DFT-ulg: Difference between revisions

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.

References

↑ ^a ^b ^c H. Kim, J.-M. Choi, and W. A. Goddard, III, J. Phys. Chem. Lett. 3, 360 (2012).

[kim:jpcl:2012-1] H. Kim, J.-M. Choi, and W. A. Goddard, III, J. Phys. Chem. Lett. 3, 360 (2012).

[1]

@@ Line 1: / Line 1: @@
 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}  s_{lg}\sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at}}  \sum_{\mathbf{L}} {}^{\prime}  \frac{2D_{0}^{ij}(R_{0}^{ij})^{6}}{r_{ij,L}^{6}+b_{lg}(R_{0}^{ij})^{6}} </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>.
+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>.
+== Usage ==
+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.
 *{{TAG|VDW_RADIUS}}=50.0 : cutoff radius (in <math>\AA</math>) for pair interactions
-*{{TAG|VDW_S6}}=0.7012 : global scaling factor <math>s_6</math> (available in VASP.5.3.5 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.5.3.5 and later)
+*{{TAG|VDW_D}}=0.6966 :  universal correction parameter <math>b_{lg}</math>
-*{{TAG|VDW_D}}=0.6966 : 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.5.3.5 and later)
+{{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.}}
 == Related tags and articles ==
@@ Line 20: / Line 25: @@
 {{TAG|VDW_R0}},
 {{TAG|LVDW_EWALD}},
-{{TAG|IVDW}}
+{{TAG|IVDW}},
+{{TAG|DFT-D2}}
 == References ==
@@ Line 26: / Line 32: @@
 ----
-[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]]
+[[Category:Exchange-correlation functionals]][[Category:van der Waals functionals]][[Category:Theory]][[Category:Howto]]