Bom -Oppenheimer regime

B. A. Hess The notion of a geometric phase generally requires an adiabatic situation, where an adiabatic connection and adiabatic transport can be defined. In the presence of many nearby avoided crossings, in a highly nonadiabatic situation (as in the case of the inverse Bom-Oppenheimer regime), the notion of a geometric phase is ill defined. 

A quantitative treatment of the Jahn-Teller effect is more challenging (46). A major issue is that many theoretical models explicitly or implicitly assume the Bom—Oppenheimer approximation which, for octahedral Cu(II) systems in the vibronic coupling regime, cannot be correct (46,51). Hitchman and co-workers solved the vibronic Hamiltonian in order to model the temperature dependence of the molecular structure and the attendant spectroscopic properties, notably EPR spectra (52). Others, including us, take a more simphstic approach (53,54) but, in either case, a similar Mexican hat potential energy description of the principal features of the Jahn-Teller effect in homoleptic Cu(II) complexes emerges (Fig. 13). 

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