Transitions vibronic

The synnnetry selection rules discussed above tell us whether a particular vibronic transition is allowed or forbidden, but they give no mfonnation about the intensity of allowed bands. That is detennined by equation (Bl.1.9) for absorption or (Bl.1.13) for emission. That usually means by the Franck-Condon principle if only the zero-order tenn in equation (B 1.1.7) is needed. So we take note of some general principles for Franck-Condon factors (FCFs). 

Condensed phase vibrational or vibronic lineshapes (vibronic transitions create vibrational excitations of electronic excited states) rarely provide infonnation about VER (see example C3.5.6.4). Experimental measurements of VER need much more than just the vibrational spectmm. The earliest VER measurements in condensed phases were ultrasonic attenuation studies of liquids [15], which provided an overall relaxation time for slowly (>10 ns) relaxing small molecule liquids. 

The easiest method for creating many vibrational excitations is to use convenient pulsed visible or near-UV lasers to pump electronic transitions of molecules which undergo fast nonradiative processes such as internal conversion (e.g. porjDhyrin [64, 65] or near-IR dyes [66, 62, 68 and 62]), photoisomerization (e.g. stilbene [12] or photodissociation (e.g. Hgl2 [8]). Creating a specific vibrational excitation D in a controlled way requires more finesse. The easiest method is to use visible or near-UV pulses to resonantly pump a vibronic transition (e.g. 

Vibronic relaxation of XeF in solid Ar at 25 K was studied by pumping vibronic transitions with a subpicosecond UV pulse, and detecting frequency-resolved emission with a fast optical gate [25]. XeF has two sites in Ar, one... 

Vibrational transitions accompanying an electronic transition are referred to as vibronic transitions. These vibronic transitions, with their accompanying rotational or, strictly, rovibronic transitions, give rise to bands in the spectrum, and the set of bands associated with a single electronic transition is called an electronic band system. This terminology is usually adhered to in high-resolution electronic spectroscopy but, in low-resolution work, particularly in the liquid phase, vibrational structure may not be resolved and the whole band system is often referred to as an electronic band. 

Vibronic transitions may be divided conveniently into progressions and sequences. A progression, as Figure 7.18 shows, involves a series of vibronic transitions with a common... 

Quite apart from the necessity for Franck-Condon intensities of vibronic transitions to be appreciable, it is essential for the initial state of a transition to be sufficiently highly populated for a transition to be observed. Under equilibrium conditions the population 1, of any v" level is related to that of the u" = 0 level by... 

The general symbolism for indicating a vibronic transition between an upper and lower level with vibrational quantum numbers v and v", respectively, is i/ — v", consistent with the general spectroscopic convention. Thus the electronic transition is labelled 0-0. 

In 1925, before the development of the Schrodinger equation, Franck put forward qualitative arguments to explain the various types of intensity distributions found in vibronic transitions. His conclusions were based on an appreciation of the fact that an electronic transition in a molecule takes place much more rapidly than a vibrational transition so that, in a vibronic transition, the nuclei have very nearly the same position and velocity before and after the transition. 

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)... 

The quantity J dr is called the vibrational overlap integral, as it is a measure of the degree to which the two vibrational wave functions overlap. Its square is known as the Franck-Condon factor to which the intensity of the vibronic transition is proportional. In carrying out the integration the requirement that r remain constant during the transition is necessarily taken into account. 

The illustration of various types of vibronic transitions in Figure 7.18 suggests that we can use the method of combination differences to obtain the separations of vibrational levels from observed transition wavenumbers. This method was introduced in Section 6.1.4.1 and was applied to obtaining rotational constants for two combining vibrational states. The method works on the simple principle that, if two transitions have an upper level in common, their wavenumber difference is a function of lower state parameters only, and vice versa if they have a lower level in common. 

In using the combination difference method to obtain vibrational parameters, cOg, etc., for two electronic states between which vibronic transitions are observed, the first step is to organize all the vibronic transition wavenumbers into a Deslandres table. An example is shown in Table 7.7 for the system of carbon monoxide. The electronic... 

For electronic or vibronic transitions there is a set of accompanying rotational transitions between the stacks of rotational levels associated with the upper and lower electronic or vibronic states, in a rather similar way to infrared vibrational transitions (Section 6.1.4.1). The main differences are caused by there being a wider range of electronic or vibronic transitions they are not confined to 2" — 2" types and the upper and lower states may not be singlet states nor need their multiplicities to be the same. These possibilities result in a variety of types of rotational fine structure, but we shall confine ourselves to 2" — 2" and — types of transitions only. 

Figure 7.25 Rotational fine structure of a electronic or vibronic transition in a...

Figure 7.28 Rotational fine structure of a 77 — electronic or vibronic transition in a diatomic molecule for which > r". The g and u subscripts and s and a labels apply only to a homonuclear molecule...

Flowever, transition metal complexes do absorb in the visible region, giving them a characteristic colour. Flow can this happen if the transitions are forbidden The answer is that interaction may occur between the motion of the electrons and vibrational motions so that some vibronic transitions are allowed (see Section 7.3.4.2b). 

If vibrations are excited in either the lower or the upper electronic state, or both, the vibronic transition moment corresponding to the electronic transition moment Rg in Equation (7.115), is given by... 

As for diatomic molecules (Section 7.2.5.2) fhe vibrational (vibronic) transitions accompanying an electronic transition fall into the general categories of progressions and sequences, as illustrated in Figure 7.18. The main differences in a polyatomic molecule are that there are 3A — 6 (or 3A — 5 for a linear molecule) vibrations - not just one - and that some of these lower the symmetry of the molecule as they are non-totally symmetric. 

In electronic spectroscopy of polyatomic molecules the system used for labelling vibronic transitions employs N, to indicate a transition in which vibration N is excited with v" quanta in the lower state and v quanta in the upper state. The pure electronic transition is labelled Og. The system is very similar to the rather less often used system for pure vibrational transitions described in Section 6.2.3.1. 

The vibronic transition Xj, together with X in which the same 2 vibration is excited only in the lower state, are illustrated in Figure 7.43. Both vibronic transitions are allowed and are... 

Figure 7.43 Some allowed electronic and vibronic transitions in a C2 molecule...

The answer, very often, is that they do not obtain any intensity. Many such vibronic transitions, involving non-totally symmetric vibrations but which are allowed by symmetry, can be devised in many electronic band systems but, in practice, few have sufficient intensity to be observed. For those that do have sufficient intensity the explanation first put forward as to how it is derived was due to Herzberg and Teller. 

The Franck-Condon approximation (see Section 7.2.5.3) assumes that an electronic transition is very rapid compared with the motion of the nuclei. One important result is that the transition moment for a vibronic transition is given by... 

The first term on the right-hand side is the same as in Equation (7.128). Herzberg and Teller suggested that the second term, in particular (dRg/dQj), may be non-zero for certain non-totally symmetric vibrations. As the intensity is proportional to Rgy this term is the source of intensity of such vibronic transitions. 

Examples of vibronic transitions involving non-totally symmetric vibrations are in the system of chlorobenzene, a C2 molecule. One 2 vibration V29, with a wavenumber of 615 cm in the X state and 523 cm in the A state, is active in 29q and 29j bands similar to the case shown in Figure 7.43. There are 10 2 vibrations in chlorobenzene but the others are much less strongly active. The reason is that (9J g/9029)eq is much greater than the corresponding terms for all the other 2 vibrations. 

Although we have considered cases where (9/ g/90,)gq in Equation (7.131) may be quite large for a non-totally symmetric vibration, a few cases are known where (9/ g/90,)gq is appreciable for totally symmetric vibrations. In such cases the second term on the right-hand side of Equation (7.131) provides an additional source of intensity forAj orX vibronic transitions when Vx is totally symmetric. 

Nevertheless, 1,4-difluorobenzene has a rich two-photon fluorescence excitation spectrum, shown in Figure 9.29. The position of the forbidden Og (labelled 0-0) band is shown. All the vibronic transitions observed in the band system are induced by non-totally symmetric vibrations, rather like the one-photon case of benzene discussed in Section 7.3.4.2(b). The two-photon transition moment may become non-zero when certain vibrations are excited. 

Substitution of Eq. (6.3) into Eq. (6.2) leads to the following expression for the vibronic transition moment... 

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