# Additional Periodicity Data¶

Periodic
{KSpace NK}
{BZStruct {enabled=yes|no} {automatic=yes|no} {fatbands=yes|no} {UseSymmetry=yes|no} {DeltaK=realVal}}
{BZPath
{Path
End}
End}
{DOS {nSteps=N} {EMin=r} {EMax=r}}
{Phonon interpol=N stepsize=N nSides=1|2 UseSymmetry=yes|no}
{SuperCell
End}
{LatticeStepSize}
{Screening
{rmadel}
{dmadel}
End}
End

KSpace

This parameter controls the number of k-points used in the calculation. By default DFTB does not do any k-space sampling and uses only the Gamma-point as the only k-point. This should be sufficient for systems with large unit cells. For smaller systems, k-space sampling can be enabled explicitly using this keyword. For very small unit cells (one atom wide) a value of 5 is advised. For medium sized unit cells 3 is adequate.

The k-space sampling is relatively new in DFTB and as of the ADF2017 release still has some incompatibilities with other features: At the moment it is not possible to use k-space sampling in combination with DFTB3, spin-polarization, l-dependent SCC cycles or density matrix purification. Furthermore, k-space sampling calculations are not parallelized and should be run in serial, e.g. by setting the NSCM environment variable to 1.

BZStruct

Options for band structure plotting. This has no effect on the calculated energy.

Warning

The band structure is only computed in case of k-space sampling, i.e. it is not computed for Gamma-only calculations (see: KSpace).

You can also specify a path by hand, setting automatic to no. The points in the path should be entered in the BZPath key.

enabled
(Default: yes) Whether or not to calculate the band structure.
automatic
(Default: yes) If yes DFTB will automatically generate the standard path through the Brillouin zone. If no DFTB will use the user-defined path in BZPath.
FatBands
(Default: yes) If yes DFTB will compute the fat bands (note: only if BZStruct%Enabled=yes). The Fat Bands are the periodic equivalent of the Mulliken population analysis. The definition of the fat bands can be found in the Band Documentation.
UseSymmetry
(Default: yes) If yes only the irreducible wedge of the Wigner-Seitz cell is sampled. If no, the whole (inversion-unique) Wigner-Seitz cell is sampled.
DeltaK
(Default: 0.1) Step (in reciprocal space, unit: 1/Bohr) for band structure interpolation. Using a smaller number (e.g. 0.03) will yield to smoother band curves, but will increase the computation time.
BZPath

If BZStruct%Automatic is no, DFTB will compute the band structure for the user-defined path in the BZPath block. You should define the vertices of your path in fractional coordinates (wrt the reciprocal lattice vectors) in the Path sub-block. If you want to make a jump in your path, you need to specify a new Path sub-block.

In the following example we define the path Gamma-X-W-K|U-X for a FCC lattice:

BZPath
Path
0.000   0.000   0.000
0.500   0.000   0.500
0.500   0.250   0.750
0.375   0.375   0.750
SubEnd
Path
0.625   0.250   0.625
0.500   0.000   0.500
SubEnd
End

DOS
The subkeys of DOS allow to customize the calculation of the density of states. The density of states is calculated at nSteps energies in the interval EMin to EMax. Energies are given in Hartree and relative to the Fermi energy. By default the density of states is evaluated at 300 points in the interval from -0.75Ha to +0.75Ha.
Phonon

This enables a phonon run. One should start from a completely optimized system. Next one should choose a super cell. The phonon spectrum converges with super cell size. How big it should be depends on the system. For the study of isotopic shift of phonons, see the AtomMasses key.

stepsize
Step size to be taken to obtain the force constants (second derivative) from the analytical gradients.
nSides
(Default: 2) By default a two-sided (or quadratic) numerical differentiation of the nuclear gradients is used. Using a single-sided (or linear) numerical differentiation is computationally faster but much less accurate. Note: In older versions of the program only the single-sided option was available.
useSymmetry
(Default: Yes) Whether or not to exploit the symmetry of the system in the phonon calculation.
SuperCell
Used for the phonon run. The super lattice is expressed in the lattice vectors. Most people will find a diagonal matrix easiest to understand.
LatticeStepSize
(Default: 1e-4) Step size for the numerical calulation of lattice gradients.
Screening

For SCC-DFTB in periodic systems the Coulomb interaction is screened with a Fermi-Dirac like function defined as $$S(r) = \left(\exp \left( \frac{r-r_\text{madel}}{d_\text{madel}} \right) + 1\right)^{-1}$$. Screening is always enable, even if this section is absent. This section allows to change some details of the screening procedure.

rmadel
Sets the range $$r_\mathrm{madel}$$ of the screening function. The default is 2x the norm of the longest lattice vector.
dmadel
Sets the smoothness $$d_\mathrm{madel}$$ of the screening function. The default is 1/10 of $$r_\mathrm{madel}$$.