  Using the \emph{ab initio} evolutionary algorithm (implemented in USPEX) and
electronic structure calculations we investigate the properties of a new
thermoelectric material FeSbAs, which is a material analog of the enigmatic
thermoelectric FeSb$_{2}$. We utilize the density functional theory and the
Gutzwiller method to check the energetics. We find that FeSbAs can be made
thermodynamically stable above $\sim$30 GPa. We investigate the electronic
structure and thermoelectric properties of FeSbAs based on the density
functional theory and compare with those of FeSb$_{2}$. Above 50 K, FeSbAs has
higher Seebeck coefficients than FeSb$_{2}$. Upon doping, the figure of merit
becomes larger for FeSbAs than for FeSb$_{2}$. Another material analog FeSbP,
was also investigated, and found thermodynamically unstable even at very high
pressure. Regarding FeSb$_{2}$ as a member of a family of compounds
(FeSb$_{2}$, FeSbAs, and FeSbP) we elucidate what are the chemical handles that
control the gaps in this series. We also investigate solubility (As or P for Sb
in FeSb$_{2}$) we found As to be more soluble. Finally, we study a two-band
model for thermoelectric properties and find that the temperature dependent
chemical potential and the presence of the ionized impurities are important to
explain the extremum in the Seebeck coefficient exhibited in experiments for
FeSb$_{2}$.
