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 firstname.lastname@example.org
The scheme for these calculations starts from the Lehmann-representation of the Green's function.
Here and are atom sites and and are the eigenstates and eigenenergies of the Kohn-Sham system respectively.
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
calculationSetup/greensFunction by inserting the
realAxis tag and at least one of the
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
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.