Rotational Transitions in Molecules

Plenary 9. J W Nibler et al, e-mail address niblerj chem.orst.edu (CARS and SRS). High resolution studies of high lymg vibration-rotational transitions in molecules excited in electrical discharges and low density monomers and clusters in free jet expansions. Ionization detected (REMPI) SRS or IDSRS. Detect Raman... 

Periodic oscillations in this dipole can act as a source term in the generation of new optical frequencies. Here a is the linear polarizability discussed in Exps. 29 and 35 on dipole moments and Raman spectra, while fi and x are the second- and third-order dielectric susceptibilities, respectively. The quantity fi is also called the hyperpolarizability and is the material property responsible for second-harmonic generation. Note that, since E cos cot, the S term can be expressed as -j(l + cos 2 wt). The next higher nonlinear term x is especially important in generating sum and difference frequencies when more than one laser frequency is incident on the sample. In the case of coherent anti-Stokes Raman scattering (CARS), X gives useful information about vibrational and rotational transitions in molecules. 

Miklavc, A. (1980) On the semi-classical theory of coUision-induced vibrational-rotational transitions in molecules. J.Chem. Phys. 72, 3805-3808. 

For the spectroscopy of vibrational-rotational transitions in molecules the laser-excited fluorescence is generally not the most sensitive tool, as was discussed at the end of Sect. 1.3.1. Optoacoustic spectroscopy, on the other hand, is based on colli-sional energy transfer and is therefore not applicable to molecular beams, where collisions are rare or even completely absent. For the infrared spectroscopy of molecules in a molecular beam therefore a new detection technique has been developed, which relies on the collision-free conditions in a beam and on the long radiative lifetimes of vibrational-rotational levels in the electronic ground state [84-86]. 

R. Schinke, Theory of Rotational Transitions in Molecules, IntT Conf. Phys. El. At. Collisions XIII (Moith-Kolland, Amsterdam, 1984), p. 429... 

Recently microwave spectroscopy has provided two new methods of estimating barrier heights In one technique the relative intensities of two absorption lines are measured. One line is due to a pure rotational transition for the molecule in its lowest state of vibration and internal torsional motion. The other line is due to the same rotational transition in molecules which are in an excited state of torsional motion. The ratio of those lino intensities measures the population ratio of the two torsional states and therefore, via the Boltzmann factor, the frequency separation, d his in tur)i is linked to the barrier height if the shape is assumed. 

An apparatus similar to the one described above but adapted to the investigation of rotational transitions in molecules has been reported recently and applied to precise Stark effect measurements in the X ground state of CaCl. ... 

The collisional broadening in a monatomic gas is characterized by values of cr of the order of (1-5) x 10 cm. If the perturbing particles are atoms or molecules of a foreign gas, then typically a 10 -10 cm. A similar mechanism of broadening occurs also for vibrational and rotational transitions in molecules. The corresponding cross-sections are much less, about (1-3) x 10 cm. ... 

The electronic transitions which produce spectra in the visible and ultraviolet are accompanied by vibrational and rotational transitions. In the condensed state, however, rotation is hindered by solvent molecules, and stray electrical fields affect the vibrational frequencies. For these reasons, electronic bands are very broad. An electronic band is characterised by the wave length and moleculai extinction coefficient at the position of maximum intensity (Xma,. and emai.). 

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. 

Microwave spectroscopy is generally defined as the high-resolution absorption spectroscopy of molecular rotational transitions in the gas phase. Microwave spectroscopy observes the transitions between the quantised rotational sublevels of a given vibrational state in the electronic ground state of free molecules. Molecular... 

Gaseous metal, reduction to, 16 146-147 Gaseous molecules, rotational transitions in, 23 129... 

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 . ... 

Upon absorption of light of an appropriate wavelength, a diatomic molecule can undergo an electronic transition, along with simultaneous vibrational and rotational transitions. In this case, there is no restriction on Au. That is, the selection rule Av = +1 valid for purely vibrational and vibrational-rotational transitions no longer applies thus numerous vibrational transitions can occur. If the molecule is at room temperature, it will normally be in its lower state, v" = 0 hence transitions corresponding to v" = 0 to v = 0,... 

Low energy photons in the far IR can only modify the term ERol. This leads to pure rotational spectra that can be easily studied for small diatomic gases. However, in the mid IR, photons have sufficient energy to modify Vib and Fr,. This leads to vibrational-rotational spectra (Fig. 10.6). Each vibrational transition is accompanied by tens of individual rotational transitions. The molecule becomes an oscillating rotor for which energy VR approximately corresponds to the following values, where 7 (./ = 0, 1, 2, 3,...) and V (V = 0, 1, 2) are the rotational and vibrational quantum numbers, respectively. 

Fig. 4.5 Frequencies of rotational transitions for molecules in the o "0 vibrational level of a diatomic molecule.

Obvious complications as compared to simple systems arise in the case of molecular targets. The potentials V (R) and V+(R) and also the width T(f ) depend on the relative orientation of the molecule to the metastable-target direction. In addition, there is the possibility of vibrational and rotational transitions in the ionization process as well as the possibility of reaction before and after the ionization. No general extension of the Pgl theory to the case of molecular targets has been formulated. 

The detection and identification of molecules in interstellar space is possible by millimeter wave spectroscopy. The independent synthesis and detection of such reactive species, e.g. by flash vaccuum thermolysis and mm wave spectroscopy, provides proof for their cosmochemical existence. The detection of the J 6 —> 7 rotational transition in the decomposition products of t-Bu2HSi—NH(CH2— C=CH) indicated the formation of HNSi (Table 20)333. 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

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