# Additional Periodicity DataΒΆ

```
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 \(r_\mathrm{madel}\).