  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.
