  A method to analyze optical transitions is developed by combining the
Kubo-Greenwood formula with the unfolding method to construct an unfolded
electronic band structure with optical transition weights, which allows us to
investigate how optical transitions are perturbed by imperfections such as
impurity, vacancy, and structural distortions. Based on the Kubo-Greenwood
formula, we first calculate frequency-dependent optical conductivity based on
the first-principles electronic structure calculations using the linear
combinations of atomic orbitals. Benefiting from the atomic orbital basis sets,
the frequency-dependent optical conductivity can be traced back to their
individual components before summations over all of $k$ points and bands. As a
result, optical transition weights of the material can be put on the unfolded
electronic band structure to show contributions at different $k$ points and
bands. This method is especially useful to study the effects of broken symmetry
in the optical transitions due to presence of impurities in the materials. As a
demonstration, decomposed optical transition weights of a monolayer Si-doped
graphene are shown in the electronic band structure.
