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Silicon materials play a key role in many technologically relevant fields, ranging from the electronic to the photovoltaic industry. A systematic search for silicon allotropes was performed by employing a modified ab initio minima hopping crystal structure prediction method. The algorithm was optimized to specifically investigate the hitherto barely explored low-density regime of the silicon phase diagram by imitating the guest-host concept of clathrate compounds. In total, 44 metastable phases are presented, of which 11 exhibit direct or quasidirect band gaps in the range of ≈1.0–1.8 eV, close to the optimal Shockley-Queisser limit of ≈1.4 eV, with a stronger overlap of the absorption spectra with the solar spectrum compared to conventional diamond silicon. Due to the structural resemblance to known clathrate compounds it is expected that the predicted phases can be synthesized.