2 Creating the proper density

In order to calculate a band structure in Density Functional Theory, at first the ground-state density for the given system must be obtained. In the DFTB picture that corresponds to obtaining self-consistent charges on the atoms. The charges must be convergent with respect to two quantities: Tolerance of the SCC cycle and quality of the k-point sampling to give the correct results. In the current tutorial, the SCC tolerance is set to 1e-5. For the k-point sampling the 8x8x8 Monkhorst-Pack set is used. Both quantities ensure good convergence in the charges for this case.

The input dftb_in.hsd for GaAs is as follows:

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
 }
}

Hamiltonian = DFTB {
  SCC = Yes
  SCCTolerance = 1e-5
  MaxAngularMomentum = {
    Ga = "d"; As = "d"
  }
  SlaterKosterFiles = Type2FileNames {
    Prefix = "./hyb-0-1/"
    Separator = "-"
    Suffix = ".skf"
  }
  KPointsAndWeights = SupercellFolding {
    8   0   0
    0   8   0
    0   0   8
    0.5 0.5 0.5
  }
}

A few notes about the input:

• The position of the atoms is specified in relative coordinates (in the coordinate system spanned by the lattice vectors):

   TypesAndCoordinates [relative] = {
     1  0.00  0.00  0.00
     2  0.25  0.25  0.25
   }
  

• The SupercellFolding method is used to specify the k-points. If only the diagonal elements are specified and the shift vectors are set to 0.5 for even numbers in the diagonal (or 0.0 for odd ones), the resulting k-point set corresponds to the appropriate Monkhorst-Pack k-point scheme. (See the manual of DFTB+ for more details.)

• The convergency with the current parameters can be checked by choosing stronger SCC tolerance criteria (e.g. SCCTolerance = 1e-8) or a higher order Monkhorst-Pack mesh (e.g. 10x10x10). The total energy does not change considerably in any of the two cases, so that the used parameters can be considered to yield convergent charges.

The calculation with dftb+ and the input above completes successfully after a few iterations. The file charges.bin is created (as well a several others), which contains the orbital population (charges) from the last iteration as a binary file.