DFT-ulg: Difference between revisions

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In the DFT-ulg method of Grimme{{cite|kim:jpcl:2012}}, the correction term takes the form:
In the DFT-ulg method of Kim et al.{{cite|kim:jpcl:2012}}, 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,\mathbf{L}}) </math>
:<math>E_{\mathrm{disp}} = -\frac{1}{2}  s_{lg}\sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}}  \sum_{\mathbf{L}} {}^{\prime}  \frac{C_{6ij}}{r_{ij,L}^{6}+b_{lg}(R_{0}^{ij})^{6}} </math>


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:
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>.


:<math>C_{6ij} = \sqrt{C_{6ii} C_{6jj}}</math>
== Usage ==


and
The DFT-ulg method can be activated by setting {{TAG|IVDW}}=''3''. The parameters in the DFT-ulg method (see Ref. {{cite|kim:jpcl:2012}} for details) that can be modified are listed below.
 
:<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 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>
 
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):


*{{TAG|VDW_RADIUS}}=50.0 : cutoff radius (in <math>\AA</math>) for pair interactions
*{{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_S6}}=0.7012 : global scaling parameter <math>s_{lg}</math>
*{{TAG|VDW_SR}}=1.00 : scaling factor <math>s_R</math> (available in VASP.5.3.4 and later)
*{{TAG|VDW_D}}=0.6966 : universal correction parameter <math>b_{lg}</math>
*{{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_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|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)
*{{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.5.3.5 and later)
 
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}}}}


{{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}}.}}
{{NB|mind|The default value of the parameter <math>s_{lg}</math> (0.7012) was determined in conjunction with the PBE {{TAG|GGA}} functional{{cite|kim:jpcl:2012}}. Therefore, it is not recommended to use the DFT-ulg dispersion correction with a {{TAG|GGA}} functional other than PBE, unless <math>s_{lg}</math> is reoptimized.}}
{{NB|mind|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}}.}}
{{NB|mind|As of VASP.5.3.4, the default value for {{TAG|VDW_RADIUS}} has been increased from 30 to 50 <math>\AA</math>.}}
{{NB|mind|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 ==
== Related tags and articles ==
{{TAG|VDW_RADIUS}},
{{TAG|VDW_RADIUS}},
{{TAG|VDW_S6}},
{{TAG|VDW_S6}},
{{TAG|VDW_SR}},
{{TAG|VDW_SCALING}},
{{TAG|VDW_D}},
{{TAG|VDW_D}},
{{TAG|VDW_C6}},
{{TAG|VDW_C6}},
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{{TAG|LVDW_EWALD}},
{{TAG|LVDW_EWALD}},
{{TAG|IVDW}},
{{TAG|IVDW}},
{{TAG|DFT-D3}},
{{TAG|DFT-D2}}
{{TAG|Tkatchenko-Scheffler method}},
{{TAG|Tkatchenko-Scheffler method with iterative Hirshfeld partitioning}},
{{TAG|Self-consistent screening in Tkatchenko-Scheffler method}},
{{TAG|Many-body dispersion energy}},
{{TAG|dDsC dispersion correction}}


== References ==
== References ==
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[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]][[Category:Howto]]

Latest revision as of 14:42, 6 March 2025

In the DFT-ulg method of Kim et al.[1], the correction term takes the form:

[math]\displaystyle{ E_{\mathrm{disp}} = -\frac{1}{2} s_{lg}\sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}} \sum_{\mathbf{L}} {}^{\prime} \frac{C_{6ij}}{r_{ij,L}^{6}+b_{lg}(R_{0}^{ij})^{6}} }[/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].

Usage

The DFT-ulg method can be activated by setting IVDW=3. The parameters in the DFT-ulg method (see Ref. [1] for details) that can be modified are listed below.

  • VDW_RADIUS=50.0 : cutoff radius (in [math]\displaystyle{ \AA }[/math]) for pair interactions
  • VDW_S6=0.7012 : global scaling parameter [math]\displaystyle{ s_{lg} }[/math]
  • VDW_D=0.6966 : universal correction parameter [math]\displaystyle{ b_{lg} }[/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.5.3.5 and later)


Mind: The default value of the parameter [math]\displaystyle{ s_{lg} }[/math] (0.7012) was determined in conjunction with the PBE GGA functional[1]. Therefore, it is not recommended to use the DFT-ulg dispersion correction with a GGA functional other than PBE, unless [math]\displaystyle{ s_{lg} }[/math] is reoptimized.

Related tags and articles

VDW_RADIUS, VDW_S6, VDW_D, VDW_C6, VDW_R0, LVDW_EWALD, IVDW, DFT-D2

References