The Jahn-Teller effect in icosahedral molecules and complexes

The Jahn - Teller (JT) problem is investigated analytically using a unitary transformation method. Minimization of the adiabatic energy surface for this problem results in wells of either or symmetry, depending on the coupling strengths. The dynamic JT problem is then solved in the tunnelling regime using projection operators to find symmetrized combinations of the states associated with the wells. By analogy to other JT systems, the ground state would be expected to have the same degeneracy as the original orbital state, and thus to be an H-type quintet. However, it is found that there are a range of couplings strengths for the g and h modes for which the tunnelling ground state for the wells can be an A-type singlet. A similar result was recently found for the pure JT system. It is also found that for wells, the limiting value of the tunnelling splitting between the H and A states for a pure system tends to in weak coupling, whilst for a pure system it tends to . For systems coupled to both modes, the value of the tunnelling splitting strongly depends upon which of the two modes is dominant. Both the level ordering in strong coupling and the anomalous behaviour in weak coupling can be shown to be fundamental symmetry properties of these JT systems, and not consequences of the details of our model. The JT systems studied here are possible models for the ground state of the cation and for an excited state of the anion .

Section: Introductionsupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

An analytical model for the Jahn - Teller system

Moate

Dunn

Bates

et al. 1997

“…The work of Ceulemans and Fowler [12] provides the general theoretical background for the study of the G ⊗ (g ⊕ h) JT system in icosahedral symmetry. This follows earlier work by Khlopin et al [13], Pooler [14] and by Cullerne and O'Brien [15] as reviewed in the book by Chancey and O'Brien [3]. Analytical expressions for the vibronic states and the energy spectrum were given explicitly in our earlier papers [16,17].…”

Section: Calculations For Icosahedral Orbital G-state Systemssupporting

confidence: 53%

Accurate calculations of second-order vibronic reduction factors for C₆₀ions

Al-Hazmi¹,

Moujaes²,

Abou-Ghantous³

et al. 2005

An effective Hamiltonian containing Jahn-Teller (JT) first-and secondorder vibronic reduction factors (RFs) is a convenient way of modelling the spectroscopic properties of solids and molecules in which vibronic interactions are important. It can act as a bridge between experimental data and basic theory. In particular, second-order RFs can give valuable information on many of the fundamental properties of strongly coupled systems. As interest in the icosahedral fullerene molecules and ions has grown over the last few years, it has become necessary to be able to calculate values for second-order RFs in icosahedral symmetry in terms of more fundamental vibronic coupling parameters. Following on from earlier work on the icosahedral T ⊗ h JT system, we present here results of such calculations of the second-order vibronic RFs for the icosahedral G ⊗ g, G ⊗ h, H ⊗ g and H ⊗ h JT systems. These systems are relevant for the ground and excited states of C 60 anions and cations. The calculations are based on the Franck-Condon approximation followed by additional non-Condon corrections. Previous work has demonstrated that such an approach can give values for the RFs close to those deduced from experiments.

“…It appears that the first example of G states studied in any detail involved icosahedral structures of boron [7][8][9]. In 1978, Khlopin et al [10] analysed a number of the simpler icosahedral systems from a theoretical point of view including the G ⊗ h subsystem. Other theoretical work has since been undertaken by Pooler [6] for the regime in which the g and h modes were equally coupled, and by Ceulemans and Fowler [1] who obtained highly significant results from an analysis of the adiabatic potential energy surface (APES) for the G ⊗ (g ⊕ h) problem.…”

Section: Introductionmentioning

confidence: 99%

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

Abou-Ghantous

Oliete

Bates

et al. 2002

Analytical expressions for the vibronic states and energy spectrum of the icosahedral G ⊗ (g ⊕ h) Jahn-Teller system are derived. From these states, expressions for first-and second-order vibronic reduction factors are determined as a function of the strengths of the coupling of the G orbital to the g and h modes of vibration. The possibility of the vibronic ground state being a singlet A state, rather than the G state that would be expected in the absence of vibronic coupling, is explored. The reduction factors obtained provide a convenient basis for the modelling of spectra involving some of the excited states of the fullerene molecule C 60 and related ions.