DFT-D2: Difference between revisions

Revision as of 10:01, 19 July 2022

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,L}) }[/math]

where the first two summations are over all [math]\displaystyle{ N_{at} }[/math] atoms in the unit cell, the third is over and 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{ 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 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 original method of Grimme^[1], 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 DFT-D2 method can be activated by setting IVDW=1|10 or by specifying 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):

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. decides whether lattice summation in [math]\displaystyle{ E_{disp} }[/math] expression by means of Ewald's summation is computed (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 ^[2].\\

IMPORTANT NOTES

The defaults for VDW_C6 and VDW_R0 are defined 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.

The defaults for parameters controlling the damping function (VDW_S6, VDW_SR, VDW_D) are available only for the PBE functional. If a functional other than PBE is used in DFT+D2 calculation, the value of VDW_S6 (or VDW_SCALING in versions before VASP.5.3.4) must 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_{disp} }[/math] calculation (controlled via LVDW_EWALD) is implemented according to reference ^[3] and is available as of VASP.5.3.4.

Related Tags and Sections

IVDW, IALGO, DFT-D3, Tkatchenko-Scheffler method, Tkatchenko-Scheffler method with iterative Hirshfeld partitioning, Self-consistent screening in Tkatchenko-Scheffler method, Many-body dispersion energy, dDsC dispersion correction

Examples that use this tag

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).

[kerber:jcc:08-3] T. Kerber and J. Sauer, J. Comput. Chem. 29, 2088 (2008).

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[2]

[3]

@@ Line 3: / Line 3: @@
 :<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>
-where the first two summations are over all <math>N_{at}</math> atoms in the unit cell, the third is over and 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,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 the equation for <math>E_{\mathrm{disp}}</math> corresponding to interactions over distances longer than a certain suitably chosen cutoff radius 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, the third is over and 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>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 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>