# A general H(k)

In addition to the more extensive Wien2k, VASP, and W90 converters,
**DFTTools** contains also a light converter. It takes only
one inputfile, and creates the necessary hdf outputfile for
the DMFT calculation. The header of this input file has a defined
format, an example is the following (do not use the text/comments in your
input file):

```
64 # number of k-points
1.0 # electron density
2 # number of total atomic shells
1 1 2 5 # atom, sort, l, dim
2 2 1 3 # atom, sort, l, dim
1 # number of correlated shells
1 1 2 5 0 0 # atom, sort, l, dim, SO, irep
1 5 # number of ireps, dim of irep
```

The lines of this header define

Number of \(\mathbf{k}\)-points used in the calculation

Electron density for setting the chemical potential

Number of total atomic shells in the hamiltonian matrix. In short, this gives the number of lines described in the following. IN the example file give above this number is 2.

The next line(s) contain four numbers each: index of the atom, index of the equivalent shell, \(l\) quantum number, dimension of this shell. Repeat this line for each atomic shell, the number of the shells is given in the previous line.

In the example input file given above, we have two inequivalent atomic shells, one on atom number 1 with a full d-shell (dimension 5), and one on atom number 2 with one p-shell (dimension 3).

Other examples for these lines are:

Full d-shell in a material with only one correlated atom in the unit cell (e.g. SrVO3). One line is sufficient and the numbers are 1 1 2 5.

Full d-shell in a material with two equivalent atoms in the unit cell (e.g. FeSe): You need two lines, one for each equivalent atom. First line is 1 1 2 5, and the second line is 2 1 2 5. The only difference is the first number, which tells on which atom the shell is located. The second number is the same in both lines, meaning that both atoms are equivalent.

t2g orbitals on two non-equivalent atoms in the unit cell: Two lines again. First line is 1 1 2 3, second line 2 2 2 3. The difference to the case above is that now also the second number differs. Therefore, the two shells are treated independently in the calculation.

d-p Hamiltonian in a system with two equivalent atoms each in the unit cell (e.g. FeSe has two Fe and two Se in the unit cell). You need for lines. First line 1 1 2 5, second line 2 1 2 5. These two lines specify Fe as in the case above. For the p orbitals you need line three as 3 2 1 3 and line four as 4 2 1 3. We have 4 atoms, since the first number runs from 1 to 4, but only two inequivalent atoms, since the second number runs only form 1 to 2.

Note that the total dimension of the hamiltonian matrices that are read in is the sum of all shell dimensions that you specified. For example number 4 given above we have a dimension of 5+5+3+3=16. It is important that the order of the shells that you give here must be the same as the order of the orbitals in the hamiltonian matrix. In the last example case above the code assumes that matrix index 1 to 5 belongs to the first d shell, 6 to 10 to the second, 11 to 13 to the first p shell, and 14 to 16 the second p shell.

Number of correlated shells in the hamiltonian matrix, in the same spirit as line 3.

The next line(s) contain six numbers: index of the atom, index of the equivalent shell, \(l\) quantum number, dimension of the correlated shells, a spin-orbit parameter, and another parameter defining interactions. Note that the latter two parameters are not used at the moment in the code, and only kept for compatibility reasons. In our example file we use only the d-shell as correlated, that is why we have only one line here.

The last line contains several numbers: the number of irreducible representations, and then the dimensions of the irreps. One possibility is as the example above, another one would be 2 2 3. This would mean, 2 irreps (eg and t2g), of dimension 2 and 3, resp.

After these header lines, the file has to contain the Hamiltonian matrix in orbital space. The standard convention is that you give for each \(\mathbf{k}\)-point first the matrix of the real part, then the matrix of the imaginary part, and then move on to the next \(\mathbf{k}\)-point.

The converter itself is used as:

```
from triqs_dft_tools.converters.hk import *
Converter = HkConverter(filename = hkinputfile)
Converter.convert_dft_input()
```

where `hkinputfile`

is the name of the input file described
above. This produces the hdf file that you need for a DMFT calculation.

For more options of this converter, have a look at the
`Converters`

section of the reference manual.