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

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  • 8 September 1997
Abstract
We find the exact semiclassical (strong coupling) zero-point energy shifts applicable to the e\otimes (n E) and t\otimes (n H) dynamic Jahn-Teller problems, for an arbitrary number n of vibrational modes simultaneously coupled to one single electronic level. We also obtain an analytical formula for the frequency of the 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. As it turns out, our approach is better for large coupling, while for intermediate coupling the effective mode is the better one, which makes them to some extent complementary. Numerical values obtained for t\otimes (n H) with n=8 and coupling constants appropriate to C_60^- are obtained and discussed in the context of fullerene.

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