DFT-D2: Difference between revisions

Latest revision as of 14:34, 6 March 2025

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

[math]\displaystyle{ 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 first two summations are over all [math]\displaystyle{ N_{at} }[/math] atoms in the unit cell and the third summation is over all translations of the unit cell [math]\displaystyle{ {\mathbf{L}}=(l_1,l_2,l_3) }[/math] where the prime indicates that [math]\displaystyle{ i\not=j }[/math] for [math]\displaystyle{ {\mathbf{L}}=0 }[/math]. [math]\displaystyle{ C_{6ij} }[/math] denotes the dispersion coefficient for the atom pair [math]\displaystyle{ ij }[/math], [math]\displaystyle{ {r}_{ij,\mathbf{L}} }[/math] is the distance between atom [math]\displaystyle{ i }[/math] located in the reference cell [math]\displaystyle{ \mathbf{L}=0 }[/math] and atom [math]\displaystyle{ j }[/math] in the cell [math]\displaystyle{ L }[/math] and the term [math]\displaystyle{ 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]\displaystyle{ E_{\mathrm{disp}} }[/math] corresponding to interactions over distances longer than a certain suitably chosen cutoff radius (VDW_RADIUS, see below) contribute only negligibly to [math]\displaystyle{ E_{\mathrm{disp}} }[/math] and can be ignored. Parameters [math]\displaystyle{ C_{6ij} }[/math] and [math]\displaystyle{ R_{0ij} }[/math] are computed using the following combination rules:

[math]\displaystyle{ C_{6ij} = \sqrt{C_{6ii} C_{6jj}} }[/math]

and

[math]\displaystyle{ R_{0ij} = R_{0i}+ R_{0j}. }[/math]

The values for [math]\displaystyle{ C_{6ii} }[/math] and [math]\displaystyle{ R_{0i} }[/math] are tabulated for each element and are insensitive to the particular chemical situation (for instance, [math]\displaystyle{ 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:

[math]\displaystyle{ f_{d,6}(r_{ij}) = \frac{s_6}{1+e^{-d(r_{ij}/(s_R\,R_{0ij})-1)}} }[/math]

whereby the global scaling parameter [math]\displaystyle{ s_6 }[/math] has been optimized for several different DFT functionals such as PBE ([math]\displaystyle{ s_6=0.75 }[/math]), BLYP ([math]\displaystyle{ s_6=1.2 }[/math]) or B3LYP ([math]\displaystyle{ s_6=1.05 }[/math]). The parameter [math]\displaystyle{ s_R }[/math] is usually fixed at 1.00.

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]

Usage

The DFT-D2 method is activated by setting IVDW=1 or 10 (or the obsolete LVDW=.TRUE.). 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 [math]\displaystyle{ \AA }[/math]) for pair interactions
VDW_S6=0.75 : global scaling factor [math]\displaystyle{ s_6 }[/math] (available in VASP.5.3.4 and later)
VDW_SR=1.00 : scaling factor [math]\displaystyle{ s_R }[/math] (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 [math]\displaystyle{ d }[/math]
VDW_C6=[real array] : [math]\displaystyle{ C_6 }[/math] parameters ([math]\displaystyle{ \mathrm{Jnm}^{6}\mathrm{mol}^{-1} }[/math]) for each species defined in the POSCAR file
VDW_R0=[real array] : [math]\displaystyle{ R_0 }[/math] parameters ([math]\displaystyle{ \AA }[/math]) for each species defined in the POSCAR file
LVDW_EWALD=.FALSE. : the lattice summation in [math]\displaystyle{ 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 VDW_RADIUS (.FALSE.). (available in VASP.5.3.4 and later)

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 [math]\displaystyle{ \AA }[/math].
Ewald's summation in the calculation of [math]\displaystyle{ E_{\mathrm{disp}} }[/math] calculation (controlled via LVDW_EWALD) is implemented according to reference ^[4] and is available as of VASP.5.3.4.

References

[grimme:jcc:06-1] S. Grimme, J. Comput. Chem. 27, 1787 (2006).

[bucko:jpca:10-2] T. Bučko, J. Hafner, S. Lebègue, and J. G. Ángyán, J. Phys. Chem. A 114, 11814 (2010).

[grimme:jcp:10-3] S. Grimme, J. Antony, S. Ehrlich, and S. Krieg, J. Chem. Phys. 132, 154104 (2010).

[kerber:jcc:08-4] T. Kerber, M. Sierka, and J. Sauer, J. Comput. Chem. 29, 2088 (2008).

[1]

[2]

[3]

[4]

@@ Line 1: / Line 1: @@
-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 <math>N_{at}</math> and all translations of the unit cell <math>{L}=(l_1,l_2,l_3)</math>. The prime indicates that <math>i\not=j</math> for <math>{L}=0</math>, <math>C_{6ij}</math> denotes the dispersion coefficient for the atom pair <math>ij</math>, <math>{r}_{ij,L}</math> is the distance between atom <math>i</math> located in the reference cell <math>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 eq.~\ref{eq:VDWenergy}
+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:
-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.
-{\tt VDW\_R0}      &= [real array] & $R_0$ parameters ({\AA}) for each species \\
-           & & defined in POSCAR\\
+The performance of PBE-D2 method in optimization of various crystalline systems has been tested systematically in reference {{cite|bucko:jpca:10}}.
-{\tt LVDW\_EWALD}      &= .FALSE.$|$.TRUE. & compute lattice summation in $E_{disp}$ expression\\
+{{NB|important|It is recommended to use the more advanced and more accurate method {{TAG|DFT-D3}}.{{cite|grimme:jcp:10}}}}
- & & by means of Ewald's summation - no$|$yes\\
-  & & (available in VASP.5.3.4 and later)\\
+== Usage ==
-\end{tabular}
-\\
+The DFT-D2 method is activated by setting {{TAG|IVDW}}=1 or 10 (or the obsolete {{TAG|LVDW}}=''.TRUE.''). Optionally, the damping function and the vdW parameters can be controlled using the following flags (the given values are the default ones):
-\\
-\noindent The performance of PBE-D2 method in optimization of
+*{{TAG|VDW_RADIUS}}=50.0 : cutoff radius (in <math>\AA</math>) for pair interactions
-various crystalline systems has been tested systematically in J. Phys. Chem. A 114, 11814 (2010).\\
+*{{TAG|VDW_S6}}=0.75 : global scaling factor <math>s_6</math> (available in VASP.5.3.4 and later)
-\vspace{5mm}
+*{{TAG|VDW_SR}}=1.00 : scaling factor <math>s_R</math> (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)
-\noindent IMPORTANT NOTES:
+*{{TAG|VDW_D}}=20.0 : damping parameter <math>d</math>
-\begin{itemize}
+*{{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
-\item
+*{{TAG|VDW_R0}}=[real array] : <math>R_0</math> parameters (<math>\AA</math>) for each species defined in the {{TAG|POSCAR}} file
-the defaults for {\tt VDW\_C6} and {\tt VDW\_R0} are defined
+*{{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)
-only for elements in the first five rows of periodic table (i.e. H-Xe)
-- if the system contains other elements the user must define these parameters in INCAR.
+{{NB|mind|
-\item
+*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}}.
-the defaults for parameters controlling damping function ({\tt VDW\_S6}, {\tt VDW\_SR}, {\tt VDW\_D})
+*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}}.
-are available only for the PBE functional. If functional other than PBE is
+*As of VASP.5.3.4, the default value for {{TAG|VDW_RADIUS}} has been increased from 30 to 50 <math>\AA</math>.
-used in DFT+D2 calculation, the value of {\tt VDW\_S6}  (or {\tt VDW\_SCALING} in versions before VASP.5.3.4)
+*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.}}
-must be defined in INCAR.
-\item
+== Related tags and articles ==
-as of VASP.5.3.4, the default value for {\tt VDW\_RADIUS} has been increased from
+{{TAG|VDW_RADIUS}},
-to 50 {\AA}.
+{{TAG|VDW_S6}},
-\item
+{{TAG|VDW_SR}},
-Ewald's summation in $E_{disp}$ calculation (controlled via {\tt LVDW\_EWALD})
+{{TAG|VDW_SCALING}},
-implemented according to Ref.~\cite{Kerber:08}
+{{TAG|VDW_D}},
-is available as of VASP.5.3.4
+{{TAG|VDW_C6}},
-\end{itemize}
+{{TAG|VDW_R0}},
+{{TAG|LVDW_EWALD}},
+{{TAG|IVDW}},
+{{TAG|DFT-ulg}},
+{{TAG|DFT-D3}},
+[[DFT-D4]]
 == 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:Howto]]
-[[Category:INCAR]]