Vibronic intensity mechanism

The lOaj band, as well as many bands built on it, and also the lOa band obtain their intensity by the Flerzberg-Teller vibronic coupling mechanism discussed in Section 7.3.4.2(b). 

E2x E2 A l +A2 +E j, and/Sj x E2 - Ex +E2, the results of Table 12 are easily found. Clearly therefore a polarised spectrum measurement, coupled with data relating to the appropriate band intensities (and their proportionality to the coth (hvj2 kT) function) at various temperatures, would provide considerable insight into the vibronic coupling mechanism for metallocene systems. 

Fig. 17. Vibronic coupling mechanisms (Herzberg-Teller couplings). The purely electronic transition between the excited state I (triplet substate) and the ground state 0 (Sq) is spin and symmetry forbidden, i.e. no intensity is found at the electronic origin I. Two mechanism are proposed. Coupling route (a) is probably more important for vibrations of metal-ligand character, while mechanism (b) preferentially induces satellite intensities by internal ligand vibrations. The electronic state S is a singlet, for which an electronic transition is dipole forbidden to the electronic ground state Sq. On the other hand, the state S , represents a singlet that carries sufficient transition probability. For detailed explanations see the text...

We therefore developed a much simplified, but mathematically exact, version of a shell model which is particularly suitable for the analysis of cross relaxation in high symmetry systems such as the lanthanide elpasolites. Since the vibronic structure in the emission and absorption spectra of these compounds is both intense and broad (relative to the electronic origins), there are many cases where the vibronic structure of one electronic transition in emission overlaps with the vibronic structure of another electronic transition of a chemically identical ion in absorption. The emission of the excited ion may then be partially quenched by energy transfer. Implicit in this formulation is the assumption that the interionic coupling is weak compared with the vibronic coupling this is certainly true for the lanthanide elpasolites where the lanthanide ions are separated by distances of more than 0.7 nm. We refer to this process as cross relaxation by the electric dipole vibronic-electric dipole vibronic (EDVEDV) mechanism. 

When the first term is nonzero the electronic transition is allowed by a particular mechanism, whereas it is forbidden when zero. It contributes mainly zero phonon line intensity when the shift in equilibrium positions of the nuclei between the two states can be ignored, so that (Zfk Xin)t 0 only for the k=n case in Eq. (17). The second and third terms contribute mainly one-phonon sideband vibronic intensity to the transition. (i/q Me i/r ) 2 is given by [68]... 

An attempt to elucidate the physical mechanisms of vibronic transitions and to avoid excessive parametrization has been made in the vibronic intensity calculations of Acevedo et al. [97, 170-173] which have been performed for individual vibronic transitions between CF states, with and without the Judd closure approximation, following the point group symme-... 

T <- Tj spectrum shows a single peak at 235 nm F 0.35) and a shoulder around 310nm (F 0.12). Vibronic mechanisms in the two-photon spectrum of benzene and also toluene, halobenzenes, and aniline have been studied by Goodman and co-workers. Two-photon excitation of benzene crystals at 4.2 K has been recorded in the 200 nm second absorption system. The data suggest that the transition is in which the vibronic intensity is derived from the state in the one photon and E g in the case of two-photon excitation. Spectral solvent effects on toluene have been reported by Macovei. Traverso and Brunet have examined the 5j Sq transition in biphenyl and confirmed the earlier conclusion that this is a forbidden process. 

R /aQy) is the displacement vector during a normal vibrational mode Qy, , and p,- are the position and momentum the ith electron, <0y is the frequency ctf the th normal mode, and , — q is the vertical electronic excitation energy. The electronic wavefunctions are denoted as <1 lor ground and excited states, respectively. The superscript VC indicates that these expressions describe a vibronic coupling mechanism for IR and VCD intensities. The subscripts (00,01) and (01,00) signify that the transition is between the 0 and 1 vibrational levels of the ground electronic state of the molecule. 

Fig. 20. Energy levels and selection rules for static (oor tt) electric-dipole transitions in hexa-coordinated trigonal d -complexes. The forbidden transition into gains some intensity by a vibronic coupling mechanism...

In 1928, Condon treated the intensities of vibronic transitions quantum mechanically. The intensity of a vibronic transition is proportional to the square of the transition moment which is given by (see Equation 2.13)... 

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