PJTE versus Renner–Teller effect in bending distortions. Linear molecules are exceptions from the JTE, and for a long time it was assumed that their bending distortions in degenerate states (observed in many molecules) is produced by the Renner–Teller effect (RTE) (the splitting of the generate state by the quadratic terms of the vibronic coupling). However, recently it was proved  that the RTE, by splitting the degenerate electronic state, just softens the lower branch of the APES, but this lowering of the energy is not enough to overcome the rigidity of the linear configuration and to produce bending distortions. It follows that the bending distortion of linear molecular systems is due to, and only to the PJTE that mixes the electronic state under consideration with higher in energy (excited) states. This statement is enhanced by the fact that many linear molecules in nondegenerate states (and hence with no RTE) are, too, bent in the equilibrium configuration. The physical reason for the difference between the PJTE and the RTE in influencing the degenerate term is that while in the former case the vibronic coupling with the excited state produces additional covalent bonding that makes the distorted configuration preferable (see above, section 2.3), the RTE has no such influence; the splitting of the degenerate term in the RTE takes place just because the charge distribution in the two states becomes nonequivalent under the bending distortion.
Peierls distortion in linear chains. In linear molecules with three or more atoms there may be PJTE distortions that do not violate the linearity but change the interatomic distances. For instance, as a result of the PJTE a centrosymmetric linear system may become non-centrosymmetric in the equilibrium configurations, as, for example, in the BNB molecule (see in ). An interesting extension of such distortions in sufficiently long (infinite) linear chains was first considered by Peierls. In this case the electronic states, combinations of atomic states, are in fact band states, and it was shown that if the chain is composed by atoms with unpaired electrons, the valence band is only half filled, and the PJTE interaction between the occupied and unoccupied band states leads to the doubling of the period of the linear chain (see also in the books ).
Broken cylindrical symmetry. It was shown also that the PJTE not only produces the bending instability of linear molecules, but if the mixing electronic states involve a Δ state (a state with a nonzero momentum with respect to the axis of the molecule, its projection quantum number being Λ=2), the APES, simultaneously with the bending, becomes warped along the coordinate of rotations around the molecular axis, thus violating both the linear and cylindrical symmetry. It happens because the PJTE, by mixing the wavefunctions of the two interacting states, transfers the high momentum of the electrons from states with Λ=2 to states with lower momentum, and this may alter significantly their expected rovibronic spectra.