Vibronic perturbations

In addition, it can be shown that second-order vibronic perturbation will make possible some intersystem crossing to the 3B3u(n, tt ) state. However, this second-order perturbation should be much less important than the first-order spin-orbit perturbation.(19) This will produce the unequal population of the spin states shown in Figure 6.1. In the absence of sir the ratios of population densities n are given by the following equations ... 

Fig. 29. Group-theoretical predictions of the polarizations of the vibronic transitions, allowed to second order, from the individual zero-field levels of the lowest triplet state of 2,3-dichIoro-quinoxaline to vibrational levels of the ground electronic state. Solid line transitions gain intensity by spin-orbit mixing between states which differ in the electronic type of one electron e.g., S n and T . The dashed line transitions require the mixing to occur between states of the same electronic type (e.g., S and T n ) and is expected to be weaker. The dash-dotted transition could involve the favorable mixing between states that differ in the electronic type of one electron, but a spin-vibronic perturbation is needed. (From Tinti and El-Sayed, Ref. ))...

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... 

Totally Symmetric Vibronic Perturbations and the Phenanthrene 3400A Spectrum. 

Taking into account the relationship of these spectra with strong bands /[Pg.183]

As was mentioned previously, two computational studies of vibronic effects in chiral trigonal systems have been reported (18, 28). Both of these studies were addressed to the general problem of vibronic perturbations on the chiroptical spectra of trigonal metal complexes. However, the calculations reported in... 

The validity of the direct substitution for Ay into the first-order expression for the CD of electric dipole allowed transitions is verified readily using, for example, a simple vibronic coupling model. The procedure is analogous to that discussed elsewhere for vibronic contributions to DICD (dispersion (dispersion-induced CD)(14). As Ay is, in itself, first-order in the vibronic perturbation, the CD strength of the d-d trans- ... 

In the standard treatment of non-radiative relaxation [95] the rate depends on the presence of a promoting mode which links the ground and excited states through the vibronic perturbation, and an accepting mode, many quanta of... 

The symmetry of the first excited state requires the promoting mode to be of nt symmetry. There are no internal modes of the uranyl ion with this symmetry so the relaxation relies on the vibronic perturbation of the equatorial ligand modes with the analogous symmetry. As we have seen, even the static influence of these equatorial ligands is small, so the promoting modes are also inefficient. 

The linear dichroism method utilizing naphthalene molecules oriented in stretched polyethylene) and polypropylene) matrices at 77 and 296 suggests that the 245—275 nm absorption of BSu polarization is due to a Bu vibronic perturbation of the 1B2u state.150 Results also showed that the orientation in polyethylene) and polypropylene) was different. Absorption spectra of crystal-... 

In addition, it can be shown that second-order vibronic perturbation will make possible some intersystem crossing to the n ) state. However,... 

Zhang et have published a quantum-mechanical treatment of absorption line shapes in bridged, mixed valent dimers. This treatment allows vibronic perturbations to mix the electronic potential-energy surfaces in complexes in which the exchanging electron is completely or partially delocalized. When this three-center treatment is applied to the Creutz-Taube ion, it is consistent with complete delocalization of the odd electron and with very little mixing of the three-center electronic states in this complex. 

To compute the intensity of the vibronic transition, S->-N, all we need do is evaluate the vibronic perturbation AVgj, it is assumed that we have experimental or theoretical knowledge of the energies AE j, hv S —> N), and hv TN) and the electronically allowed oscillator strength f TN). [Experimentally, the latter may be obtained by the evaluation of the area under the absorption curve when its ordinate is the extinction coefficient. e v), and its abscissa is the frequency of absorption, r(cm ), according to the formula / = 4.33 Theoretically, it... 

The remaining vibronic perturbation terms are readily obtained from Eqs. (11) and (12) upon application of a counterclockwise rotation of 120° about the (111) direction. Such a rotation replaces by z, y by x, z by y, and correspondingly, a-type displacements by 6-type, -type by c-type, and c-type by a-type thus, it replaces by... 

In the computation of the oscillator strengths in reference 13a, a common vibronic perturbation denominator, — was utilized for both the and e, orbitals, for reasons of simplicity. Also, the Rydberg constant R entered the final formulas as an abbreviation for the quantity... 

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