Vibronic couplings Renner-Teller coupling

Abstract Several examples are presented in order to illustrate the crucial role of high spin multiplicity electronic states on the formation and decomposition of the corresponding molecular systems. For instance, these states are good candidates where electronically excited, metastable negative ions can be found. Moreover, they are needed in order to explain fully unimolecular and bimolecular reaction pathways. During these reactions, the importance of the couplings between these states, such as vibronic and Renner-Teller, and with the states of lower spin multiplicity, such as spin-orbit, are pointed out. 

These overtone REPs have much in common with and thus may be difficult to distinguish from those due to pseudo-Renner-Teller coupling between excited states, discussed in Section IV,C and illustrated in Fig. 12. Conceptually, the present vibronic coupling mechanism is simpler than the pseudo-Renner-Teller mechanism in that it involves only a single excited state. It is restricted, however, to modes that are infrared active, whereas the pseudo-Renner-Teller mechanism applies to all modes. For all of these mechanisms, only one element of the scattering tensor is nonzero at resonance so that Pi = j without dispersion. 

As shown by ab initio calculations (Gillispie and Khan, 1976), the upper state of this transition results from a strong coupling between the radiant B2, weakly radiant A2 and Bj, and high vibronic levels of the ground (nonradiant) A, state via vibronic and Renner-Teller effects (Jungen and Merer, 1976). Because of the importance of the Renner-Teller effect, and pronounced differences between equilibrium configurations, the breakdown of rotational selection rules may be expected. 

Hamiltonian equations, 627-628 perturbative handling, 641-646 II electronic states, 631-633 vibronic coupling, 630-631 ABC bond angle, Renner-Teller effect, triatomic molecules, 611-615 ABCD bond angle, Renner-Teller effect, tetraatomic molecules, 626-628 perturbative handling, 641-646 II electronic states, 634-640 vibronic coupling, 630-631 Abelian theory, molecular systems, Yang-Mills fields ... 

Fig. 1. Conical intersection surface topologies (top), and Renner-Teller surface topologies (bottom). Top left is a generic circular cone, such as is obtained from a Jahn-Teller problem involving only the linear vibronic coupling. Top right is a sloped conical intersection obtained in a general vibronic coupling problem where all three linear vibronic coupling constants are different. Bottom left to right show type-1, -II, -III Renner-Teller surfaces. These are obtained when only second-order vibronic coupling is included.

Ch. Jungen You are quite right. The Renner-Teller effect in the water ion is an example of this kind. The strong vibronic coupling in the core leads to nonadiabatic effects in the Rydberg states of the neutral species, which are of course not accounted for by the coordinate dependence of the quantum defect and have to be taken into account separately. 

We consider now the complete basis set of vibronic functions I f m, n) obtained as the direct product of the electronic functions l/+) and 1/1) by the phonons wave functions Im, n), where the integer numbers m and n (positive or zero) label the occupation numbers of the boson operators b b+ and b b, respectively. The Renner-Teller Hamiltonian (14) when applied to any vibronic function I f m,n) couples it with three states (at most) in fact it holds that ... 

The above formulation of the JTE without the exception of linear molecules was given first by L. Landau in a discussion with E. Teller of his student s (Renner s) work on the Unear CO2 molecule [3]. Since in the Unear vibronic coupling approximation linear molecules are exceptions from the JTE, TeUer claimed that in this case Landau was wrong and that this was the only argument he won in discussions with Landau . It turns out that Teller did not win this argument, because when the fuU vibronic coupling is taken into account (as was impUed in Landau s statement) Unear molecules are not exceptions. 

Spin-Orbit Vibronic Coupling in Jahn-Teller and Renner Systems... 

Totally symmetric modes are not subject to symmetry restrictions. Their potentials may contain odd and even terms in Q so that the harmonic-oscillator approximation imposes unwarranted symmetry restrictions. Similarly, the corresponding vibronic coupling operator may contain both odd and even terms so that the distinction between pseudo-Jahn-Teller and pseudo-Renner-Teller coupling disappears. Since the potential energy minimum of a totally symmetric mode is different in different electronic states, the pseudo-Jahn Teller/Renner-Teller limit is quite different from the limiting cases discussed in Section I V,B,C. Finally, the transition moments... 

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