Rare-earth perovskites $\left(R^{3+}{\mathrm{M}}^{3+}{\mathrm{O}}_3\right)$, with $e_g^1$ electronic occupation of the M $d$ states, display different types of metal-insulator transition. For manganites (M = Mn), the metal-insulator transition is usually induced by Jahn-Teller distortions, which stabilize orbital orderings (OO) at Mn sites. Among them, ${\mathrm{LaMnO}}_3$ shows a $C$-type OO and crystallizes with $Pbnm$ structure. Instead, ${\mathrm{TlMnO}}_3$ shows a very distinct $G$-type OO with an unusual $P\overline{1}$ structure. Employing first-principles calculations and symmetry-mode analysis, we rationalize structural and electronic origin of $G$-type OO in ${\mathrm{TlMnO}}_3$. Going further, we also consider ${\mathrm{TlNiO}}_3$, showing a metal-insulator transition driven by a breathing distortion, which stabilizes charge ordering (CO) at Ni sites. Interestingly, distinct Jahn-Teller and breathing distortions appearing in these compounds are very similar distortions of ${\mathrm{MO}}_6$ octahedra and stem from high-frequency phonon modes of their reference $Pm\overline{3}m$ structure. Our comparative study of ${\mathrm{TlMnO}}_3$, ${\mathrm{LaMnO}}_3$, and ${\mathrm{TlNiO}}_3$ highlights that, in spite of their distinct ground states, these compounds show a generic triggering of Jahn-Teller and breathing distortions by oxygen octahedra rotations, according to a mechanism previously reported in rare-earth nickelates.

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• Jahn-Teller effect
• Metal-insulator transition
• Orbital order
• Transition metal oxides
• Density functional theory