We have performed systematic first principles study of the electronic structure and band topology properties of $LnPn$ compounds ($Ln$=Ce, Pr, Gd, Sm, Yb; $Pn$=Sb, Bi). Assuming the $f$-electrons are well localized in these materials, both hybrid functional and modified Becke-Johnson calculations yield electronic structure in good agreement with experimental observations, while generalized gradient approximation calculations severely overestimate the band