Pseudo-Jahn-Teller effects

In some respects arenediazonium ions show analogies to acetylene. Acetylene has two deformation vibrations, v4 at 613.5 cm-1 and v6 at 729.6 cm-1, as shown in Figure 7-1 (Feldmann et al., 1956). The fact that the symmetrical vibration v4 has a lower frequency than v6 can be understood from BartelPs valence-shell electron-pair repulsion (VSEPR) model (1968) on the basis of a <pseudo-Jahn-Teller> effect. 

Recently, a symmetry rule for predicting stable molecular shapes has been developed by Pearson Salem and Bartell" . This rule is based on the second-order, or pseudo, Jahn-Teller effect and follows from the earlier work by Bader . According to the symmetry rule, the symmetries of the ground state and the lowest excited state determine which kind of nuclear motion occurs most easily in the ground state of a molecule. Pearson has shown that this approximation is justified in a large variety of inorganic and small organic molecules. 

VIBRONIC COUPLING IN INORGANIC SYSTEMS PHOTOCHEMISTRY, CONICAL INTERSECTIONS, AND THE JAHN-TELLER AND PSEUDO-JAHN-TELLER EFFECTS... 

B. Computational Studies of the Pseudo-Jahn-Teller Effect 378... 

In fact, as we discuss in section 4 below, pJT coupling gives surfaces resembling the type-II Renner-Teller surfaces shown in Fig. 1, but separated by a finite energy difference. Many theoretical formulations of the pseudo-Jahn-Teller effect have been proposed. The simplest is perhaps the perturbative expansion originally due to Pearson (51)... 

Much work on the theory of Jahn-Teller and pseudo-Jahn-Teller effects has been reported by Bersuker and co-workers. They have proved that the pJT effect is the only possible source of instabilities of high symmetry molecular systems in nondegenerate states. These researchers have investigated the pJT effect in many systems, including planar BFLf, CH4, BH3, CH3", NH3, octahedral metal complexes MHe (M = Sc3-, V, Cr), and a series of octahedral hexafluoride systems (45, 46, 49, 50). 

Fig. 5. The pseudo-Jahn-Teller effect in ammonia (NH3). (a) CCSD(T) ground state potential energy curve breakdown of energy into expectation value of electronic Hamiltonian (He), and nuclear-nuclear repulsion VNN. (b) CASSCF frequency analysis of pseudo-Jahn-Teller effect showing the effect of including CSFs of B2 symmetry is to couple the ground and 1(ncr ) states to give a negative curvature to the adiabatic ground state potential energy surface for the inversion mode.

Fig. 7. Potential energy surfaces for ground and first excited state of Mo2(DXylF)2(02CCH3)2(n2-0)2 complex. The pseudo-Jahn-Teller effect results from a coupling between So and the excited 1( 6 ) state, causing the central Mo2(p2-0)2 motif to be rhomboidal (C2h), rather than square (D2h) [Adapted from Ref. (55) with permission].

The radical cation of [2,2,2]bicyclooct-2-ene and its 2,3-dimethyl derivative possess two interconverting twisted geometries with lowered symmetry. This structure is attributed to a pseudo-Jahn-Teller effect caused through vibronic coupling25. 

There is good reason to believe that the pseudo Jahn-Teller effect commonly assumes an important role in a number of molecular processes including electronic relaxation. Large classes of heterocyclic molecules whose zero-order BO electronic states may be very close to one another are ideal candidates for these types of vibronic interaction.127 Should the lowest state 0X of a given multiplicity be strongly coupled to a nearby electronic state 02 the following spectral effects can be expected ... 

Notice how the near degeneracy of levels in a large molecule resembles the situation encountered in the treatment of the pseudo Jahn-Teller effect. However, in the present case the coupling between many quasidegenerate... 

The presence of vibronic structure in the emission spectra of ions in solids does not depend on the nature of the particular ion alone, but also on the nature of its surroundings. In the case of ns2 ions the strength of the spin-orbit interaction relative to the Jahn-Teller effect determines whether the progression will be in v1 or v2. However, it is not usually possible to observe any vibronic structure at all due to deviations from high symmetry (pseudo Jahn-Teller effect in the ground state). Our present understanding is of a qualitative nature. Further progress is hampered by the fact that the presence of vibronic structure in the spectra is for these ions more exception that rule. 

Note that in the vicinity of the point considered, the potential V2 up to quadratic terms included does not depend on qy i.e., this potential is on the verge of the dynamical instability with respect to a shift in the q2 direction. Note also that the Jahn-Teller distortion parameter p0 increases if the quadratic interaction parameter w2 decreases. The reason for such a decrease may be, as it was already noticed above, the pseudo-Jahn-Teller effect. 

Combined Jahn-Teller and Pseudo-Jahn- Teller Effects in the Benzene Radical Cation... 

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