Vibronic overlap

The interpretation of the results was hindered to some extent by the inability to observe more than the gz absorption, except in the Kr matrix, but it was found that although the Fermi contact term, k0, showed some lattice dependence, the main feature of the results was that whilst A ranged from 286 cm-1 in Ne to 668 cm-1 in Kr, the vibronic overlap term varied only between 0.30 and 0.25, thus bearing out the authors predictions concerning the origin of the static distortion, A. 

Table 12.1 Fitting parameters which were obtaind in (41). Differing from (41), the values e+, e and M listed here already contain the vibronic overlap factor.

The difficulties noted above can be avoided by comparing the data presented in Tables 7.6 and 7.7. The nearly invariant Wnr listed in Table 7.6 and the calculated vibronic overlaps reported in Table 7.7 indicate that neither the electronic nor the vibrational factors vary essentially within the group of investigated DAPs. The former can be estimated by means of Equation 7.42, using the data in Tables 7.6 and 7.7. 

The quantity J dr is called the vibrational overlap integral, as it is a measure of the degree to which the two vibrational wave functions overlap. Its square is known as the Franck-Condon factor to which the intensity of the vibronic transition is proportional. In carrying out the integration the requirement that r remain constant during the transition is necessarily taken into account. 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

The assumption of a large crystal-field interaction for Pu5+ spectra makes it necessary to conclude that while certain aspects of earlier free-ion estimates (37) are valid, the "assignment" of free-ion states to observed absorption bands was premature. Much of the structure must be due to crystal-field components of many free-ion groups that overlap in energy or to vibronic satellites similar to those encountered in CS2UCI6 (33). Thus, while the present computations would agree with earlier work in interpreting the levels observed in... 

The intensity of a vibronic transition depends upon the square of the overlap integral of the vibrational wave functions,... 

Nonradiative transfer of excitation energy requires some interaction between donor and acceptor molecules and occurs if the emission spectrum of the donor overlaps the absorption spectrum of the acceptor, so that several vibronic transitions in the donor must have practically the same energy as the corresponding transitions in the acceptor. Such transitions are coupled, i.e., they are in resonance, and that is why the term resonance energy transfer (RET) or electronic energy transfer (EET) are often used. 

It should be noted that the calculated anisotropy may not be applied to fs time-resolved anisotropy measurements because fs time-resolved experiments involve pumping and probing conditions and may involve overlapping between the vibronic structures of several electronic states due to the use of fs laser pulses. Nevertheless, we think the calculated anisotropy using Eq. (2.54) can provide a reference in comparing models. 

We consider a model for the pump-probe stimulated emission measurement in which a pumping laser pulse excites molecules in a ground vibronic manifold g to an excited vibronic manifold 11 and a probing pulse applied to the system after the excitation. The probing laser induces stimulated emission in which transitions from the manifold 11 to the ground-state manifold m take place. We assume that there is no overlap between the two optical processes and that they are separated by a time interval x. On the basis of the perturbative density operator method, we can derive an expression for the time-resolved profiles, which are associated with the imaginary part of the transient linear susceptibility, that is,... 

Radiative transitions may be considered as vertical transitions and may therefore be explained in terms of the Franck-Condon principle. The intensity of any vibrational fine structure associated with such transitions will, therefore, be related to the overlap between the square of the wavefunctions of the vibronic levels of the excited state and ground state. This overlap is maximised for the most probable electronic transition (the most intense band in the fluorescence spectrum). Figure... 

Reinen D, Atanasov M (2004) The Angular Overlap Model and Vibronic Coupling in Treating s-p and d-s Mixing - a DFT Study 107 159-178 Reisfeld R (2003) Rare Earth Ions Their Spectroscopy of Cryptates and Related Complexes in Glasses 106 209-237 Renz F, see Gutlich P (2004) 107 27-76 Reyes M, see Contreras RR (2003) 106 71-79 Ricciardi G, see Rosa A (2004) 112 49-116... 

The most likely electronic transition will occur without changes in the positions of the nuclei (e.g., little change in the distance between atoms) in the molecular entity and its environment. Such a state is known as a Franck-Condon state, and the transition is referred to as a vertical transition. In such transitions, the intensity of the vibronic transition is proportional to the square of the overlap interval between the vibrational wavefunctions of the two states. See Fluorescence Jablonski Diagram Comm, on Photochem. (1988) Pure and Appl. Chem. 60, 1055. 

A possible explanation for this increase in lifetime is a reduction of the nonradiative processes. As pointed out by Robinson (95), these radiationless rates must depend upon the magnitudes of the product of the vibrational overlap integrals between the initial and final states. The substitution of deuterium for hydrogen results in lower vibronic amplitudes, yielding a smaller overlap product. 

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