The coexistence of Mott localized $f$ states with wide conduction and valence bands in $f$-electron semiconductors results, quite generically, in a complex optical response with the nature of the absorption edge difficult to resolve both experimentally and theoretically. Here, we combine a dynamical mean-field theory approach to localized $4f$ shells with an improved description of band gaps by a semilocal exchange-correlation potential to calculate the optical properties of the light rare-earth fluorosulfides $Ln\mathrm{SF}$ ($Ln=\mathrm{Pr}$, Nd, Sm, Gd) from first principles. In agreement with experiment, we find the absorption edge in SmSF to stem from $\mathrm{S}\text{−}3p$ to $\mathrm{Sm}\text{−}4f$ transitions, while the Gd compound behaves as an ordinary $p\text{−}d$ gap semiconductor. In the unexplored PrSF and NdSF systems we predict a rather unique occurrence of strongly hybridized $4f\text{−}5d$ states at the bottom of the conduction band. The nature of the absorption edge results in a characteristic anisotropy of the optical conductivity in each system, which may be used as a fingerprint of the relative energetic positions of different states.

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• Electronic structure
• First-principles calculations
• Optical conductivity