  Determining the nature of band gaps in transition-metal compounds remains
challenging. We present a first-principles study on electronic and optical
properties of CoO using hybrid functional pseudopotentials. We show that
optical absorption spectrum can provide a clear fingerprint to distinguish
between Mott-Hubbard, intermediate and charge-transfer insulators. This
discrimination is reflected by the qualitative difference in peak satellites
due to unique interplay between $d$-$d$ and $p$-$d$ excitations, thus allowing
identification from experimental data alone, unlike the existing methods that
require additional theoretical interpretation. We conclude that the CoO is an
intermediate, rather than a Mott-Hubbard insulator as is initially believed.
