Vibronic lines

Table I. Vibrational structure in the spectra of Cs2NaYCl, Bi3 + at 4.2 K (after Ref. [7]). All data in cm . For 0-0 lines the actual spectral position is given, for vibronic lines the position relative to the corresponding 0-0 line...

Fig. 13. Emission spectra of Ba5(P04)3Cl Mn5 + and Ca2VC>4Cl Mn5 + at 8 K. The zero-phonon transition is the dominating line on the right-hand side. The vibronic lines are assigned in terms of the Mn-O bending (5) and stretching (v) vibrations. Reproduced with permission from Ref. [45]...

There are experimental disadvantages that detract from the advantages just listed. The extinction coefficients may be so low that lines are obscured even by remote tails from spin-allowed transitions. The transition energies may span a wide range, requiring UV-visible, near-IR, and mid-IR instrumentation. Electronic lines may also be accompanied by many vibrational satellites whose intensities are high enough to make the distinction between electronic and vibronic lines very difficult. 

Among the problems in applying these techniques to determine geometry or AOM parameter values, or both, is that it is quite often difficult to identify the sharp electronic lines in the spectrum. There are several factors at work. Vibronic lines associated with one sharp electronic line can often mask other electronic lines. When the metal is at a site that is nearly centrosymmetric, the electronic origins can be extremely weak. 

Another possible means of distinguishing electronic from vibronic lines is two-photon spectroscopy. The relevant matrix element for a single beam two-photon transition is... 

In the calculations reported below, the MCTDH method has been employed for all calculations involving more than a single 2/i electronic state, i.e., involving PJT interactions. As a drawback, vibronic line spectra are not directly obtained from this (as with any wave-packet propagation) method. The spectral envelope is, however, easily obtained as a Fourier transform according to Ref. [26] ... 

With increasing resolution, vibronic line spectra can at least be approximately mimicked by the calculations. Finally, also electronic populations are directly extracted from the time-dependent wave-packet [27]. 

The positions of the vibronic line, reported in Section II.B.3.a above, allow us to situate the 0-0 center of gravity at Egg = 25279 cm- which is 40 cm-1 below the a component the 392 0-1 vibron provides the same value, Egg 25 280 cm 1. This remarkable coincidence reinforces our confidence in the vibron model of Section II.B. 1. b. 

Figure 12-2 shows data we obtained for three isolated GC base pair structures. Row A shows results for the Watson-Crick (WC) structure, while rows B and C represent the second and third lowest energy structures, respectively, which are not WC. The second column shows the IR-UV double resonance data, compared with the ab initio calculations of the vibrational frequencies. These data allow us to assign the structures. The third column shows the UV excitation spectra, measured by resonant two-photon ionization (R2PI). The UV spectrum is broad for the WC structure (A) and exhibits sharp vibronic lines for the other structures. 

Fig. 34. Emission spectrum of LaFa Gd at 300 K under X-ray excitation. Va and v, are the anti-Stokes and Stokes vibronic lines.

Let us now look somewhat more closely at the theory. The intensity of vibronic lines in the f-f spectra of rare earth ions is a complicated problem. Through the recent years the following approaches were made. 

A comparable situation in a completely different system is the emission spectrum of [Gd C 2.2.1] (211). In addition to vibronic lines related to the vibrations of the cryptand, there are vibronic lines due to the presence of H2O. This shows that the cage-like ligand does not shield completely from the hydrate water molecules, but that the molecules participate in the Gd coordination. This has no consequences for... 

To reproduce the inherent broadening of the experimental vibronic spectrum, the stick vibronic lines obtained from the matrix diagonalization calculations are usually convoluted [7] with a Lorentzian line shape function... 

Figure 13 shows the dispersed fluorescence spectra for laser excitation directly into the different vibronic lines labelled a-h in Fig. 12. Under the experimental conditions there is no relaxation from these excited vibronic levels within the 20 ns fluorescence lifetime. Figure 12 thus contains the A —> E transitions from the lowest vibrational level of the ground electronic state, and Fig. 13 contains the A E transitions for a number of initial vibronic E levels to the numerous vibrational levels of the ground electronic state.

Features associated with 02 that have been assigned to coupling with are also magnetic-dipole vibronically allowed transitions. The vibronic lines show a progression in the Vi totally symmetric mode. The frequency of this mode amounts to 708 cm" for the features associated with the 552.8 nm electric origin 01, and 713 cm" for the features associated with 02. The repetition frequency of the vibronic features in the excitation spectrum associated with 01 amounts to 653 cm". ... 

Because of the low relative transition probability of the A l -> Aj transition only one electronic origin has been observed in the excitation spectrum of the (UOfi Vp) centre. In the excitation spectrum of the (UOg Vp) emission otdy vibronic lines involving the mode have clearly been observed. Vibronic features due to coupling with other vibrational modes are weak. 

A common feature of rare-earth and actinide spectra is the appearance of vibronic companions to the lines that represent purely electronic transitions. In solutions, vapors, and melts, these two types of lines may become blended, and separate intensity measurements become impossible. For ions at sites possessing a center of inversion, all the intensity resides in the vibronic lines. It is clear that any analysis of hypersensitivity should include the vibronic components. 

NO L 241 0. The fact that twelve oxygen ions are packed around the neodymium ion makes the ion-to-ligand separation unusually large. A glance at the absorption spectrum (18) reveals that most sharp electronic lines do not appear to have noticeable vibronic components the only case where well-defined vibronic lines appear is in group which corresponds to precisely the... 

Fig. 12. Upper part Schematic excitation spectrum of vibronic lines relative to the origin at 16,331 cm . Lower part homogeneous width of the same lines from hole-burning measurements. (After Ref. 64.)...

Fie- 3.23. The emission speetrum of Ba2ZnWOft U " at 4.2 K. The zero-phonon line is indicated by O, the vibronic lines are indicated by the octahedral vibrational modes with which the coupling with the electronic transition takes place... 

Fig. 3.24. The Sp-Znoa donor-accepior pair emission in GaP at 1.6 K. At the bottom R indicates he donor-acceptor distance of the relevant emitting pair. The lines are indicated by their shell number (shell I means nearest-neighbour pairs, etc.). On the right-hand side we see the zero-phonon lines of the individual lines on the left-hand side we sec mainly vibronic lines (in the semiconductor field often called replicas) due to coupling with host-laiiicc modes. Modifted from A.T. Vink, thesis, Technical University Eindhoven, 1974...

Since the spectroscopy of this phosphor is incorrectly described in the book on lamp phosphors [2], we add here, also as an illustration of the theory, a few comments on the spectroscopy. In view of its electron configuration (d ), the Mn ion will be octahedrally coordinated. The emission lines are tabulated in Table 6.3. There is a zero-phonon transition (Sect. 2.1) which at low temperatures is followed by vibronic lines due to coupling with the asymmetric Mn -0 deformation and stretching modes, 1/4 and 1/3, respectively. These uneven modes relax the parity selection rule. At room temperature there occur also anti-Stokes vibronics (Pigs. 6.21 and 6.22). The vibrational modes in the excited state and ground state are equal within the experimental accuracy as is to be expected for the narrow A2 transition [25,26]. The intensity ratio of the Stokes and anti-Stokes vibronic lines agrees with the Bose-Einstein distribution [26]. 

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