Pseudo-Jahn-Teller

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 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. 

Of the cata-condensed nonalternant hydrocarbons undergoing a pseudo Jahn-Teller distortion, pentalene (I) and heptalene (VII), having the largest value, are predicted to possess a strong bond alternation. This confirms the results of the previous theoretical investi-gations " and agrees with the available experimental facts ... 

One study (DeLeo et al., 1988 Fowler et al., 1989) has found that neutral H at the B site in Si has a tendency to preferentially bind to one of the two Si neighbors, leading to an asymmetric configuration, with Si—H distances of 1.48 A and 1.77 A respectively. This tendency was interpreted in terms of a pseudo-Jahn-Teller distortion. However, the potential barrier that leads to the asymmetric position is so low (< 0.2 eV) that it can readily be surmounted by zero-point motion of the proton. Experimental observation of such an asymmetry is therefore unlikely, except maybe through an isotope shift measurement in an infrared experiment (DeLeo et al., 1988). None of the other theoretical approaches has produced this type of asymmetry. 

SA quite different approach (Biirgi and Dunitz, 1983), using atomic vibration tensors to estimate torsional energy barriers (assumed sinusoidal) about single bonds, is described by Trueblood and Dunitz (1983) and has been applied to pseudo-Jahn-Teller deformations of octahedral complexes by Stebler and Biirgi (1987). 

It is well known that crystal and electronic structures are interdependent and define the reactivity of chemical substances. In Section 1.4.2, it was noted that copper-porphyrin complex gives cation-radicals with significant reactivity at the molecular periphery. This reactivity appears to be that of nucleophilic attack on this cation-radical, which belongs to n-type. The literature sources note, however, some differences in the reactivity of individual positions. A frequently observed feature in these n-cation derivatives is the appearance of an alternating bond distance pattern in the inner ring of porphyrin consistent with a localized structure rather than the delocalized structure usually ascribed to cation-radical. A pseudo Jahn-Teller distortion has been named as a possible cause of this alternation, and it was revealed by X-ray diffraction method (Scheidt 2001). 

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. 

Bader 46) considered the implications of the pseudo Jahn-Teller theorem for this and deduced that the bond stretching E mode would be the most likely reaction coordinate, and one can see from Fig. 10 that this would lead to the required products if continued to dissociation. 

The 3d ab initio simulations [4] for Na3 are based, in a similar way, on three ab initio potential-energy surfaces for Na3(X), Na3(B), and Na3(X), with 3d ab initio dipole coupling between Na3(X) and Na3(B) evaluated by V. Bonacic-Koutecky et al. [5] plus Condon-type coupling between Na3(B) and Na3(X). Additional potential-energy surfaces interfere at the conical intersections of the pseudo-Jahn-Teller distorted Na3(B) state (see Ref. 6), but we have tested carefully [4] that these interferences are negligible in the frequency domains of the experimental femtosecond/picosecond laser pulse experiments [7] as well as in the continuous-wave experiments [8]. 

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 ... 

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