Rotational fine structure

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. 

The intensity distribution among the rotational transitions is governed by the population distribution among the rotational levels of the initial electronic or vibronic state of the transition. For absorption, the relative populations at a temperature T are given by the Boltzmann distribution law (Equation 5.15) and intensities show a characteristic rise and fall, along each branch, as J increases. 

If the spectrum is observed in emission it is the rotational populations in the upper state which determine relative intensities. They may or may not be equilibrium Boltzmann populations, depending on the conditions under which the molecule got into the upper state. 

By obtaining values for B in various vibrational states within the ground electronic state (usually from an emission spectrum) or an excited electronic state (usually from an absorption spectrum) the vibration-rotation interaction constant a and, more importantly, B may be obtained, from Equation (7.92), for that electronic state. From B the value of for that state easily follows. 

It is important to realize that electronic spectroscopy provides the fifth method, for heteronuclear diatomic molecules, of obtaining the intemuclear distance in the ground electronic state. The other four arise through the techniques of rotational spectroscopy (microwave, millimetre wave or far-infrared, and Raman) and vibration-rotation spectroscopy (infrared and Raman). In homonuclear diatomics, only the Raman techniques may be used. However, if the molecule is short-lived, as is the case, for example, with CuH and C2, electronic spectroscopy, because of its high sensitivity, is often the only means of determining the ground state intemuclear distance. 

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The distinction between in-plane A symmetry) and out-of-plane (A" symmetry) vibrations resulted from the study of the polarization of the diffusion lines and of the rotational fine structure of the vibration-rotation bands in the infrared spectrum of thiazole vapor. 

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...

As is the case for diatomic molecules, rotational fine structure of electronic spectra of polyatomic molecules is very similar, in principle, to that of their infrared vibrational spectra. For linear, symmetric rotor, spherical rotor and asymmetric rotor molecules the selection mles are the same as those discussed in Sections 6.2.4.1 to 6.2.4.4. The major difference, in practice, is that, as for diatomics, there is likely to be a much larger change of geometry, and therefore of rotational constants, from one electronic state to another than from one vibrational state to another. 

From the ground to an excited electronic state the electron promotion involved is likely to be to a less strongly bonding orbital, leading to an increase in molecular size and a decrease in rotational constants. The effect on the rotational fine structure is to degrade it to low wavenumber to give a strongly asymmetrical structure, unlike the symmetrical structure typical of vibrational transitions. 

Examples of this degradation of bands are shown in Figures 7.44 and 7.45. Figure 7.44(a) shows the rotational fine structure of the Oj] band of the —X Ag system of 1,4-diffuorobenzene, belonging to the >2 point group. The fine structure is in the form of a contour of tens of thousands of unresolved rotational transitions which, nevertheless, shows well-defined features (B is an overlapping weaker band of a similar type). Since Biu = r(T ), as given by Table A.32 in Appendix A, the electronic transition is allowed and... 

Each of the lasing vibrational transitions has associated rotational fine structure, discussed for linear molecules in Section 6.2.4.1. The Sgli transition is — Ig with associated P and R branches, for which AJ = — 1 and +1, respectively, similar to the 3q band of HCN in Figure 6.25. The 3q22 band is, again, with a P and R branch. 

Interatomic distances calculated from the detailed analysis of rotational fine structure of the UV spectrum of pyrazine are in close agreement with those observed in (7) and (8), with the calculated bond lengths for C—C of 1.395, C—N 1.341 and C—H 1.085 A (60DIS(20)4291). Thermochemical data have provided a figure of 75 kJ moP for the delocalization energy of the pyrazine ring (B-67MI21400). 

From the rotational fine-structure of the A levels Hori (16) obtained the value... 

Figure 4.22. The infrared spectrum of gas phase CO shows rotational fine structure, which disappears upon adsorption, as shown by the spectrum of CO adsorbed on an Ir/Si02 catalyst. [J.W. Niemantsverdriet, Spectroscopy in Catalysis, An Introduction (2000), Wiley-VCH, Weinheim.]...

In the liquid, the P and R rotational fine structure becomes broadened Into rotational wings. In addition, the missing Q branch In C0(g) Is observed In CO(4) at about 2140 cm l. Ewlng(24) has postulated that the width of the Q branch In C0(i) Is due to the population of low-lying llbratlonal modes for CO molecules In their... 

As with solution experiments, flash photolysis in the gas phase has produced evidence for the existence of intermediates but no information about their structure. In principle gas phase IR spectra can provide much more information, although the small rotational B value of gaseous carbonyls and low lying vibrational excited states preclude the observation of rotational fine structure. As described in Section II, time-resolved IR experiments in the gas phase do not suffer from problems of solvent absorption, but they do require very fast detection systems. This requirement arises because gas-kinetic reactions in the gas phase are usually one... 

If we consider FTIR instrumentation then the situation is trickier, since the equivalent resolution in nm varies across the spectrum. But even keeping the spectrum in its natural wavenumber units, we again find that, except for rotational fine structure of gases, the natural bandwidth of many (most) absorbance bands is greater than 10 wavenumbers. So again, using that figure shows the typical user how he can expect his own measured spectra to behave. 

Apart from molecular vibrations, also rotational states bear a significant influence on the appearance of vibrational spectra. Similar to electronic transitions that are influenced by the vibrational states of the molecules (e.g. fluorescence, Figure 3-f), vibrational transitions involve the rotational state of a molecule. In the gas phase the rotational states may superimpose a rotational fine structure on the (mid-)IR bands, like the multitude of narrow water vapour absorption bands. In condensed phases, intermolecular interactions blur the rotational states, resulting in band broadening and band shifting effects rather than isolated bands. 

In the electronic transitions in visible and ultraviolet region with liquids or solutions, we do not get vibrational bands along with rotational fine structure, but we get a continuous broad electronic band and hence such curves do not give much valuable information. This is because the vibrational fine structure gets suppressed due to overlapping of vibrational spacings. 

Kratzer and Loomis as well as Haas (1921) also discussed the isotope effect on the rotational energy levels of a diatomic molecule resulting from the isotope effect on the moment of inertia, which for a diatomic molecule, again depends on the reduced mass. They noted that isotope effects should be seen in pure rotational spectra, as well as in vibrational spectra with rotational fine structure, and in electronic spectra with fine structure. They pointed out the lack of experimental data then available for making comparison. 

If we are concerned with the bonding in an isolated molecule, then ideally we should concern ourselves with vapour phase spectra. Unfortunately, only a handful of the species of interest are volatile enough for this to be possible. In any case, vapour phase spectra are complicated by broadening due to unresolved rotational fine structure, and are thus greatly inferior in quality to solution spectra. 

Sharp absorption bands are typically not observed in UV and visible absorption spectra of liquid samples. This is the consequence of the presence of the vibrational and rotational fine structure that become superimposed on the potential energy surfaces of the electronic transitions. Fine structure in UV/vis absorption spectra can be detected for samples in vapor phase or in nonpolar solvents. 

Besides a transition to a continuum level of an excited electronic state, dissociation can occur by another mechanism in electronic absorption spectroscopy. If the potential-energy curve of an excited electronic state A that has a minimum in UA(R) happens to be intersected by the U(R) curve of an unstable excited state B with no minimum in U, then a vibrational level of A whose energy lies near the point of intersection of UA and UB has a substantial probability to make a radiationless transition to state B, which then dissociates. This phenomenon is called predissociation. Predissociation shortens the lifetimes of those vibrational levels of A that are involved, and therefore by the uncertainty principle gives broad vibrational bands with rotational fine structure washed out. 

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