Franck-Condon Herzberg-Teller

Within this approximation the transition occurs between vibrational states with the highest overlap. Moreover, electric dipole forbidden transitions (i.e. when /tnm(QQ " ) = 0) cannot be described within this approximation. They can be treated however by considering the expansion in Eq. (4.18) to first order, which yields the Franck-Condon-Herzberg-Teller approximation [58, 61]. 

Additionally, various approximations on the transition dipole moment, namely Franck-Condon (FC), Herzberg-Teller (HT), or Franck-Condon Herzberg-Teller (FCHT) can be appfied. From the computational perspective, the state-of-the-art methods rooted into TD-DFT are nowadays the most effective routes to treat medium-to-large molecular systems. Since analytical second... 

Hizhnyakov V and Tehver I 1988 Transform method in resonance Raman scattering with quadratic Franck-Condon and Herzberg-Teller interactions J. Raman Spectrosc. 19 383-8... 

The vibronic theory of the RR effect distinguishes two major intensity enhancement mechanisms that play a dominant role in the RR spectra (i) Franck-Condon (FC) principle and (ii) Herzberg-Teller (FIT) vibronic coupling, which have quite different properties. The FC scattering mechanism involves displacement of the potential minima of the ground and excited electronic states along a vibrational normal... 

For completeness, it is mentioned already here that besides the occurrence of Franck-Condon induced vibrational satellites one also observes Herzberg-Teller (HT) induced satellites in the emission spectrum shown in Fig. 3a. These are mainly found in the emission from the triplet substate I, since the transition between substate I and the ground state 0(So) is strongly forbidden at the electronic origin. One representative HT-satellite is induced by the 528 cm vibration. We come back to this important issue in Sects. 3.1.3 to 3.1.5. The background for this assignment becomes particularly clear from the companion studies with the platinum compound (Sects. 4.2.2 and 4.2.4). 

Fig. 5. Energy level diagram for Pd(2-thpy)2 dissolved in n-octane. The Tj state at 18,418 cm is zero-field split on the order of 0.2 cm. The emission decay times refer to the individual triplet suhstates I, II, and III, respectively, at T = 1.3 K. (Compare Fig. 6.) These suhstates are radiatively deactivated as purely electronic transitions, as well as by Franck-Condon (FC) and Herzberg-Teller (HT) vibrational activity, respectively. This leads the different vibrational satellites. (Compare also Sects. 4.2.2 and 4.2.3.) The lifetime of the S, state is determined from the homogeneous linewidth of the spectrally resolved Sq —> S, electronic origin. (Sect. 3.2) The electronic state at 24.7 x 10 cm is not yet assigned...

The vibrational satellite structures that occur in the emission and excitation spectra (e.g.see Figs. 13 to 15) result from different vibrational activities, namely from vibronic or Herzberg-Teller activity, as introduced in this section, and from Franck-Condon activity, as discussed in the next section. 

Characterization of the radiative deactivation processes. HT Herzberg-Teller active vibrational mode FC Franck-Condon active mode. 

Fig. 24. Triplet substates I, II, and III of Pt(2-thpy)2 dissolved in an n-octane matrix, T=1.3 K. The vibrational levels of the excited states are given as examples. They refer to the substates II and III, respectively. By use of the new method of time-resolved excitation spectroscopy (Sect. 4.2.9), it is demonstrated that an inter-substate crossing does not occur via excited vibrational states, but it takes place after a fast relaxation to the zero-point vibrational level of the respective triplet substate by relatively slow processes of spin-lattice relaxation [60]. The rates kj[j [24,60,62,64,65] and k%j [65] are determined in the references given (see also text). The intra-state relaxation rate of k ,- = 10 s has been estimated for Pd(2-thpy)2 (Sect. 3.1.2.5). Several vibrational levels of the ground state are also given. PC and HT, respectively, refer to Franck-Condon and Herzberg-Teller activity in the respective radiative deactivations. (Compare Sect. 4.2.4)...

Fig. 26. Energy level diagram for the triplet sublevels of (a) perprotonated, (b) partially deu-terated, and (c) perdeuterated Pt(2-thpy)2 dissolved in an n-octane matrix (Shpol skii matrix). Emission decay times and spin-lattice relaxation times are given for T= 1.3 K. Several vibrational satellites are specified, HT = Herzberg-Teller active vibration, FC = Franck-Condon active vibration. The emission spectrum of the partially deuterated compound (b) exhibits vibrational satellites of the two different ligands. (Compare Fig. 27b.) The data given for Pt(2-thpy-hg)(2-thpy-d6) (b) refer to the lower lying site A. (Compare Ref. [23])...

Vibrational Satellites Induced by Herzberg-Teller and Franck-Condon Activities... 

In centrosymmetric molecules, HRS gains intensity via Herzberg-Teller term (the first vibronic B-term), indicating that IR-active modes and silent modes are enhanced. In the case of non-centrosymmetric molecules, however, Franck-Condon mechanism (A-term) dominantly contributes to the enhancement. Moreover, the mutual exclusive rules between HRS and RS are broken, and hence, some of RS-active modes selectively appear in the spectra. In the case of plasmonic enhancement, the spectral appearance is more sensitive to molecular orientations at the metal surface because of the surface selection rules [25]. 

Excitation into electronic absorption results in intensity enhancement of normal modes of vibration which are coupled to electronic transition by either Franck-Condon or Herzberg-Teller coupling allows for study of chromophoric active sites in biological molecules at low concentrations allows assignment of CT (and in some cases LF) transitions based on nature of excited state distortion can provide information on metal-ligand bonding as described above for vibrational spectroscopy... 

Figure 3.8 Vibronic two-photon absorption spectra of Sila-1f and 2 2a-2f of 4-dimethylamino-4 -Me-trans-stilbene calculated with B3LYP at the HF geomet7. Franck-Condon contribution, Herzberg-Teller contribution, and total spectra are shown for lifetime broadening of 0.10 eV (left panels) and 0.01 eV (right panels), respectively. The dashed line corresponds to the vertical transition [18]. (Reproduced with permission.)...

In principle, coupling terms of this type also arise in the Herzberg-Teller scheme (Section IV,A), but are of little importance there, since they give intensity to (weak) bands that also derive intensity via Franck-Condon effects. However, if two electronic states are close in energy, pseudo-Renner-Teller coupling can shift levels and redistribute intensities in a way comparable to the real Renner-Teller effect. 

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