dDsC dispersion correction

The expression for dispersion energy within the dDsC dispersion correction [139,138] (DFT-dDsC) is very similar to that of DFT-D2 method (see eq. 6.87), the important difference is, however, that the dispersion coefficients and damping function are charge-density dependent. The dDsC method is therefore able to take into account variations in vdW contributions of atoms due to their local chemical environment. In this method, polarizability, dispersion coeficients, charge and charge-overlap of an atom in molecule or solid are computed in the basis of a simplified exchange-hole dipole moment formalism,[139] pioneered by Becke and Johnson[140].

The dDsC dispersion energy is expressed as follows

where is the number of atoms in the system and is the Tang and Toennies (TT) damping factor. The damping function is defined as follows

(6.111) |

and its role is to attenuate the correction at short internuclear distances. A key component of the dDsC method is the damping factor :

(6.112) |

where the fitted parameter controls the short-range behavior and is the damping argument for the TT-damping factor associated with two separated atoms ( ). The term is computed according to the combination rule:

(6.113) |

with being estimated from effective atomic polarizabilities:

(6.114) |

The effective atom-in-molecule polarizabilities are computed from the tabulated free-atomic polarizabilities (available for the elements of the first six rows of the periodic table except of lanthanides) in the same way as in the method of Tkatchenko and Scheffler (see Sec. 6.77.3) but the Hirshfeld-dominant instead of the conventional Hirshfeld partitioning is used. The last element of the correction is the damping argument

where and are the nuclear charge and Hirshfeld dominant population of atom , respectively. The term is a covalent bond index based on the overlap of conventional Hirshfeld populations , and the fractional term in the parentheses is a distance-dependent ionic bond index.

The DFT-dDsC calculation is invoked by setting `IVDW`=4.
The default values for damping function parameters are available for
the functionals
PBE (`GGA=PE`) and revPBE (`GGA=RP`).
If other functional is used, the user must
define these parameters via corresponding tags in
INCAR (parameters for common DFT functionals can be found in Ref. [138])
The following parameters can be optionally defined in `INCAR`:

VDW_RADIUS |
= 50.0 | cutoff radius (Å) for pair interactions |

VDW_S6 |
= 13.96 | scaling factor |

VDW_SR |
= 1.32 | scaling factor |

Performance of PBE-dDsC in description of the adsorption of
hydrocarbons on Pt(111)
has been examined in Ref. [141] PCCP 17, 28921 (2015).

IMPORTANT NOTES:

- the dDsC method has been implemented into VASP by Stephan N. Steinmann
- this method requires the use of POTCAR files from the PAW dataset version 52 or later
- the input reference polarizabilities for non-interacting atoms are available only for elements of the first six rows of periodic table except of lanthanides
- it is essential that a sufficiently dense FFT grid (controlled via
`NGFX(Y,Z)`) is used in the DFT-dDsC, especially for accurate gradients - we strongly recommend to use`PREC=Accurate`for this type of calculations (in any case, avoid using`PREC=Low`). - the charge-density dependence of gradients is neglected. This approximation has been thoroughly investigated and validated.[142]