  Density functional theory (DFT) is a powerful tool for predicting the
electronic band structures of functional materials. However, it is often
difficult to intuit how major band structure features$-$such as band gap
magnitude, location of band extrema, effective masses, etc.$-$arise from the
underlying crystal chemistry of a material. Band structure is represented in
reciprocal space, but arises from the orbital and bonding interactions between
atoms in real space. Here, we present a conceptual and computable framework to
extract chemical bonding origins of DFT-calculated band structure features. As
a key example, we explain here the indirect band gap of silicon, which
profoundly impacts its properties for use in photovoltaics and electronics.
Even in this basic semiconductor material, our approach leads to new insights
to understand and engineer its conduction band minimum position. These
calculation techniques can be broadly applied to reveal the crystal chemistry
origins of electronic structure features in other optical, electronic, and
magnetic materials.
