Vibronic mixing

Vibronic mixing of levels, leading to an overall finite value of a transition probability, even when /9el is zero because of symmetry, may occur if nonsymmetric vibrational levels of the product are used in the internal conversion process. The effect is well known in the case of optical transitions and may be the best interpretation of the Woodward-Hoffman rules. 

An unresolved puzzle remains22 the first two vibrational peaks in the first band in the photoelectron spectrum are separated only by 360 20 cm4, less than the lowest frequency vibration observed in neutral propellane (529 cm4), and very much less than its lowest totally symmetric vibration (908 cm 1). Yet, the authors calculations22 suggest that the lowest frequency totally symmetrical vibration of the radical cation will be at higher and not lower frequencies. The authors suggested that the vibrational structure may be due to vibronic mixing with the lowest excited state of the radical cation. 

It is interesting to note that the ground and first excited states, which, in line with the state-of-the-art VB calculation are revealed to have a Kekule preponderant parentage [8] span the symmetry related to the bond alternation due to vibronic mixing effects. 

A DFT Based Parameterization of the Vibronic Mixing between Two Non-degenerate Electronic States and the Application to s2-lone Pairs... 

We discuss here two examples of vibronic effects in polynuclear highly symmetrical transition metal clusters. The existence of degenerate and quasi-degenerate molecular orbitals in their energy spectra results in the Jahn-Teller effect or in the vibronic mixing of different electronic states. We show that both quantum-chemical methods and model approaches can provide valuable information about these vibronic effects. In the case of the hexanuclear rhenium tri-anion, the Jahn-Teller effect is responsible for the experimentally observed tetragonal distortion of the cluster. The vibronic model of mixed-valence compounds allows to explain the nature of a transient in the photo-catalytic reaction of the decatungstate cluster. 

We shall employ the adiabatic approximation that was shown to provide a rather good accuracy in the calculation of the magnetic susceptibility for the vibronic mixed valence systems exhibiting PJT in a wide range of parameters [9]. At the same time this approximation allows us to gain a descriptive comprehension of the physical role of the JT interaction. The full Hamiltonian of the system in the adiabatic approximation can be written as follows ... 

The Jahn-Teller effect within the ground term Eg at each centre n is reduced to vibronic mixing of the one-electron functions i f H and i/ of the orbital doublet eg, Fig. 3, by two symmetrized components of the deformation of octahedra, also belonging to a twofold degenerate manifold Eg, qnE0 and qEe [1], This is described by vibronic operator ... 

Several explanations have been advanced to explain the radical-like reactivity of excited ketones with 71,71 lowest triplets. Vibronic mixing of the two proximate... 

The only studies specifically designed to differentiate between vibronic mixing and equilibration as the source of ,jr -reactivity in ketones with 71,71 lowest triplets have been performed here at Michigan State University. Perhaps the best evidence that equilibration is the major mechanism involves a comparison of intramolecular triplet state hydrogen abstraction by a series of phenyl ketones hi,71 lowest) and an analogous series of p-methoxyphenyl ketones (37i,n lowest). 

A careful study of polymethyl substituted butyrophenones has revealed that their observed rates of triplet state y-hydrogen abstraction are no greater than what would be predicted from estimates of AEy, if equilibration of triplets is the only source of reactivity 63). In fact, meta- and >ara-methyl ketones are less reactive than would have been expected. In these cases, the n,7i and 71,71 triplets are so close that they presumably undergo maximum vibronic mixing, moving the... 

The absolute magnitude of the predicted rates are consistent with known vibronic mixing coefficients. 

Enhancement via Albrecht s 5-term derives from the non-Condon dependence of the electronic transition moment upon the vibrational coordinate. Unlike the A-term, the 6-term arises from the vibronic mixing of two excited states and it is non-zero for scattering due to both totally symmetric and non-totally symmetric fundamentals, provided that they are responsible for vibronic coupling of the states. The latter only takes place for a vibrational fundamental whose irreducible representation is contained in the direct product of the irreducible representations of the two states. Thus, 6-term activity for a totally symmetric mode requires that the latter must vibronically couple two states of the same symmetry. As a consequence of the non-crossing rule this holds only for few excited states which are lying very close together. 

The spectroscopic behavior of a JT system is to a large extent governed by the quenching of electronic operators (Ham effect), which causes a shift of the absorption (or emission) bands and a modification of their shapes. Moreover the vibronic mixing of different electronic states can strongly affect relaxation processes, which also modify spectral band shapes. 

Finally, I wish to recall that the vibronic mixing of thermally accessible electronic levels can affect to a large extent the temperature dependence of magnetic susceptibil-ity62- ) pf Mossbauer spectra as it will be better seen in Sect. 3. 

---