Modelling of theH⊗(g⊕h) Jahn-Teller system: extension to vibronic reduction factors

Abstract

First- and second-order vibronic reduction factors are calculated analytically for the H⊗(g⊕h) Jahn-Teller system in Ih symmetry. Results are given as a function of the strength of the coupling of the H orbital to the vibrations of h and g symmetries. As the product systems H⊗g and H⊗h contain repeated representations, the calculations of many of the reduction factors are more complicated than in other systems. These complications and their implications are analysed in detail. This system models the ground state of hole-doped C60 material, which has possible applications for high-temperature superconductivity.

The Jahn-Teller vibronic reduction factors in icosahedral G$\otimes$(g$\oplus$h) systems

“…The object of this paper is to analyse the G ⊗ (g ⊕ h) JT system and calculate the RFs for this system and its subsystems covering all ranges of coupling strengths to the two modes. The methodology to be used here follows that described by the authors for the analytical calculation of the first-and second-order RFs for the T ⊗h [15] and H ⊗(g ⊕h) JT systems [16], although the nature of the high symmetries involved means that application to this system is far from trivial. It is sufficient for our purposes here to limit the discussion to linear JT interactions (in which the normal-mode coordinates enter the interaction in linear fashion) since these are capable of illustrating the general features of vibronic couplings considered in this paper.…”

Accurate calculations of second-order vibronic reduction factors for C60ions

“…It appears that the literature contains very few references to RFs in icosahedral systems with which the results reported here can be compared, and none of these include reference to experimental data. However, our Nottingham Group and their collaborators have used a shift transformation (ST) method to deduce values for the first-and second-order RFs in the T ⊗ h [10], in the H ⊗ (g ⊕ h) [19] and in the G ⊗ (g ⊕ h) [16] icosahedral JT systems. In principle, it should be possible to compare results from the ST approach with results obtained…”

“…The JT instabilities present were extensively studied by Ceulemans and Fowler [18]. The current authors [19] followed up their earlier modelling work [20,21] and that of Manini and coworkers [22] by studying the motion of the system along possible tunnelling paths between different pairs of wells in the APES. Here, we are interested in calculating the soRFs for the icosahedral H ⊗ (g ⊕ h) JT system and the corresponding JT subsystems.…”

“…We now comment, secondly, on a few results involving the more complicated H orbital. We thus consider the H ⊗ h b JT system for which the ST calculations are reported in figure 4 of [19] and the NC results here in figure 5. The soRF with the largest magnitude is K (2) A (T 1 ⊗ T 1 ) in both approaches.…”

Anisotropic effect on the vibronic reduction factors

“…These factors can describe the energy splitting caused by magnetic field, strain and hyperfine effects because the reduction factor can not only reflect the influence of JT effect of the crystal on the spectrum, but also sufficiently describe the JT effect on some weak-perturbed systems. Therefore, many authors carried on the research of the reduction factors [2][3][4][5] of JT systems, including the icosahedral systems related to C 60 molecules. The experiments proved that the vibronic coupling have a quenching effect on the spin-orbit couplings, random strains and internal stresses, etc., and these effects can be explained by reduction factors.…”