Pseudo Jahn–Teller effect

The pseudo Jahn–Teller effect (PJTE), occasionally also known as second-order JTE, is a direct extension of the Jahn–Teller effect (JTE) where spontaneous symmetry breaking in polyatomic systems (molecules and solids) occurs even in nondegenerate electronic states under the influence of sufficiently low-lying excited states of appropriate symmetry.'The pseudo Jahn–Teller effect is the only source of instability and distortions of high-symmetry configurations of polyatomic systems in nondegenerate states, and it contributes significantly to the instability in degenerate states'.In the first publication in 1957 on the (what is now called) pseudo Jahn–Teller effect (PJTE), Öpik and Pryce showed that a small splitting of the degenerate electronic term does not necessarily remove the instability and distortion of the polyatomic system induced by the Jahn–Teller effect (JTE), provided the splitting is sufficiently small (the two split states remain “pseudodegenerate”), and the vibronic coupling between them is strong enough. From another perspective, the idea of vibronic admixture of different electronic terms by low-symmetry vibrations was introduced in 1933 by Herzberg and Teller to explore forbidden electronic transitions, and extended in the late 1950s by Murrell and Pople and by Liehr. The role of excited states in softening the ground state with respect to distortions in benzene was demonstrated qualitatively by Longuet-Higgins and Salem by analyzing the π electron levels in the Hückel approximation, while a general second-order perturbation formula for such vibronic softening was derived by Bader in 1960. In 1961 Fulton and Gouterman presented a symmetry analysis of the two-level case in dimers and introduced the term 'pseudo Jahn–Teller effect'. The first application of the PJTE to solving a major solid-state structural problem with regard to the origin of ferroelectricity was published in 1966 by Bersuker, and the first book on the JTE covering the PJTE was published in 1972 by Englman. The second-order perturbation approach was employed by Pearson in 1975 to predict instabilities and distortions in molecular systems; he called it 'second-order JTE' (SOJTE). The first explanation of PJT origin of puckering distortion as due to the vibronic coupling to the excited state was given for the N3H32+ radical by Borden, Davidson, and Feller in 1980 (they called it 'piramidalization'). Methods of numerical calculation of the PJT vibronic coupling effect with applications to spectroscopic problems were developed in the early 1980s A significant step forward in this field was achieved in 1984 when it was shown by numerical calculations that the energy gap to the active excited state may not be the ultimate limiting factor in the PJTE, as there are two other compensating parameters in the condition of instability. It was also shown that, in extension of the initial definition, the PJT interacting electronic states are not necessarily components emerging from the same symmetry type (as in the split degenerate term). As a result, the applicability of the PJTE became a priory unlimited. Moreover, it was shown by Bersuker that the PJTE is the only source of instability of high-symmetry configurations of polyatomic systems in nondegenerate states (works cited in Refs.), and degeneracy and pseudodegeneracy are the only source of spontaneous symmetry breaking in matter in all its forms. The many applications of the PJTE to the study of a variety of properties of molecular systems and solids are reflected in a number of reviews and books ), as well as in proceedings of conferences on the JTE.The equilibrium geometry of any polyatomic system in nondegenerate states is defined as corresponding to the point of the minimum of the adiabatic potential energy surface (APES), where its first derivatives are zero and the second derivatives are positive. If we denote the energy of the system as a function of normal displacements Qα as E(Qα), at the minimum point of the APES (Qα=0), the curvature K of E(Qα) in direction Q,Examples of the PJTE being used to explain chemical, physical, biological, and materials science phenomena are innumerable; as stated above, the PJTE is the only source of instability and distortions in high-symmetry configurations of molecular systems and solids with nondegenerate states, hence any phenomenon stemming from such instability can be explained in terms of the PJTE. Below are some illustrative examples.