Rotational perturbations

In molecular spectra, perturbations cause Uie displacement of a band from its regular position in the band system (vibrational perturbation) or the displacement (and/or weakening) of corresponding lines in the different branches of a band (rotational perturbation). A perturbation observed in the spectrum is indicative of the presence of a perturbation (shift) of one of the energy levels involved due to interaction with another level of the same, or nearly the same, energy. 

The need for an account of inertial effects in relaxation at hi frequencies has been known for a considerable time. - In dilute gases a description in terms of free rotation perturbed by collision is substantially developed to account for the shapes of i.r. and Raman lines. In crystals at sufficiently low temperature, description in terms of bands of regular oscillations perturbed by anharmonicity provides a regular sequence of approximations. In dense gases and in liquids - it is necessary to face simultaneously a complex pattern of molecular motions and a difficult question of the delayed electrical interaction which gives rise to the internal... 

Liquid alcohols display an extremely broad absorption near 650 cm (half-width 200-300 cm"" ). Stuart and Sutherland recognized the importance of this band and have attributed it to the hindered rotation perturbed by the formation of the H bond (1967, 1966). They find this band centered at 670 cm"" for pure liquid methanol, and at 475 cm"" for methanol-. The ratio of these frequencies, 1.41, is characteristic of a motion dominated by hydrogen atom movement. The band is present in CCI4 and CS2 solutions of methanol at concentrations above 1 M and is very much weaker at concentrations below 0.1 M. In spectra of dilute solutions, the absorption is presumed to shift below the limit of observation, to about 350 cm . The over-all spectral behavior is as striking and unusual as that of the stretching mode, as shown in Fig. 3-26. In sharp contrast are the relatively minor spectral... 

Population of the CO d A, v =5 level by absorption of Fourth Positive radiation from a CO discharge has been attributed (30) to rotational perturbations between the d A and A" n states. The existence of these perturbations has been demonstrated by Slanger and Black (33) who investigated the emissions from the three sublevels of the d A state to the a II state following absorption by CO of d A -> X E" " radiation from a CO discharge. This work has been extended by these authors (34) to perturbations between A II and e E . Elastic cross-relcixation was demonstrated between A II and d3A and e j ". Perturbations coupling the a 3r+ state to v = 1 of A II have been observed by Burnham et al. (35) in a level-crossing experiment. 

The L-uncoupling operator, —(l/2//ii2)(J+L-+J-L+), which is responsible for the evolution as J increases from Hund s case (a) to case (d), causes numerous perturbations between states that differ by AO = AA = 1 and with AS = 0. This specific type of rotational perturbation is often called a gyroscopic perturbation. 

The lower-state rovibrational bands were found in agreement with measurements and analyses of previous authors, notably those of the high-resolution four-wave mixing spectroscopy of the d Flg - a IIu (0-0) band by Lloyd and Ewart [99Llo]. The Swan system is complicated by overlapping lines, and by rotational perturbations which are possibly caused by interactions with the b Eg state [07Tan]. 

Two new bands — in-phase (ui) and out-of-phase (I ls) antisymmetric CH2 stretching vibrations of allyl radical have been obtained in the slit jet discharge spectrometer, as the sample spectra shown in the top panel of Fig. 5.18. The data have been successfully analyzed with a Watson asymmetric rotor Hamiltonian, yielding precise band origins and rotational constants for both bands. The high quality of least squares fits to ground state combination differences indicates that the rotational level structure in the lower state is well behaved, while the reduced quality of fits to the vibrational transitions, on the other hand, suggest the presence of Coriolis mediated rotational perturbations in the upper state. Due to sub-Doppler resolution (Ai/ 70 MHz) in the slit jet expansion. 

It is appropriate to refer these quantities to the molecular-principal-axis system (o, b, c). In this way, the tensor components Dj., g -, and uj,. become uniquely defined molecular properties (g, g = , b, c). However, only the diagonal tensor components are useful in analysing hfs spectra as non-diagonal terms, g+g, do not enter matrix elements diagonal in J, and higher-than-first-order rotational perturbations of JT are barely observable. Thus it is sufficient to consider an effective Hamiltonian diagonal in J. This Hamiltonian is customarily written in terms of rotationally dependent interaction strengths g(A-, ... 

Perturbations between close-lying energy levels can occur for all types of molecules. These perturbations may be caused by either Fermi resonance or Coriolis interaction. Both phenomena can produce either vibrational or rotational perturbations. The rotational perturbations will affect only levels of the same over-all species and the same J value. The restriction to the same species also holds true for vibrational perturbations in the case of Fermi resonance, but in the case of Coriolis interaction perturbation can occur between vibrational levels of different species. We shall discuss Fermi resonance first. 

Fermi resonance can produce a vibrational or a rotational perturbation. The former involves a shift of a vibrational level from its normal position. In addition, the vibrational change will alter the rotational constant B for the two interacting energy levels. Although the change in the rotational constant B could be thought of as a rotational perturbation, we shall restrict the use of this term to cases for which a rotational perturbation occurs without a vibrational disturbance and consider the vibrational level shift as a vibrational perturbation. 

Fermi Resonance (Rotational Perturbation). A rotational perturbation of the Fermi resonance type can occur even if the interaction between two vibrational levels of the same species is slight. If the two vibrational energy states are near each other, then some lines of the rotational fine-line structure may be perturbed. The rotational lines which have nearly the same energy will be the ones which perturb each other. We shall not give an example of such a perturbation here however, examples of this type of perturbation will be found in the spectra interpreted in the later sections of this chapter. 

Coriolis interactions can be classified as rotational perturbations, when the interaction between two vibrational levels of different species results in a change in the rotational constant B, or they may be vibrational perturbations, when the energy levels of the band are shifted from their normal positions. 

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