Feasibility of band gap engineering of pyrite FeS<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow/><mml:mn>2</mml:mn></mml:msub></mml:math>

We use first-principles computations to investigate whether the band gap of pyrite FeS${}_{2}$ can be increased by alloying in order to make it a more effective photovoltaic material. In addition to the isostructural compounds that have a larger band gap (ZnS${}_{2}$, RuS${}_{2}$, OsS${}_{2}$), we evaluate non-rare-earth isovalent alloying candidates among all metals, transition metals, and semiconductor elements up to group IV and period 6 in the periodic table. From this screening procedure, we find that the group II elements (Be, Mg, Ca, Sr, Ba) and Cd have higher band gaps in the pyrite structure than FeS${}_{2}$. Practical band gap enhancement is observed only in the Ru and Os alloyed systems, but their incorporation into pyrite may be severely limited by the large positive enthalpy of mixing. All other candidate $(\mathrm{Fe},\mathrm{M}){\mathrm{S}}_{2}$ systems exhibit very large gap bowing effects such that the band gap at intermediate compositions is even lower than that of FeS${}_{2}$. Positive correlations between immiscibility and differences in electronegativity and Shannon ionic radius are observed.