  The Jahn-Teller (JT) distortion that can remove electronic degeneracies in
partially occupied states and results in systematic atomic displacements is a
common underlying feature to many of the intriguing phenomena observed in 3d
perovskites, encompassing magnetism, superconductivity, orbital ordering and
colossal magnetoresistance. Although the seminal Jahn and Teller theorem has
been postulated almost a century ago, the origins of this effect in perovskite
materials are still debated, including propositions such as super exchange,
spin-phonon coupling, sterically induced lattice distortions, and strong
dynamical correlation effects. Here we analyze the driving forces behind the
Jahn-Teller motions and associated electronic fingerprints in a full range of
ABX3 compounds. We identify (i) compounds that are prone to an
electronically-driven instabilities (i.e. a pure JT effect) such as KCrF3,
KCuF3 or LaVO3 and proceed to relax the structures, finding quantitatively the
JTD in excellent agreement with experiment; (ii) compounds such as LaMnO3 or
LaTiO3 that do not show electronically driven JTD despite orbital degeneracies,
because their strongly hybridized B, d-X, p states supply but too weak JT
forces to overcome the needed atomic distortions; (iii) although LaVO3 exhibits
similar B, d-X, p hybridizations as LaTiO3, the former compound exhibits a
robust electronic instability while LaTiO3 has zero stabilization energy, the
reason being that LaVO3 has two electrons t2g2 relative to LaTiO3 with just one
t2g1. (iv) We explain the trends in "orbital ordering" whereby electrons occupy
orbitals that point to orthogonal directions between all nearest-neighbor 3d
atoms. We thereby provide a unified vision to explain octahedra deformations in
perovskites that, at odds with common wisdom, does not require the celebrated
Mott-Hubbard mechanism.
