Tkatchenko-Scheffler method

The expression for dispersion energy within the method of Tkatchenko and Scheffler [131] (DFT-TS) is formally identical 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 DFT-TS 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, and atomic radii of an atom in molecule or solid are computed from their free-atomic values using the following relations:

(6.96) |

The free-atomic quantities
,
, and
are tabulated for all elements from the first
six rows of the periodic table except of
lanthanides. If a DFT-TS calculation is performed for
the system containing the unsupported elements, the user must
define corresponding values using the tags `VDW_ALPHA`, `VDW_C6`, and
`VDW_R0`, see below. The effective atomic volumes are
determined using the Hirshfeld partitioning
of the all-electron density:

(6.97) |

where is the total electron density, and is the spherically averaged electron density of the neutral free atomic species . The Hirshfeld weight is defined by free atomic densities as follows:

The combination rule to define the strength of the dipole-dipole dispersion interaction between unlike species is:

(6.99) |

The parameter used in damping function (see eq. 6.90) is obtained from the atom-in-molecule vdW radii as follows:

(6.100) |

The DFT-TS calculation is invoked by setting `IVDW`=220.
The following parameters can be optionally defined in `INCAR`:

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

VDW_S6 |
= 1.00 | global scaling factor |

VDW_SR |
= 0.94 | scaling factor |

VDW_D |
= 20.0 | damping parameter |

VDW_ALPHA |
= [real array] | free-atomic polarizabilities (atomic units) for each species |

defined in POSCAR | ||

VDW_C6AU |
= [real array] | free-atomic parameters (atomic units) for each species |

defined in POSCAR | ||

VDW_C6 |
= [real array] | free-atomic parameters ( ) for each species |

defined in POSCAR (this parameter overrides VDW_C6AU) |
||

VDW_R0AU |
= [real array] | free-atomic parameters (atomic units) for each species |

defined in POSCAR | ||

VDW_R0 |
= [real array] | parameters (Å) for each species |

defined in POSCAR (this parameter overrides VDW_R0AU) |
||

LVDW_EWALD |
= .FALSE..TRUE. | compute lattice summation in expression |

by means of Ewald's summation - noyes | ||

(available in VASP.5.3.4 and later) |

Performance of PBE-TS method in optimization of
various crystalline systems has been examined in Phys. Rev. B. 87, 064110 (2013).

IMPORTANT NOTES:

- this method requires the use of POTCAR files from the PAW dataset version 52 or later
- the input reference
data for non-interacting atoms are available only for elements
of the first six rows of periodic table except of lanthanides.
If the system contains other elements, the user must provide
the free-atomic parameters for all atoms in the system
via
`VDW_alpha`,`VDW_C6`,`VDW_R0`defined in the INCAR file. - the charge-density dependence of gradients is neglected
- the DFT-TS method is incompatible with the setting
`ADDGRID=.TRUE.` - it is essential that a sufficiently dense FFT grid (controlled via
`NGFX(Y,Z)`) is used in the DFT-TS calculation - we strongly recommend to use`PREC=Accurate`for this type of calculations (in any case, avoid using`PREC=Low`). - defaults for the parameters controlling damping function (
`VDW_S6`,`VDW_SR`,`VDW_D`) are available only for the PBE functional. If the functional other than PBE is used, the value of`VDW_SR`must be specified in INCAR. - Ewald's summation in calculation (controlled via
`LVDW_EWALD`) implemented according to Ref. [132] is available as of VASP.5.3.4 - parameters
`VDW_C6AU`and`VDW_R0AU`are available as of VASP.5.3.4 - Hirshfeld charges for all configurations generated in a calculation are written in OUTCAR, the corresponding table is introduced by the expression "Hirshfeld charges:".