  We suggest here the method of the mapping of DFT calculations on the
multiorbital model in a following way: the parameters of the formulated
multiorbital model should be determined from the requirement that the
self-consistent charge and spin densities found from the ab initio and model
calculations have to be as close to each other as possible. The analysis of the
model allows for detailed understanding of the role played by different
parameters of the model in the physics of interest. As an example of the
approach we present the study of the effect of silicon atoms substitution by
the iron atoms and vice versa on the magnetic properties in the iron silicide
alpha-FeSi2. The DFT+GGA calculations are mapped to the model with intraatomic
Coulomb and exchange interactions, hoppings to nearest and next nearest atoms
and exchange of the delocalized electrons between iron atoms; the magnetic
moments on atoms and charge densities of the material are found
self-consistently within the Hartree-Fock approximation. We find that while the
stoichiometric alpha-FeSi2 is nonmagnetic, the substitutions generate different
magnetic structures. For example, the substitution of three Si atoms by the Fe
atoms results in the ferrimagnetic structure whereas the substitution of four
Si atoms by Fe atoms gives rise to either the nonmagnetic or the ferromagnetic
state depending on the type of local enviroment of the substitutional Fe atoms.
Besides, contrary to the commonly accepted statement that the destruction of
the magnetic moment is controlled only by the number of Fe-Si nearest
neighbors, we find that actually it is controlled by the Fe-Fe
next-nearest-neighbors. This finding led us to the counterintuitive conclusion:
an increase of Si concentration in Fe1-xSi2+x ordered alloys may lead to a
ferromagnetism. This conclusion is confirmed by the calculation within
GGA-to-DFT.
