We conduct first-principles total-energy density functional calculations to study the band structures in Ge 1− x Sn x infrared semiconductor alloys. The norm-conserving optimized pseudopotentials of Ge and Sn have been constructed for electronic structure calculations. The composition-bandgap relationships in Ge 1−x Sn x lattices are evaluated by a detailed comparison of structural models and their electronic band structures. The critical Sn composition related to the transition from indirect- to direct-gap in Ge 1−x Sn x alloys is estimated to be as low as x∼ 0.016 determined from the parametric fit. Our results show that the crossover Sn concentration occurs at a lower critical Sn concentration than the values predicted from the absorption measurements. However, early results indicate that the reliability of the critical Sn concentration from such measurements is hard to establish, since the indirect gap absorption is much weaker than the direct gap absorption. We find that the direct band gap decreases exponentially with the Sn composition over the range 0 <x<0.375 and the alloys become metallic for x> 0.375, in very good agreement with the theoretical observed behavior [D. W. Jenkins and J. D. Dow, Phys. Rev. B 36, 7994, 1987]. For homonuclear and heteronuclear complexes of Ge 1−x Sn x alloys, the indirect band gap at L-pointis is found to decrease homonuclear Ge-Ge bonds or increase homonuclear Sn-Sn bonds as a result of the reduced L valley. All findings agree with previously reported experimental and theoretical results. The analysis suggests that the top of valence band exhibits the localization of bond charge and the bottom of the conduction band is composed of the Ge 4s4p and/or Sn 5s5p atomic orbits.