DFT-ulg: Difference between revisions

Revision as of 15:22, 1 February 2023

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{2D_{0}^{ij}(R_{0}^{ij})^{6}}{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].

References

↑ 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 3: / Line 3: @@
 :<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>
-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} = \sqrt{C_{6ii} C_{6jj}}</math>
-and
-:<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_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)
-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 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.}}
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