We have investigated the structural properties, vibrational spectra, and electronic band structures of crystalline cellulose allomorphs and chemically modified cellulose with quantum chemical methods. The electronic band gaps of cellulose allomorphs Iα, Iβ, II, and III1 lie in the range of 5.0 to 5.6 eV. We show that extra states can be created in the band gap of cellulose by chemical modification. Experimentally feasible amidation of cellulose Iβ with aniline or 4,4′ diaminoazobenzene creates narrow bands in the cellulose band gap, reducing the difference between the occupied and empty states to 4.0 or 1.8 eV, respectively. The predicted states 4,4′diaminoazobenzene-modified cellulose Iβ fall in the visible spectrum, suggesting uses in optical applications.