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We perform a systematic {\it ab initio} study of the electronic structure ofSr(V,Mo,Mn)O$_3$ perovskites, using the parameter-free $GW$+EDMFT method. Thisapproach self-consistently calculates effective interaction parameters, takinginto account screening effects due to nonlocal charge fluctuations. Comparingthe results of a 3-band ($t_{2g}$) description to those of a 5-band($t_{2g}$+$e_g$) model, it is shown that the $e_g$ states have little effect onthe low-energy properties and the plasmonic features for the first twocompounds but play a more active role in SrMnO$_3$. In the case of SrMnO$_3$paramagnetic $GW$+EDMFT yields a metallic low-temperature solution on the vergeof a Mott transition, while antiferromagnetic $GW$+EDMFT produces an insulatingsolution with the correct gap size. We discuss the possible implications ofthis result for the nature of the insulating state above the N\'eeltemperature, and the reliability of the $GW$+EDMFT scheme.

Screening from $e_g$ states and antiferromagnetic correlations in $d^{(1,2,3)}$ perovskites: A $GW$+EDMFT investigation