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We find the exact semiclassical (strong coupling) zero-point energy shiftsapplicable to the $e\otimes (n E)$ and $t\otimes (n H)$ dynamic Jahn-Tellerproblems, for an arbitrary number $n$ of discrete vibrational modessimultaneously coupled to one single electronic level. We also obtain ananalytical formula for the frequency of the resulting normal modes, which hasan attractive and apparently general Slater-Koster form. The limits of validityof this approach are assessed by comparison with O'Brien's previouseffective-mode approach, and with accurate numerical diagonalizations.Numerical values obtained for $t\otimes (n H)$ with $n =8$ and couplingconstants appropriate to C$_{60}^-$ are used for this purpose, and arediscussed in the context of fullerene.Comment: 20 pages, 4 ps figure

physical review. b, condensed matter

Exact zero-point energy shift in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi><mml:mo>⊗</mml:mo><mml:mn /><mml:mo>(</mml:mo><mml:mi>nE</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mo>⊗</mml:mo><mml:mn /><mml:mo>(</mml:mo><mml:mi>nH</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math>many-modes dynamic Jahn-Teller systems at strong coupling

Exact zero-point energy shift in thee⊗(nE),t⊗(nH)many-modes dynamic Jahn-Teller systems at strong coupling