A novel class of semiconductors is introduced, based on computational design, to solve the long-standing problem of lattice and polarity mismatch in heteroepitaxial growth of III-V alloys on silicon substrates. Ab initio total-energy calculations and quasiparticle CW calculations are used to investigate the physical properties of these new semiconductors. One particular configuration is designed to match lattice constant and polarity with the Si(100) surface and to possess a direct band gap of 1.59 mu m, which is close to the canonical frequency used by the optoelectronics industry. These results could pave the way for eventual monolithic integration of optical materials on silicon.