Tkatchenko-Scheffler method with iterative Hirshfeld partitioning

The Tkatchenkoâˆ’Scheffler (TS) dispersion correction method which uses fixed neutral atoms as a reference to estimate the effective volumes of atoms-in-molecule (AIM) and to calibrate their polarizabilities and dispersion coefficients (see Sec. 6.77.3) fails to describe the structure and the energetics of ionic solids. As shown in Ref. [133,134], this problem can be solved by replacing the conventional Hirshfeld partitioning used to compute properties of interacting atoms by the iterative scheme proposed by Bultinck [135]. In this iterative Hirshfeld algorithm (HI), the neutral reference atoms are replaced with ions with fractional charges determined together with the AIM charge densities in a single iterative procedure. The algorithm is initialized with a promolecular density defined by non-interacting neutral atoms. The iterative procedure then runs in the following steps:

- the Hirshfeld weight function for the step is computed as
(6.101)

where the sum extends over all atoms in the system - the number of electrons per atom
is determined using

- new reference charge densities are computed using

where lint expresses the integer part of and uintlint.

Steps (1) to (3) are iterated until the difference in the electronic populations between two subsequent steps ( ) is less than a predefined threshold for all atoms. The converged interative Hirshfeld weights () are then used to define the AIM properties needed to evaluate dispersion energy, see Sec. 6.77.3.

The DFT-TS calculation with iterative Hirshfeld partitioning (DFT-TS/HI) is invoked by setting `IVDW`=21. The convergence criterion for iterative Hirshfeld partitioning (in e)
can optionally be defined via parameter `HITOLER` (the default value is 5e-5).
Other optional parameters controlling the input for the calculation
are as in the conventional TS method
(Sec. 6.77.3). The default value
of the adjustable parameter `VDW_SR` is 0.95 and corresponds to the PBE functional.

The PBE-TS/HI method is described in detail in J. Chem. Theory Comput. 9, 4293 (2013)
and its performance
in optimization of
various crystalline systems is examined in
J. Chem. Phys. 141, 034114 (2014).

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`(described in sec. 6.77.3) defined in the INCAR file. - the charge-density dependence of gradients is neglected
- the DFT-TS/HI 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/HI - 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 - conventional and iterative Hirshfeld charges for all configurations generated in a calculation are written in OUTCAR. The corresponding tables are introduced by expressions "Hirshfeld charges:" and "Hirshfeld-I charges:".