Rotator transition

Vibrational transitions, usually associated with simultaneous rotational transitions, occur in the i.r. and near i.r., and give rise to bands characteristic of the vibrational and rotational... 

If the experunental technique has sufficient resolution, and if the molecule is fairly light, the vibronic bands discussed above will be found to have a fine structure due to transitions among rotational levels in the two states. Even when the individual rotational lines caimot be resolved, the overall shape of the vibronic band will be related to the rotational structure and its analysis may help in identifying the vibronic symmetry. The analysis of the band appearance depends on calculation of the rotational energy levels and on the selection rules and relative intensity of different rotational transitions. These both come from the fonn of the rotational wavefunctions and are treated by angnlar momentum theory. It is not possible to do more than mention a simple example here. 

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... 

Rotational transition frequencies acquired in the THz region expand upon and complement those acquired in the microwave. Two types of molecules undergo rotational transitions that fall in the FIR molecules witli rotation about an axis having a small moment of inertia, and molecules in high-J states. FIR spectra of the first type of molecules are... 

CHgCN = 16 17 rotational transitions near 312 GHz. (a) The speetnim for ordinary CN. 

Winnewisser G, Belov S P, Klaus T and Sohieder R 1997 Sub-Doppler measurements on the rotational transitions of oarbon monoxide J. Mol. Spectrosc. 184 468-72... 

Electron-impact energy-loss spectroscopy (EELS) differs from other electron spectroscopies in that it is possible to observe transitions to states below the first ionization edge electronic transitions to excited states of the neutral, vibrational and even rotational transitions can be observed. This is a consequence of the detected electrons not originating in the sample. Conversely, there is a problem when electron impact induces an ionizing transition. For each such event there are two outgoing electrons. To precisely account for the energy deposited in the target, the two electrons must be measured in coincidence. 

Figure B2.3.12. Rotational transitions between a speeifie pair of vibrational levels in a eleetronie...

Hiind s ease (a) eoupling is assumed for the state. Conventional speetroseopie designations [M] are given for the allowed rotational transitions. 

In a conventional spectroscopic experiment, the intensity of a rotational transition within a given vibrational band can be written as... 

Chidsey I L and Crosley D R 1980 Calculated rotational transition probabilities for the A-X system of CH J. Quant. Spectrose. Radiat. Transfer 23 187-99... 

It is also possible to measure microwave spectra of some more strongly bound Van der Waals complexes in a gas cell ratlier tlian a molecular beam. Indeed, tire first microwave studies on molecular clusters were of this type, on carboxylic acid dimers [jd]. The resolution tliat can be achieved is not as high as in a molecular beam, but bulk gas studies have tire advantage tliat vibrational satellites, due to pure rotational transitions in complexes witli intennolecular bending and stretching modes excited, can often be identified. The frequencies of tire vibrational satellites contain infonnation on how the vibrationally averaged stmcture changes in tire excited states, while their intensities allow tire vibrational frequencies to be estimated. 

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.). 

The energies at whieh the rotational transitions oeeur appear to fit the AE = 2B (J+1) formula rather well. The intensities of transitions from level J to level J+1 vary strongly with J primarily beeause the population of moleeules in the absorbing level varies with J. 

In mierowave speetroseopy, the energy of the radiation lies in the range of fraetions of a em-i through several em-i sueh energies are adequate to exeite rotational motions of moleeules but are not high enough to exeite any but the weakest vibrations (e.g., those of weakly bound Van der Waals eomplexes). In rotational transitions, the eleetronie and vibrational states are thus left unehanged by the exeitation proeess henee /ei = /ef and Xvi... 

The result of all of the vibrational modes contributions to la (3 J-/3Ra) is a vector p-trans that is termed the vibrational "transition dipole" moment. This is a vector with components along, in principle, all three of the internal axes of the molecule. For each particular vibrational transition (i.e., each particular X and Xf) its orientation in space depends only on the orientation of the molecule it is thus said to be locked to the molecule s coordinate frame. As such, its orientation relative to the lab-fixed coordinates (which is needed to effect a derivation of rotational selection rules as was done earlier in this Chapter) can be described much as was done above for the vibrationally averaged dipole moment that arises in purely rotational transitions. There are, however, important differences in detail. In particular. 

For purely rotational transitions, the initial and final eleetronie and vibrational states are the same. Moreover, the eleetronie and vibrational states are not summed over in the analog of the above development beeause one is interested in obtaining an expression for a partieular Xiv /ie ==> Xfv Vfe eleetronie-vibrational transition s lineshape. As a result, the... 

For vibration-rotation transitions within a single electronic state, the initial and final electronic states are the same, but the initial and final vibrational and rotational states... 

This integral would arise in the eleetronie-vibration-rotation ease the other two eases would involve integrals of the same form but with the AEi f/h absent in the vibration-rotation situation and with cofy, iv + AEi f/h missing for pure rotation transitions. All sueh integrals ean be earried out analytieally and yield ... 

Table 5.1 Frequencies and wavenumbers of rotational transitions of CO observed in the millimetre wave region...

Question. By making measurements ffom Figure 5.3 determine the average separation of rotational transitions in and hence estimate the bond length. 

Answer. To obtain the best value of 2B, the separation between adjacent rotational transitions, measure the total distance between the J= 3 and J= 9 transitions. This can be converted into cm using the scale at the bottom of the figure. The separation between the J =3 and J =9... 

It will be seen in Section 5.2.1.4 that, since these rotational transitions of CO are associated with the zero-point (v = 0) level, the value of B obtained here is, in fact. Bo and not the equilibrium value B. Equation (5.25) shows how these values are related. 

At a simple level, the rotational transitions of near-symmetric rotors (see Equations 5.8 and 5.9) are easier to understand. For a prolate or oblate near-symmetric rotor the rotational term values are given, approximately, by... 

Examples of prolate near-symmetric rotors are the s-trans and s-cis isomers of crotonic acid, shown in Figure 5.8, the a axis straddling a chain of the heavier atoms in both species. The rotational term values for both isomers are given approximately by Equation (5.37) but, because A and B are different for each of them, their rotational transitions are not quite coincident. Figure 5.9 shows a part of a low-resolution microwave spectmm of crotonic acid in which the weaker series of lines is due to the less abundant s-cis isomer and the stronger series is due to the more abundant s-trans isomer. 

Electronic, vibrational and rotational transitions may be involved in Raman scattering but, in this chapter, we consider only rotational transitions. 

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

We have seen in Section 5.2.1.4 that there is a stack of rotational energy levels associated with all vibrational levels. In rotational spectroscopy we observe transitions between rotational energy levels associated with the same vibrational level (usually v = 0). In vibration-rotation spectroscopy we observe transitions between stacks of rotational energy levels associated with two different vibrational levels. These transitions accompany all vibrational transitions but, whereas vibrational transitions may be observed even when the sample is in the liquid or solid phase, the rotational transitions may be observed only in the gas phase at low pressure and usually in an absorption process. 

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

The intensity distribution among rotational transitions in a vibration-rotation band is governed principally by the Boltzmann distribution of population among the initial states, giving... 

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...

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