Varying spin state composition by the choice of capping ligand in a family of molecular chains: detailed analysis of magnetic properties of chromium(III) horseshoes

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Constructing, solving and applying the vibronic Hamiltonian

The Jahn–Teller effect is shrouded in mysticism and cynicism. To paraphrase a remark that a colleague recently relayed, “For every anomalous spectrum, structural distortion or novel physical property, there is a vibronic Hamiltonian and ensuing explanation that few can appreciate or comprehend.” The aim of this article is to provide a basic introduction to the Jahn–Teller effect, pitched at a level that undergraduates in chemistry can understand, with an emphasis on how to calculate a given experimental quantity. We show that armed with just a little group theory and matrix mechanics, vibronic Hamiltonians can be readily constructed, solved, and the molecular property of interest extracted from the eigenvalues and eigenfunctions. The manifestation of the Jahn–Teller effect does indeed come in many shapes and forms, three signatures of which are briefly discussed. (1) The vibronic energy spectrum is best revealed by spectroscopy and two examples are taken from the literature that elucidate the intricate energy-level pattern of the E ⊗ e vibronic interaction. (2) ‘The Ham effect’, ‘Ham factors’ and ‘Ham quenching’ are now common parlance in spectroscopy and the phenomenon is aptly illustrated by the magnetic and spectroscopic data of the titanium(III) and vanadium(III) aqua ions. (3) The plasticity of the co-ordination sphere is the quintessential feature of transition metals exhibiting strong Jahn–Teller coupling. We show how a concomitant description of structural and spectroscopic data can be obtained employing a model in which the potential energy surface resulting from the cubic Jahn–Teller Hamiltonian is perturbed by anisotropic strain

The dynamic Jahn-Teller effect in Cu(II) doped MgO

The electron paramagnetic resonance spectra of Cu(II) doped MgO single crystals have been re-examined in detail within the framework of a dynamic Jahn–Teller effect. The experimental 1.8 K X-band spectra can be modeled in terms of a cubic spin Hamiltonian operating within the set of four Kramers doublets corresponding to the lowest vibronic energy levels of an E⊗e Jahn–Teller problem. This “four state” model must also include vibronic (Ham) reduction factors and a random distribution of the crystal strain. It was found to be important to treat the Zeeman, hyperfine, quadrupole, tunneling, and strain terms without recourse to perturbation theory or other approximations and this has been carried out using the eigenfield method. We find that the first excited singlet is of A2 symmetry, indicating that the CuO6 center has the expected E⊗e Jahn–Teller potential energy surface with three equivalent minima at tetragonally elongated octahedral geometries. Small random crystal strains have a dominant influence on the spectra and we find that the major features can be reproduced by averaging over the strain in the angular direction ϕs with a small magnitude centered about zero. Details of the strain broadening require a distribution of strains centered at zero with a larger spread; however, the use of a single intrinsic linewidth could not account for all linewidth features. Our analysis also differs from that of previous workers in that different hyperfine values (A1 = −20.0×10−4 and A2 = −86.0×10−4 cm−1) are required as well as a nuclear quadrupole term (P2 = +8.75×10−4 cm−1) to account for the observed structure and the angular dependence. The transitions within the lowest excited singlet are observed directly, giving an estimate of the tunneling splitting as ∼ 4 cm−1. These parameter values are related to the intrinsic Jahn–Teller coupling parameters of the potential energy surface. We conclude that the Cu(II)/MgO system can be described as an almost pure dynamic Jahn–Teller case, with most spectral features accounted for by using a single isolated Γ8(math) vibronic state