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 $d\text{−}d$ and $p\text{−}d$ 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.

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• Band gap
• Electronic structure
• Strongly correlated systems
• Density functional calculations
• First-principles calculations