Infrared rotational transitions

Figure 6.7 Rotational transitions accompanying a vibrational transition in (a) an infrared spectrum and (b) a Raman spectrum of a diatomic molecule...

Raman scattering is normally of such very low intensity that gas phase Raman spectroscopy is one of the more difficult techniques. This is particularly the case for vibration-rotation Raman spectroscopy since scattering involving vibrational transitions is much weaker than that involving rotational transitions, which were described in Sections 5.3.3 and 5.3.5. For this reason we shall consider here only the more easily studied infrared vibration-rotation spectroscopy which must also be investigated in the gas phase (or in a supersonic jet, see Section 9.3.8). 

Figure 6.24 Rotational transitions accompanying a infrared vibrational transition in a...

This general behaviour is characteristic of type A, B and C bands and is further illustrated in Figure 6.34. This shows part of the infrared spectrum of fluorobenzene, a prolate asymmetric rotor. The bands at about 1156 cm, 1067 cm and 893 cm are type A, B and C bands, respectively. They show less resolved rotational stmcture than those of ethylene. The reason for this is that the molecule is much larger, resulting in far greater congestion of rotational transitions. Nevertheless, it is clear that observation of such rotational contours, and the consequent identification of the direction of the vibrational transition moment, is very useful in fhe assignmenf of vibrational modes. 

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 range of photon energies (160 to 0.12 kJ/mol (38-0.03 kcal/mol)) within the infrared region corresponds to the energies of vibrational and rotational transitions of individual molecules, of electronic transitions in many semiconductors, and of vibrational transitions in crystalline lattices. Semiconductor electronics and crystal lattice transitions are beyond the scope of this article. 

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

For molecules in which at least one internal rotating part has a dipole moment component perpendicular to the axis of rotation, there should appear directly in the infrared spectrum transitions between the torsional states. For most cases these would be quite far in the infrared region and therefore more difficult to observe. Nevertheless a few molecules of this type have been studied in this region, and such transitions have been reported.6... 

Vibrational transitions (e.g., vo-vx) require more energy than rotational transitions and this amount of energy is generally found in the infrared region of the spectrum. Infrared spectra have sharp peaks with some width to them. 

The earliest experiments with lasers in absorption spectroscopy were performed with the high-gain infrared line X = 3.39p of the He-Ne laser the first gas laser Several authors Miscovered that this laser line is absorbed by many hydrocarbon molecules, causing a vibrational-rotational transition in a band which belongs to the excitation of a C-H stretching vibration . ... 

Microwave (rotational) spectra are very complex, even for diatomic molecules, and give little useful information on organic molecules, which are relatively large. Rotational transitions are often responsible for the broadness of infrared (IR) bands, since each vibrational transition has a number of rotational transitions associated with it. The use of microwave spectroscopy is extremely rare in organic chemistry, and it too will be discussed no further here. 

A translational line like the one seen above in rare gas mixtures is relatively weak but discernible in pure hydrogen at low frequencies (<230 cm-1), Fig. 3.10. However, if a(v)/[l —exp (—hcv/kT)] is plotted instead of a(v), the line at zero frequency is prominent, Fig. 3.11 the 6o(l) line that corresponds to an orientational transition of ortho-H2. Other absorption lines are prominent, Fig. 3.10. Especially at low temperatures, strong but diffuse So(0) and So(l) lines appear near the rotational transition frequencies at 354 and 587 cm-1, respectively. These rotational transitions of H2 are, of course, well known from Raman studies and correspond to J = 0 -> 2 and J = 1 — 3 transitions J designates the rotational quantum number. These transitions are infrared inactive in the isolated molecule. At higher temperatures, rotational lines So(J) with J > 1 are also discernible these may be seen more clearly in mixtures of hydrogen with the heavier rare gases, see for example Fig. 3.14 below. 

Fig. 7.3. Upper figure Emission spectrum of Jupiter in the far infrared two diffuse, dark fringes are seen at the H2 Sb(0) and Sb(l) rotational transition frequencies, caused by collision-induced absorption in the upper, cool regions. The lower figure presents an enlarged portion which shows the dimer structures near the So(0) transition frequency [150].

Now consider the rotational structure of vibration-rotation absorption bands. Since the rotational energy is small compared to the vibrational energy, we can have A/ = — 1, as well as A/= + I, in an infrared absorption transition. Vibration-rotation absorption transitions with A/ = +1 form the R branch of a vibration-rotation band, while A/= — 1 vibration-rotation transitions form the P branch of the band. 

The rotational fine structures of infrared vibration-rotation transitions are determined by the same integrals IXOa,..., IZOc as determine pure-rotation transitions. Consider first symmetric tops. As a consequence of symmetry, it can be shown that any allowed vibrational transition of a symmetric top changes either the component of d along the symmetry axis or a component of d perpendicular to the symmetry axis. These two kinds of transitions are called parallel ( ) and perpendicular ( L), respectively. Consider first a parallel transition, which has... 

IR wavelengths are traditionally divided into three regions. The portion that adjoins the visible region is the near infrared = 0.8-2.5 jam the mid infrared extends from 2.5 to 50 /xm the far infrared extends from 50 to 1000 [im. Most commercial IR spectrometers operate in the mid IR. Pure rotational transitions of light molecules, and low-frequency vibrational transitions of heavy molecules occur in the far IR. 

For a heavier system, such as N2O + Ar, a calculation of rotational transitions and microwave or infrared line widths would follow the same course through the flow chart, as that followed above in detail for HC1 + Ar. However, at the last stage (low j, small b collisions), the number of coupled states would probably be too large for the non-perturbative, fixed classical path calculation to be practical. Then one should calculate "classical S matrices" including interference between trajectories, to cover these remaining collisions. 

Figure 9-10 Schematic vibrational and rotational energy levels. The arrows correspond to infrared vibrational-rotational transitions of different energies.

In the mid-infrared, molecules with a dipole moment have active vibrational rotational transitions, which can be observed both in emission and absorption. For the observation... 

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