Real-space study of the optical absorption in alternative phases of silicon

We introduce a real-space approach to understand the relationship between optical absorption and crystal structure. We apply this approach to alternative phases of silicon, with a focus on the Si$_{20}$ crystal phase as a case study. We find that about 83% of the changes in the calculated low-energy absorption in Si$_{20}$ as compared to Si in the diamond structure can be attributed to reducing the differences between the on-site energies of the bonding and anti-bonding orbitals as well as increasing the hopping integrals for specific Si-Si bonds.