### Calculating Green's functions

Experimental Green's function features

Many of the features involving Green's functions are to be considered experimental in the MaX5 Release.
This is the case especially for intersite and interorbital Green's functions. If you are interested in these features please contact he.janssen@fz-juelich.de

TODO

The scheme for these calculations starts from the Lehmann-representation of the Green's function.

Here $\alpha$ and $\alpha^\prime$ are atom sites and $\Psi_{\mathbf{k}\nu}$ and $E_{\mathbf{k}\nu}$ are the eigenstates and eigenenergies of the Kohn-Sham system respectively.

TODO

By utilizing the following decomposition of the denominator

the imaginary part of the expression above is much easier to compute. The complete Green's function can be calculated from the imaginary part via the Kramers-Kronig-Transformation.

Here we also deform the energy grid into the complex plane to reduce the number of necessary points on the contour to achieve accurate results.

Necessary energy contours

For a Green's function calculation two energy contours have to be defined. One equidistant energy grid close to the real axis and a complex energy contour on which the Green's function is obtained. This is done inside the tag calculationSetup/greensFunction by inserting the realAxis tag and at least one of the contourSemicircle, contourDOS, contourRectangle. For detailed information about each tag and the corresponding contours you can refer to this section

Output of Green's function calculations

It is strongly encouraged to use Green's function calculations with a version compiled with the HDF5 library. This way much more meaningful output is produced. All calculated Green's functions are provided in the greensf.hdf file for further calculations in this case. Without HDF5 only basic information beyond any specific calculation like the occupation matrix for all Green's function is provided.