DFT-D2: Difference between revisions
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In the D2 method of Grimme{{cite|grimme:jcc:06}} | 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 | 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: | ||
:<math>C_{6ij} = \sqrt{C_{6ii} C_{6jj}}</math> | :<math>C_{6ij} = \sqrt{C_{6ii} C_{6jj}}</math> | ||
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and | and | ||
<math>R_{0ij} = R_{0i}+ R_{0j}. </math> | :<math>R_{0ij} = R_{0i}+ R_{0j}. </math> | ||
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 | 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: | ||
:<math>f_{d,6}(r_{ij}) = \frac{s_6}{1+e^{-d(r_{ij}/(s_R\,R_{0ij})-1)}}</math> | :<math>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>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>) | 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 performance of PBE-D2 method in optimization of various crystalline systems has been tested systematically in reference {{cite|bucko:jpca:10}}. | |||
{{NB|important|It is recommended to use the more advanced and more accurate method {{TAG|DFT-D3}}.{{cite|grimme:jcp:10}}}} | |||
== Usage == | |||
== | 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): | ||
* | *{{TAG|VDW_RADIUS}}=50.0 : cutoff radius (in <math>\AA</math>) for pair interactions | ||
*{{TAG|VDW_S6}}=0.75 : global scaling factor <math>s_6</math> (available in VASP.5.3.4 and later) | |||
* | *{{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) | |||
*{{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 | |||
*{{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) | |||
{{NB|mind| | |||
*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 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}}. | |||
*As of VASP.5.3.4, the default value for {{TAG|VDW_RADIUS}} has been increased from 30 to 50 <math>\AA</math>. | *As of VASP.5.3.4, the default value for {{TAG|VDW_RADIUS}} has been increased from 30 to 50 <math>\AA</math>. | ||
*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.}} | |||
== Related tags and articles == | |||
{{TAG|VDW_RADIUS}}, | |||
{{TAG|VDW_S6}}, | |||
{{TAG|VDW_SR}}, | |||
{{TAG|VDW_SCALING}}, | |||
{{TAG|VDW_D}}, | |||
{{TAG|VDW_C6}}, | |||
{{TAG|VDW_R0}}, | |||
{{TAG|LVDW_EWALD}}, | |||
{{TAG|IVDW}}, | {{TAG|IVDW}}, | ||
{{TAG| | {{TAG|DFT-ulg}}, | ||
{{TAG|DFT-D3}}, | {{TAG|DFT-D3}}, | ||
[[DFT-D4]] | |||
== References == | == References == | ||
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---- | ---- | ||
[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]][[Category:Howto]] | |||
[[Category:Exchange-correlation functionals]][[Category:van der Waals]][[Category:Howto]] | |||
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:
|
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