Pseudo Jahn–Teller effect

[5] The role of excited states in softening the ground state with respect to distortions in benzene was demonstrated qualitatively by Longuet-Higgins and Salem[6] by analyzing the π electron levels in the Hückel approximation, while a general second-order perturbation formula for such vibronic softening was derived by Bader in 1960.

[7] In 1961 Fulton and Gouterman[8] presented a symmetry analysis of the two-level case in dimers and introduced the term "pseudo Jahn–Teller effect".

The first explanation of PJT origin of puckering distortion as due to the vibronic coupling to the excited state, was given for the N3H32+ radical by Borden, Davidson, and Feller in 1980[12] (they called it "pyramidalization").

Methods of numerical calculation of the PJT vibronic coupling effect with applications to spectroscopic problems were developed in the early 1980s[13] A significant step forward in this field was achieved in 1984 when it was shown by numerical calculations[14] that the energy gap to the active excited state may not be the ultimate limiting factor in the PJTE, as there are two other compensating parameters in the condition of instability.

It was also shown that, in extension of the initial definition,[2] the PJT interacting electronic states are not necessarily components emerging from the same symmetry type (as in the split degenerate term).

Moreover, it was shown by Bersuker that the PJTE is the only source of instability of high-symmetry configurations of polyatomic systems in nondegenerate states (works cited in Refs.

[17] The many applications of the PJTE to the study of a variety of properties of molecular systems and solids are reflected in a number of reviews and books [1][10][11][15][16][17][18][19]), as well as in proceedings of conferences on the JTE.

The PJTE is the general driving force of all these distortions if they occur in the nondegenerate electronic states of the high-symmetry (reference) geometry.

in this direction, the system becomes unstable with respect to the distortions under consideration, leading to its equilibrium geometry of lower symmetry, or to dissociation.

In such cases the symmetry breaking is produced by a hidden PJTE (similar to a hidden JTE); it takes place due to a strong PJTE mixing of two excited states, one of which crosses the ground state to create a new (lower) minimum of the APES with a distorted configuration.

In this case, we should consider the contribution of the lowest excited states (that make the total curvature negative) in a pseudo degenerate problem of perturbation theory.

In other words, what is the physical driving force of the PJTE distortions (transformations) in terms of well-known electronic structure and bonding?

[1][16] Indeed, in the starting high-symmetry configuration the wavefunctions of the electronic states, ground and excited, are orthogonal by definition.

If for two near-neighbor atoms the ground state wavefunction pertains (mainly) to one atom and the excited state wavefunction belongs (mainly) to the other, the orbital overlap resulting from the distortion adds covalency to the bond between them, so the distortion becomes energetically favorable (Fig.

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).

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.

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 [1]).

An interesting extension of such distortions in sufficiently long (infinite) linear chains was first considered by Peierls.

An interesting typical situation of hidden PJTE emerges in molecular and solid-state systems with valence half-filed closed shells electronic configurations e2 and t3.

3 illustrates the hidden PJTE in the CuF3 molecule, showing also the singlet-triplet spin crossover and the resulting two coexisting configurations of the molecule: high-symmetry (undistorted) spin-triplet state with a nonzero magnetic moment, and a lower in energy dipolar-distorted singlet state with zero magnetic moment.

Special attention has been paid recently to 2D systems in view of a variety of their planar-surface-specific physical and chemical properties and possible graphene-like applications in electronics.

One of the main important features of these systems is their planarity or quasi-planarity, but many of the quasi-2D compounds are subject to out-of-plane deviations known as puckering (buckling).

The instability and distortions of the planar configuration (as in any other systems in nondegenerate state) was shown to be due to the PJTE.

[1][15][16] Detailed exploration of the PJTE in such systems allows one to identify the excited states that are responsible for the puckering, and suggest possible external influence that restores their planarity, including oxidation, reduction, substitutions, or coordination to other species.

Provided the criterion for PJTE is met, each [BO6] center has an APES with eight equivalent minima along the trigonal axes, six orthorhombic, and (higher) twelve tetragonal saddle-points between them.

With temperature, the gradually reached transitions between the minima via the different kind of saddle-points explains the origin of all the four phases (three ferroelectric and one paraelectric) in perovskites of the type BaTiO3 and their properties.

Similar to the above-mentioned molecular bistability induced by the hidden PJTE, a magnetic-dielectric bistability due to two coexisting equilibrium configurations with corresponding properties may take place also in crystals with transition metal centers, subject to the electronic configuration with half-filled e2 or t3 shells.

In a recent development it was shown that in inorganic crystals with PJTE centers, in which the local distortions are not ordered (before the phase transition to the cooperative phase), the effect of interaction with external perturbations contains an orientational contribution which enhances the observable properties by several orders of magnitude.

This was demonstrated on the properties of crystals like paraelectric BaTiO3 in interaction with electric fields (in permittivity and electrostriction), or under a strain gradient (flexoelectricity).

These giant enhancement effects occur due to the dynamic nature of the PJTE local dipolar distortions (their tunneling between the equivalent minima); the independently rotating dipole moments on each center become oriented (frozen) along the external perturbation resulting in an orientational polarization which is not there in the absence of the PJTE[31][32]