Jahn–Teller effect

Such complexes distort along one of the molecular fourfold axes (always labelled the z axis), which has the effect of removing the orbital and electronic degeneracies and lowering the overall energy.

[4] Additional, detailed information about the anisotropy of such complexes and the nature of the ligand binding can be however obtained from the fine structure of the low-temperature electron spin resonance spectra.

[6] The JT theorem can be stated in different forms, two of which are given here: Alternatively and considerably shorter: Spin-degeneracy was an exception in the original treatment and was later treated separately.

[8] The formal mathematical proof of the Jahn–Teller theorem rests heavily on symmetry arguments, more specifically the theory of molecular point groups.

A further breakthrough occurred upon the advent of modern ("ab initio") electronic structure calculations whereby the relevant parameters characterising JT systems can be reliably determined from first principles.

Even systems that in the undistorted symmetric configuration present electronic states which are near in energy but not precisely degenerate, can show a similar tendency to distort.

This mechanism is associated to the vibronic couplings between adiabatic PES separated by nonzero energy gaps across the configuration space: its inclusion extends the applicability of JT-related models to symmetry breaking in a far broader range of molecular and solid-state systems.

JT problems are conventionally classified using labels for the irreducible representations (irreps) that apply to the symmetry of the electronic and vibrational states.

To arrive at a quantitative description of the JT effect, the forces appearing between the component wave functions are described by expanding the Hamiltonian in a power series in the

Generally, the APESs take the characteristic appearance of a double cone, circular or elliptic, where the point of contact, i.e. degeneracy, denotes the high-symmetry configuration for which the JT theorem applies.

The conical shape near the degeneracy at the origin makes it immediately clear that this point cannot be stationary, that is, the system is unstable against asymmetric distortions, which leads to a symmetry lowering.

Conical intersections have received wide attention in the literature starting in the 1990s and are now considered paradigms of nonadiabatic excited-state dynamics, with far-reaching consequences in molecular spectroscopy, photochemistry and photophysics.

This effect leads, for example, to a partial quenching of the spin–orbit interaction[21][31] and allowed the results of previous Electron Paramagnetic Resonance (EPR) experiments to be explained.

[9] Reduction factors are particularly useful for describing experimental results, such as EPR and optical spectra, of paramagnetic impurities in semiconducting, dielectric, diamagnetic and ferrimagnetic hosts.

The situation changed in the 1980s when efficient ab initio methods were developed and computational resources became powerful enough to allow for a reliable determination of these parameters from first principles.

[32] Apart from wave function-based techniques (which are sometimes considered genuinely ab initio in the literature) the advent of density functional theory (DFT) opened up new avenues to treat larger systems including solids.

The JT distortion of small molecules (or molecular ions) is directly deduced from electronic structure calculations of their APES (through DFT and/or ab initio computations).

The JT distortion reduces the symmetry from D3h to C2v (see figure), and it depends on the details of the interactions whether the isosceles triangle has an acute or an obtuse-angled (such as Na3) minimum energy structure.

The dynamics of Jahn-Teller distortion in CH4+ has been characterized by transient X-ray absorption spectroscopy, revealing that symmetry breaking occurs within ten femtoseconds in this prototypical system.

Already in the early 1980s, a wealth of information emerged from the detailed analysis of experimental emission spectra of 1,3,5- trifluoro- and hexafluoro (and chloro) benzene radical cations.

For the parent benzene cation one has to rely on photoelectron spectra with comparatively lower resolution because this species does not fluoresce (see also section § Spectroscopy and reactivity).

level, which antibonding orbital the final geometry of the complex would be elongated as the axial ligands will be pushed away to reduce the global energy of the system.

To be sure, photochemical reactivity emerges when the internal conversion makes the system explore the nuclear configuration space such that new chemical species are formed.

As proposed originally by Landau[35] free electrons in a solid, introduced for example by doping or irradiation, can interact with the vibrations of the lattice to form a localized quasi-particle known as a polaron.

These Jahn–Teller polarons break both translational and point group symmetries of the lattice where they are found and have been attributed important roles in effects like colossal magnetoresistance and superconductivity.

However, in many periodic high-symmetry solid-state systems, like perovskites, some crystalline sites allow for electronic degeneracy giving rise under adequate compositions to lattices of JT-active centers.

However, under the perturbation of the symmetry-breaking distortion associated to the cooperative JTE, the degeneracies in the electronic structure are destroyed and the ground state of these systems is often found to be insulating (see e.g.[44]).

In many important cases like the parent compound for colossal magnetoresistance perovskites, LaMnO3, an increase of temperature leads to disorder in the distortions which lowers the band splitting due to the cooperative JTE, thus triggering a metal–insulator transition.

In modern solid-state physics, it is common to classify systems according to the kind of degrees of freedom they have available, like electron (metals) or spin (magnetism).

Even when starting from a relatively high-symmetry structure the combined effect of exchange interactions, spin–orbit coupling, orbital-ordering and crystal deformations activated by the JTE can lead to very low symmetry magnetic patterns with specific properties.

The Jahn–Teller effect is responsible for the tetragonal distortion of the hexaaquacopper(II) complex ion, [Cu(OH 2 ) 6 ] 2+ , which might otherwise possess regular octahedral geometry. The two axial Cu−O distances are 238 pm , whereas the four equatorial Cu−O distances are ~195 pm. This geometry is common in crystal structures ; the geometry in solution is uncertain. [ 1 ]
Above : JT effect is observed as tetragonal elongation and compression in octahedral high-spin d 4 complexes due to net change in the energy of electrons (notice odd amount of electrons in e g -orbital). Below : JT effect doesn't occur if there is no net change in energy (notice even amount of electrons in e g -orbital).
The Jahn–Teller effect forces the radical anion of cyclooctatetraene (−1) to be non-symmetric (see text)
A conceptual comparison of the Jahn–Teller and pseudo Jahn–Teller effects, showing the mutual relation of two potential energy surfaces (PES) in the two cases. The number of PES is two in this picture but it can be more in actual molecular or solid-state systems.
The potential energy surfaces of an E ⊗ e Jahn–Teller effect
Two possible ways in which an equilateral triangle could distort due to a Jahn–Teller effect
Images of d orbitals transforming as and embedded in an octahedron
Effect of a JT distortion on d orbitals