The Vibron Model

Iachello, F., Manini, N., and Oss, S. (1992), Quasi-linear Four-Atomic Molecules in the Vibron Model, 7. Mol. Spectrosc. 156, 190. 

Iachello, F., Oss, S., and Viola, L. (1993a), Vibrational Analysis of Monofluoroacetylene (HCCF) in the Vibron Model, Mol. Phys. 78, 545. 

Leviatan, A. (1989), Point Groups in the Vibron Model, J. Chem. Phys. 91,1706. 

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. 

Calculations of the level spectra of Ra isotopes using the Vibron model [7] were performed [18]. In these calculations only one parameter was varied between the different isotopes of radium and the results are shown in Fig. 6. The good fits obtained suggest that the cluster model can reproduce the available data of heavy nuclei. 

I would like to acknowledge discussions with D.A. Bromley, F. Iachello and J.F. Shriner, and. the cooperation of M. Ruscev, J.F. Ennis and P.D. Cottle, who worked on °0, °Ra and °Ra respectively, and of H.J. Daley, who worked on the Vibron model code. I also wish to thank R. Bonito and 5. Sicignano for preparation of the camera-ready manuscript. This work was supported in part by U.S. Department of Energy Contract DE-AC02-76ER03074. 

In accord with an approach originally outlined by Jortner and coworkers,41 42 the influence of changing AG° upon the 180 KIE has been modeled using a saddle point approximation.43 At this stage, the experimental variations in 180 KIEs for reactions of O2 and O2" are yet to be determined. The vibronic model of Hammes-Schiffer, which has been used to model proton-coupled electron transfer in accord with a Bom-Oppenheimer separation of timescales, may also be applicable here.44 The objective is to account for the change in 0—0 vibrational frequency together with potential contributions from overlap of vibrationally excited states. The overlap factors involving these states are expected to become more important as AG° deviates from 0 kcal mol 1,39... 

The importance of the vibron model lies in the fact that it is the doorway state of the optical absorption. (The two-particle states have no oscillator strength, since we cannot create vibrations in the ground state.) Indeed, the creation of vibrations is subsequent to an electronic excitation of a molecule, in the approximation where the absorbing dipole is the sum of molecular dipoles (with the appropriate phase), which is the approximation of weak intermolecular forces. 

The positions of the vibronic line, reported in Section II.B.3.a above, allow us to situate the 0-0 center of gravity at Egg = 25279 cm- which is 40 cm-1 below the a component the 392 0-1 vibron provides the same value, Egg 25 280 cm 1. This remarkable coincidence reinforces our confidence in the vibron model of Section II.B. 1. b. 

At low temperatures, narrower bands with better resolution are expected, and the vibronic model predicts lower intensities as well. The polarized spectra at liquid helium temperatures confirm these predictions. Thus, shoulders at 24,000 cm"1 and in the region of 17,000-19,000 cm"1... 

One remarkable consequence of the concept introduced is that in the case of strong vibronic interaction (Equation (2b)), the off-diagonal vibronic energy JSF1 is correlated with the chemical hardness r] of the distorted complex or molecule (Equation (4)). This is an observable quantity thus, the vibronic model is directly linked to the experiment.5... 

The vibronic model provides precise information about the distortion mechanisms and pathways, and explains why certain complexes remain with the high-symmetry parent geometry while others undergo deformation. 

Dynamical Symmetries for Molecular Spectroscopy The Vibron Model... 

To reiterate, we prefer to describe the one-dimensional model first because of its mathematical simplicity in comparison to the three-dimensional model. From a strictly historical point of view, the situation is slightly more involved. The vibron model was officially introduced in 1981 by lachello [26]. In his work one can find the fundamental idea of the dynamical symmetry, based on U(4), for realizing an algebraic version of the three-dimensional Hamiltonian operator of a single diatomic molecule. After this work, many other realizations followed (see specific... 

The theoretical basis of the inelastic scattering, or Raman effect, as it is known nowadays, can be understood involving physical approaches the classical, where the contributions of the elastic and the inelastic effects can be seen clearly, and the quantum approach, where it seems very clear that the effect can be explained on the basis of a mixture of electronic and vibrational states of the matter, giving rise to the vibronic model to explain the physical vision. 

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