4 Calculating the band structure

Once the orbital population (charges) for the system had been obtained, the band structure can be calculated at any chosen k-points. The following input calculates the GaAs band structure along the line L- $\Gamma$ -X.

Geometry = {
  Periodic = Yes
  LatticeVectors [Angstrom] = {
    2.80  2.80  0.00
    2.80  0.00  2.80
    0.00  2.80  2.80
  }
 TypeNames = { "Ga" "As" }
 TypesAndCoordinates [relative] = {
   1  0.00  0.00  0.00
   2  0.25  0.25  0.25
 }
}

Driver = {}

Hamiltonian = DFTB {
  SCC = Yes
  SCCTolerance = 1e-5
  MaxSCCIterations = 1
  Mixer = Broyden {}
  MaxAngularMomentum = {
    Ga = "d"; As = "d"
  }
  SlaterKosterFiles = Type2FileNames {
    Prefix = "./hyb-0-1/"
    Separator = "-"
    Suffix = ".skf"
  }
  KPointsAndWeights = KLines {
    1   0.5  0.0  0.0   # L (11-1)
    20  0.0  0.0  0.0   # Gamma (000)
    20  0.5  0.5  0.0   # X (100)
  }
  ReadInitialCharges = Yes
}

Options = {
  RestartFrequency = 0
}

Some notes on the input:

The geometry must be exact the same as the previous calculation where the charges were obtained.
The Driver option must to be set to the empty value, since geometry optimisation during band structure calculation does not make any sense.
The number of maximal SCC cycles had been set to 1:
```
  MaxSCCIterations = 1
```
This is essential in order to prevent DFTB+ from making SCC cycles that may change the charges.
The DFTB block contains the
```
  ReadInitialCharges = Yes
```
option, which advises DFTB+ to read in the charges from the file charges.bin and use those to initialise the SCC loop. The charges.bin file should be the one containing the converged charges for the current structure (produced by the previous DFTB+ run).
The K-points are specified using the KLines directive:
```
  KPointsAndWeights = KLines {
    1   0.5  0.0  0.0   # L (11-1)
    20  0.0  0.0  0.0   # Gamma (000)
    20  0.5  0.5  0.0   # X (100)
  }
```
Every line specifies a line segment. The first column gives the number of K-points along the line segment between (but excluding) the end of the previous line segment and the K-point specified in the next three columns (which is the end point of the current line segment). The specified number of K-points is evenly distributed along the line, the last K-point coincides with the end point of the segment. The coordinates of the K-points are relative coordinates (given in the coordinate system spawned by the reciprocal lattice vectors of the periodic structures). The starting point of the first line segment is the $\Gamma$ point.
The example above calculates first the line segment between the $\Gamma$ point and the L-point using only one K-point. The starting point of a line segment is always excluded and the last K-point along it always coincides with the specified end point, therefore, the line
```
    1   0.5  0.0  0.0   # L (11-1)
```
instructs DFTB+ to do a single K-point calculation for the L point. Then 20 K-points are calculated along the L- $\Gamma$ line (the last one being the $\Gamma$ point itself). Finally additional 20 K-points are calculated along the $\Gamma$ -X line. All together 41 K-points will be calculated, whereby the 1st one corresponds to L, the 21st to $\Gamma$ and the 41st to X.
The Options block contains
```
 RestartFrequency = 0
```
This prevents DFTB+ from writing restart information to the disc and thus from overwriting the charges.bin file (with the converged charges) with meaningless charges obtained during the band structure calculation.

Running DFTB+ with the input above, the eigenlevel spectrum is calculated at the required k-points. The results are written to the file detailed.out and in more readable format to band.out. You can again use the script band2dat to extract the data from it, which can be then directly plotted by some data visualisation tool (like xmgrace):

  band2dat band.out bandstruct.dat

If you import the data file bandstruct.dat into xmgrace as NXY set, you should obtain a band structure similar to Fig.

**Figure:** Band structure of GaAs calculated with DFTB+ along the L- $\Gamma$ -X line using the parametrisation hyb-0-1.