Renner-Teller splitting

Fig. 7. Cross sections of potential surfaces for a n state of a linear molecule showing the Renner-Teller splitting. This may (a) or may not (Z>) give rise to a stable bent configuration.

Fig. 27. Calculated angular potential energy curves of the lowest FI and states in various AH2 molecules showing Renner-Teller splitting.

Renner-Teller effect Splittings in the vibrational levels of molecular entities due to even terms in the vibronic perturbation expansion. This is generally a minor effect for nonlinear molecular entities compared to the Jahn-Teller effect which is due to... 

Keywords lodocarbene Enthalpy of formation MRCI Singlet-triplet splitting Renner-Teller effect Electronic excitation... 

There are certain interactions due to nuclear motion which are not readily apparent from the appearance of the potential curves. A typical example is the Renner-Teller effect in triatomic molecules, in which the two components of an orbitally degenerate state split into two states of different symmetry upon bending motion, as seen in Fig. 27. A strong coupling between the two components is observed, however, and spectral patterns can be understood only by coupling the electronic and nuclear motions, as has been pointed out already in numerous textbooks. From an ab initio point of view, one can treat this problem in analogy to the previous examples by calculating the Born-Oppenheimer potential surfaces and the interaction matrix element, in this case < Pa 5/34 Pb> and (and the same for Pg) as... 

Simple examples of these effects were discussed in Section IV as limiting cases of the pseudo-Jahn Teller and pseudo-Renner-Teller effects. There it was shown that instead of using the adiabatic approximation, we should, in the interest of convenience, adopt a diabatic approximation in which the electronic degeneracy is maintained in zeroth order. The splitting can then simply be ascribed to adiabatic coupling proportional to Q, (or Qf, etc.) or to Qf (or Qf, etc.) between the two electronic components that remain degenerate at Q, = 0. The selection rule for pseudo-Jahn Teller coupling is thus <0° 0 or, iff denotes representation, T , x F,- x F 3-4,. 

It follows from Table 2 that nondegenerate modes can be Jahn-Teller but not Renner-Teller active. Their Jahn-Teller activity lifts the electronic but not the vibronic degeneracy since these modes do not add degeneracies of their own (see also Section IV,B)- Degenerate modes can be Jahn-Teller active, Renner-Teller active, or both. This activity generally leads to splitting of vibronic energy levels. 

The electronic states involved can be briefly described in the following way. At linear H-O-H geometry there is a binding E state, 1 E+, which leads to electronically excited OH( A E), and a repulsive II state, 1 11, which correlates with OH(X II). The two potential curves cross around an O-H separation of about 3.2 ao, when the other O-H bond distance is in the range of 1.8 ao. When water bends, the FE+ becomes the ground electronic state, X A, with an equilibrium angle of 104°, and the H state splits into the states A A and B A, which form a Renner-Teller (RT) pair. The lower... 

For the quantum numbers of the bending vibration, the correlation between linear- and bent-molecule notation is V2(linear) = 2v2(bent) + Kg +1 see for example [3, 4]. Most authors prefer the linear molecule notation which is used in this chapter. Energy levels due to vibronic splitting (Renner-Teller effect, see p. 171) [5] are shown in Fig. 6, p. 172. 

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