Franck-Condon active vibrational modes

Long progressions of feature states in the two Franck-Condon active vibrational modes (CC stretch and /rani-bend) contain information about wavepacket dynamics in a two dimensional configuration space. Each feature state actually corresponds to a polyad, which is specified by three approximately conserved vibrational quantum numbers (the polyad quantum numbers nslretch, "resonance, and /total, [ r, res,fl)> and every symmetry accessible polyad is initially illuminated by exactly one a priori known Franck-Condon bright state. 

This means that the total emission intensity depends only on the purely electronic transition dipole moment. Thus, the electronic allowedness represents the source of intensity which is distributed according to the Franck-Condon factor to the different vibrational satelHtes. With respect to the symmetry of the Franck-Condon active vibrations, it is remarked that this factor can only be nonzero for totally symmetric modes (if it is referred to fundamentals), since the vibrational ground state n(v = 0) is totally symmetric (e.g.see [154,p. 113]). 

As is ISC, IC is very slow for electronic states with similarly shaped potential energy surfaces. When the potential surfaces have very different shapes, there will be a small number of vibrational doorway states that are especially effective in coupling to the bright state. Conical intersections are a special class of potential surfaces of very different shapes. But even when potential surfaces have very different shapes, many normal coordinate displacements and the associated vibrational normal modes will have nearly identical forms on both surfaces. These normal modes are Franck-Condon inactive and do not contribute to IC. The normal coordinate displacements that express the differences in shapes of the potential surfaces are embodied in vibrational normal modes that are Franck-Condon active. These modes are called promoting modes because, when such a mode on one potential surface is plucked from an eigenstate on the other surface, intramolecular dynamics is promoted or initiated. 

The polyad model for acetylene is an example of a hybrid scheme, combining ball-and-spring motion in a two-dimensional configuration space [the two Franck-Condon active modes, the C-C stretch (Q2) and the tram-bend (Q4)] with abstract motion in a state space defined by the three approximate constants of motion (the polyad quantum numbers). This state space is four dimensional the three polyad quantum numbers reduce the accessible dimensionality of state space from the seven internal vibrational degrees of freedom of a linear four-atom molecule to 7 - 3 = 4. 

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

For completeness, it is also mentioned that pressure-induced shifts of several vibrational satellites have been determined. These measurements were carried out at T = 5 K and one could monitor the more intense vibrational satellites that correspond to Franck-Condon active modes up to p = 14 kbar for Pt(2-thpy)2 dissolved in n-decane. In this matrix, some of the vibrational modes are found at slightly different energies. Here, we only want to give the values of pressure-induced shifts (blue shifts) that have been observed (error 0.1 cm Vkbar) 383 cm (shift Av/Ap = -I- 0.85 cm Vkbar), 457 cm ( 0.0), 718 cm (-1- 0.25), 1400 cm (-1- 0.6), and 1489 cm (-1- 0.75) [63]. (With respect to further investigations under high pressure application compare the recent review by K. Bray [150].)... 

It is important that, according to Fig. 25, the information concerning the correspondence of high frequency vibrations of the deuterated ligand relative to those of the protonated figand is available. A similar correlation has also been carried out for those vibrational modes that are Franck-Condon active with respect to the emission from state II, for details see Ref. [23]. 

Dominance of Radiative Deactivation by Franck-Condon Active Modes. The observed vibrational satellites can be induced by different mechanisms. In particular, they may result from Franck-Condon (FC) and Herzberg-Teller (HT)... 

Herzberg-Teller Versus Franck-Condon Activity in [Ru(bpy)3]. The vibrational satellite structure resolved in the emission from state 11) is clearly different to the emission structure connceted with state II). This is demonstrated in Fig. 12a,b (cf. also the time-resolved spectra shown in Fig. 16). Several vibrational satellites occur only in the spectrum from state 11) and are not resolved in the state III) emission. Prominent modes with this behavior are found, for example, at 296, 349, 370, 439, 477, 1015, 1569 cm" (see Fig. 12a Table 4). Most of these modes are IR active [212]. On the other hand, a number of dominant modes observed in the emission from state II) (Fig. 12b) are also seen in the state (I) emission (e.g., 158,667,767,1029,1174,1275,1325,1495 cm" see also Table 4). Nearly aU of these vibrations exhibit a Raman activity with strong resonance enhancements, when exciting into the MLCT states [106,211]. 

Another conventional simplification is replacing the whole vibration spectrum by a single harmonic vibration with an effective frequency co. In doing so one has to leave the reversibility problem out of consideration. It is again the model of an active oscillator mentioned in section 2.2 and, in fact, it is friction in the active mode that renders the transition irreversible. Such an approach leads to the well known Kubo-Toyozawa problem [Kubo and Toyozava 1955], in which the Franck-Condon factor FC depends on two parameters, the order of multiphonon process N and the coupling parameter S... 

With temperature increase to 4.2 K, a completely different situation develops. Now, the emission stems dominantly from the substates n/ni, which carry much higher allowedness with respect to the purely electronic transition to the ground state at 21,461 cm As consequence, the vibrational modes, which are active in the emission process, are different from those found in the emission of substate I at T=1.2 K. In particular, for several fundamentals such as the 1,056 and 1,497 cm-1 modes, one can also observe weak second members of progressions (not displayed in Fig. 6). Therefore, it can be concluded that these modes represent totally symmetric Franck-Condon (FC) active modes [63, 90, 94-97], The assignment concerning FC activity is in accordance with the observation that many of the FC modes (e.g., 530, 743,1,056 cm-1) are also built upon the false origins and occur as combinations in the 1.2 K spectrum. Using the equation (see for example [49, 63, 95-98])... 

Fig. 7 c. The detection is carried out on a vibrational satellite that belongs to the emission from the triplet substates II and III. The 447 cm mode represents a Franck-Condon (FC) active vibration.[58] (Compare Sect. 3.1.4.)... 

Time-resolved emission spectra (Sect. 3.1.4, Fig. 8) show that the triplet sublevels I and III exhibit very different emission spectra with respect to their vibrational satellite structures. The long-lived state I is mainly vibronically (Herz-berg-Teller, HT) deactivated, while the emission from state III is dominated by vibrational satellites due to Franck-Condon (FC) activities, whereby both types of vibrational modes exhibit different frequencies. This behavior makes it attractive to measure a PMDR spectrum. 

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