  A new parameter set has been derived for FeSi using the Albe-Erhart-type bond
order potential (BOP) and the PONTIFIX code for fitting the parameters on a
large training set of various polymorphs. Ab initio calculations are also
carried out to study the relative stability of various polymorphs and to use
the obtained data in the training set. The original BOP formalism was unable to
account for the correct energetic relationship between the B20
($\epsilon$-FeSi) and B2 (CsCl) phases and notoriusly slightly favors
incorrectly the B2 polymorph. In order to correct this improper behavior the
BOP potential has been extended by a Columbic term (BOP+C) in order to account
for the partial ionic character of FeSi. Using this potential we are able to
account for the correct phase order between the most stable B20 and B2 (CsCl)
polymorphs when the net atomic charges are properly set. Although this brings
in a new somewhat uncertain parameter (the net charges) one can adjust properly
the BOP+C potential for specific problems. To demonstrate this we study under
high pressure the B2 phase which becomes more stable vs. B20 as it is found
experimentally and expected to be taken place in the Earth mantle. The obtained
BOP has also been tested for the metallic and semiconducting disilicides
($\alpha$-FeSi$_2$ and $\beta$-FeSi$_2$) and for the Si/$\beta$-FeSi$_2$
heterostructure. The obtained BOP, as many other BOP, overestimates the melting
point ($T_m$) of the B20 phase by $\sim 1000$ K if the parameters in the radial
part of the potential were obtained according to the Pauling relation (regular
way).
