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We present first-principles electronic structural calculations of the quasiparticle and optical spectra of two silicon phases, Si-XII and the recently predicted phase of Si in the body-centered-tetragonal structure. The quasiparticle spectra calculated within the GW approximation predict that both of these materials are indirect bandgap semiconductors with small bandgaps. The optical spectra of these materials are obtained by solving the Bethe-Salpeter equation taking into account electron-hole interactions. Comparison is made to other phases of silicon commonly used in photovoltaic applications. The results suggest the possible utility of these materials as photovoltaics.