Recent Developments in the Jahn–Teller Effect Theory

Abstract

In a review paper an updated formulation of the Jahn–Teller (JT) effect (JTE) (including proper JT, pseudo JT, and Renner–Teller (RT) effects) is given ased on the latest achievements in this field, including the conclusion that the JTE is the only source of instability and distortion of any polyatomic system from its high-symmetry configuration. Together with the statement in particle physics that “symmetry breaking is always associated with a degeneracy” the extended formulation of the JTE leads us to the speculation that Nature tends to avoid degeneracies. In the updated formulation the presence of two or more electronic states, degenerate or within a limited energy gap, that mix strongly enough under nuclear displacements is the necessary and sufficient condition of instability. Distinguished from the usually considered electron-vibrational (electron–phonon) interaction in which one electronic state interacts with totally symmetric vibrations, the JTE, mixing two or more electronic states, involves also low-symmetry displacements.

It is shown that if in the global minimum of the adiabatic potential energy surface (APES) the polyatomic system is distorted from its high-symmetry configuration, while the electronic term in the latter is neither degenerate nor pseudo degenerate, and hence there is no apparent JTE or pseudo-JTE (PJTE), the distortion is due to these effects in the higher excited states. This is possible when the JT stabilization energy is larger than the energy gap to the ground state. Since the JT origin of the distortion is not seen explicitly from the calculation of the ground state, we call it hidden JTE (HJTE). There are two kinds of HJTE: (1) induced by proper JTE in an excited state, and (2) produced by the PJTE which mixes two exited states. Both types of HJTE are confirmed by ab initio calculations of a variety of molecular systems. While the first type of HJTE is more “accidental” (ozone, O3, is shown to be a nice example), the second type occurs in e² and t³ electron configurations and it is accompanied by orbital disproportionation, making the spin state in the global minimum different from that of the high-symmetry configuration. This in turn results in two minima of the APES with relatively close energies, but different electronic states and spin, and a spin crossover between the two minima. With the PJTE and HJTE included, the role of excited states in the analysis of structure and properties of molecular systems in the ground state becomes most important. It can be said that no full treatment of polyatomic systems is possible without involving excited states, even when the properties in the ground state are considered.