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

Abstract

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.

Accurate calculations of second-order vibronic reduction factors for C60ions

“…where k Gh = −V Gh /(2µhω 3 h ) 1/2 . (Note that the above expressions for the JT energies correct those given in [16].) In mixed systems involving coupling to both modes simultaneously, the minima arise from the most strongly coupled mode.…”

“…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]. In [16], the first calculations of Table 1.…”

“…Analytical expressions for the vibronic states and the energy spectrum were given explicitly in our earlier papers [16,17]. In [16], the first calculations of Table 1. The calculated values of the FC and NC contributions to the soRFs K (2) M ( ⊗ ) for the G ⊗ g JT system in terms of the parameters M and .…”

“…Here we are studying an orbital G state, so the general vibronic Hamiltonian in equation ( 1) can be written explicitly in terms of 4 × 4 matrices as given, for example, in [16]. However, it is desirable to enhance the notation to give explicitly the particular JT systems involved.…”

“…In mixed systems involving coupling to both modes simultaneously, the minima arise from the most strongly coupled mode. For certain specific values of coupling in which neither mode is dominant, the JT distortion space can consist of an equipotential minimal energy trough [12,16], but we will not consider this special case in this paper.…”