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# DFT-D2

In the D2 method of Grimme^{[1]}, the correction term takes the form:

where the summations are over all atoms and all translations of the unit cell . The prime indicates that for , denotes the dispersion coefficient for the atom pair , is the distance between atom located in the reference cell and atom in the cell and the term 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 corresponding to interactions over distances longer than a certain suitably chosen cutoff radius contribute only negligibly to and can be ignored. Parameters and are computed using the following combination rules:

and

The values for and
are tabulated for each element and are insensitive to the particular chemical situation (for instance,
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:

whereby the global scaling parameter has been optimized for several different DFT functionals such as PBE (
), BLYP (
) and B3LYP (
). The parameter
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IVDW=*1|10* or by specifying LVDW=*.TRUE.* (this parameter is obsolete as of VASP.5.3.3).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 ) for pair interactions
- VDW_S6=0.75 global scaling factor (available in VASP.5.3.4 and later)
- VDW_SR=1.00 scaling factor (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
- VDW_C6=[real array] parameters ( ) for each species defined in the POSCAR file
- VDW_R0=[real array] parameters ( ) for each species defined in the POSCAR file
- LVDW_EWALD=
*.FALSE.*decides whether lattice summation in 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 .

- Ewald's summation in the calculation of 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

## References

- ↑
^{a}^{b}S. Grimme, J. Comp. Chem. 27, 1787 (2006). - ↑ T. Bučko, J. Hafner, S. Lebègue and J. G. Ángyán, J. Phys. Chem. A 114, 11814 (2010).
- ↑ . Kerber and J. Sauer, J. Comp. Chem. 29, 2088 (2008).