3.4 and later)
  • VDW_SCALING=0.75 : the same as VDW_S6 (obsolete as of VASP.5.3.4)
  • VDW_D=20.0 : damping parameter
  • VDW_C6=[real array] : parameters () for each species defined in the POSCAR file
  • VDW_R0=[real array] : parameters () for each species defined in the POSCAR file
  • LVDW_EWALD=.FALSE. : the lattice summation in expression is computed by means of Ewald's summation (.TRUE. ) or via a real space summation over all atomic pairs within cutoff radius VDW_RADIUS (.FALSE.). (available in VASP.5.3.4 and later)

The performance of PBE-D2 method in optimization of various crystalline systems has been tested systematically in reference [2].


Important: It is recommended to use the more advanced and more accurate method DFT-D3.[3]


Mind:
  • The defaults for VDW_C6 and VDW_R0 are defined only for elements in the first five rows of the periodic table (i.e. H-Xe). If the system contains other elements the user has to define these parameters in INCAR.
  • The defaults for parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available for the PBE (GGA=PE), BP, revPBE, PBE0, TPSS, and B3LYP functionals. If any other functional is used in a DFT-D2 calculation, the value of VDW_S6 (or VDW_SCALING in versions before VASP.5.3.4) has to be defined in INCAR.
  • As of VASP.5.3.4, the default value for VDW_RADIUS has been increased from 30 to 50 .
  • Ewald's summation in the calculation of calculation (controlled via LVDW_EWALD) is implemented according to reference [4] and is available as of VASP.5.3.4.

Related tags and articles

VDW_RADIUS, VDW_S6, VDW_SR, VDW_SCALING, VDW_D, VDW_C6, VDW_R0, LVDW_EWALD, IVDW, DFT-ulg, DFT-D3, DFT-D4

References