Zero-vibrational transition

The emission transition will usually be situated at lower energy than the absorption transition. This phenomenon is known as the Stokes shift. Only the zero-vibrational transition is expected to occur at the same energy in the absorption and emission spectra. The Stokes shift is a direct consequence of the relaxation processes that occur after the optical transitions. It is obvious that the larger Q a Qo is, the larger the Stokes shift will be. If the two parabolas have the same shape and vibrational frequency, it is possible to define a parameter S (the so-called Huang-Rhys parameter) as follows... 

It can be shown that the relative intensity of the zero-vibrational transition ug = 0 Ue = 0) is exp(-S) (5, 7). We can now divide our luminescent centers into three classes, viz.,... 

Figure 4 shows three emission spectra that are representative of the three cases. Characteristic examples of case (a) are the trivalent rare earth ions. The value of S is so small for these ions that the spectra consist in good approximation of the zero-vibrational transitions only. Figure 4a gives as an example the emission spectrum of the Gd " ion in LaBaOe. It consists of one strong electronic line at about 310 nm,... 

A characteristic example of case (b) is the uranyl ion (UO ). The Tie = 0— rig = 2 line dominates in the spectrum (Fig. 4b). The tungstate ion (WC)4 ) is a good example of case (c). The very broad emission spectrum (see Fig. 4c) does not show any vibrational structure at all, the Stokes shift is very large (—16,000 cm" ) and the zero-vibrational transition is not observable, not even at the lowest possible temperatures nor for the highest possible resolving powers. 

The first case to be considered here is the luminescence of complexes with as the central ion. Their spectra consist of zero-vibrational transitions followed by a rich vibrational structure (sec Fig. 3.5). Examples are UOj, octahedral UO ", trigonal prismatic UO and tetrahedral UO. ... 

In the most usual cases, where the lower level is the zero-point level, F(i/ ") = A and the requirement for a Raman vibrational transition becomes... 

For a molecule belonging to the D2h point group deduce whether the following vibrational transitions, all from the zero-point level, are allowed in the infrared spectmm and/or Raman spectmm, stating the direction of the transition moment and/or the component of the polarizability involved ... 

It might be thought that the small number of molecules in a typical supersonic jet or beam would seriously limit the sensitivity of observation of the spectra. Flowever, the severe rotational cooling which may be produced results in a collapsing of the overall intensity of a band into many fewer rotational transitions. Vibrational cooling, which greatly increases the population of the zero-point level, concentrates the intensity in few vibrational transitions, and these two effects tend to compensate for the small number of molecules. 

With its substitution in Eq. (99) it becomes evident from the orthogonality of the Hermite polynomials, that all matrix elements are equal to zero, with the exception of v = v — 1 and vf = u +1. Thus, the selection rule for vibrational transitions (in the harmonic approximation) is An — 1. It is not necessary to evaluate the matrix elements unless there is an interest in calculating the intensities of spectral features resulting from vibrational transitions (see problem 18). It should be evident that transitions such as Av - 3 are forbidden under this more restrictive selection rule, although they are permitted under the symmetry selection rule developed in the previous paragraphs. 

Two different values of the ionization potential / have to be considered2 3,7 (1) the adiabatic Ip, which corresponds to a transition from the zero-vibration level of the ground state of the molecule to that of the ground state of the molecular ion (2) the vertical which corresponds... 

The wave function for the zero vibrational level has a maximum in the centre, indicating the region of maximum probability (Figure 4.2). Therefore, the most probable transition during the act of lighl absorption is that,... 

These discussions provide an explanation for the fact that fluorescence emission is normally observed from the zero vibrational level of the first excited state of a molecule (Kasha s rule). The photochemical behaviour of polyatomic molecules is almost always decided by the chemical properties of their first excited state. Azulenes and substituted azulenes are some important exceptions to this rule observed so far. The fluorescence from azulene originates from S2 state and is the mirror image of S2 S0 transition in absorption. It appears that in this molecule, S1 - S0 absorption energy is lost in a time less than the fluorescence lifetime, whereas certain restrictions are imposed for S2 -> S0 nonradiative transitions. In azulene, the energy gap AE, between S2 and St is large compared with that between S2 and S0. The small value of AE facilitates radiationless conversion from 5, but that from S2 cannot compete with fluorescence emission. Recently, more sensitive measurement techniques such as picosecond flash fluorimetry have led to the observation of S - - S0 fluorescence also. The emission is extremely weak. Higher energy states of some other molecules have been observed to emit very weak fluorescence. The effect is controlled by the relative rate constants of the photophysical processes. 

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]...

Coupling to other vibrational channels is zero and transitions from one vibrational state to another are therefore prohibited. Within the adiabatic approximation the partial photodissociation wavefunctions separate into a translational and an internal part, the latter depending parametrically on R, i.e.,... 

To determine the excitation energy of the lowest electronic level the contributions in the absorption spectrum from transitions to different vibrational modes of the excited state have to be separated. In the deconvolution of the absorption spectra Gaussian line shapes are assumed for the transitions to the different vibrational levels. The analysis leads to the transition wavelength A00 for the excitation from the ground state to the zero vibrational level of the excited state. 

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