1. Critical Review of Contributions to the Jahn-Teller Symposium JT2010 and Beyond

A review of some important problems presented at the XX International Symposium on the Jahn-Teller effect (JTE) is given, outlining also the author’s view on some controversial issues. It is shown that the presentation of the pseudo JTE (PJTE) as a second order perturbation-theory correction (and hence called “second order JTE”) is misleading. The PJTE is a two-level (multilevel) problem that can only be reduced to a second order perturbation in very limited cases when there is no term crossover or when the crossing between the interaction states is avoided. This statement is illustrated by several examples demonstrating also the possibilities of the PJTE as a tool for molecular and solid state problem solving. The possible reason of the puzzling, drastically different results obtained for the magnitude of tunneling splitting in the impurity system MgO : Cu^{2 +} by experimental EPR measurements and theoretical ab initio calculations is discussed. More specifically, it is suggested that a reinterpretation of the experimental results is needed, while the calculations can be improved by taking into account the multimode nature of the problem. A brief discussion of the relation between orbital ordering and the cooperative JTE is given in view of a talk presented to the Symposium under an incorrect (wrong) title of “failure of the JTE physics”. More elaborate is the controversy around the origin of ferroelectricity in perovskite type crystals, mostly BaTiO₃, discussed in a plenary talk to the Symposium. The vibronic PJT origin and order-disorder nature of the ferroelectric phase transitions in these crystals, predicted many years ago and presently fully confirmed experimentally, serves also as an indication of the predictive ability of the PJTE and should be recognized as such. Some historical notes were also made with regard of the JT origin of high-temperature superconductivity discussed in a plenary talk to the Symposium.