Exact zero-point energy shift in the $e\otimes (nE)$, $t\otimes (nH)$ many modes dynamic Jahn-Teller systems at strong coupling

Abstract

We find the exact semiclassical (strong coupling) zero-point energy shifts applicable to the $e\otimes (nE)$ and $t\otimes (nH)$ dynamic Jahn-Teller problems, for an arbitrary number $n$ of discrete vibrational modes simultaneously coupled to one single electronic level. We also obtain an analytical formula for the frequency of the resulting normal modes, which has an attractive and apparently general Slater-Koster form. The limits of validity of this approach are assessed by comparison with O'Brien's previous effective-mode approach, and with accurate numerical diagonalizations. Numerical values obtained for $t\otimes (nH)$ with $n=8$ and coupling constants appropriate to C${}_{60}^{-}$ are used for this purpose, and are discussed in the context of fullerene.

20 pages, 4 ps figures

References in corpus (2)

• Electron--Vibron Interactions and Berry Phases in Charged Buckminsterfullerene: Part I
• Electron--Vibron Interactions in Charged Buckminsterfullerene: Pair Energies and Spectra (Part II)

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• Electron-vibration coupling constants in positively charged fullerene
• Theory of the Metal-Paramagnetic Mott-Jahn-Teller Insulator Transition in A_4C_{60}
• Berry Phase and Ground State Symmetry in H x h Dynamical Jahn-Teller Systems
• Coulomb couplings in positively charged fullerene
• Hund's rule Magnetism in C60 ions?
• Dynamical Jahn-Teller effect of fullerene anions
• Generalized "Quasi-classical" Ground State for an Interacting Two Level System
• Jahn-Teller distortions and excitation energies in C60(n+)
• Dynamical Jahn-Teller effect in the first excited C${}_{60}^{-}$
• Low-energy excitations of a linearly Jahn-Teller coupled orbital quintet