Coriolis resonance

Coriolis resonance interactions spect Perturbationof two vibrations of a polyatomic molecule, having nearly equal frequencies, on each other, due to the energy contribution of the Coriolis operator. kor e o las rez-on-ons, in-tor,ak-shonz ) corresponding states phys chem The condition when two or more substances are at the same reduced pressures, the same reduced temperatures, and the same reduced volumes., kar-3 spand ir) stats )... 

Several investigations concerned with the identification of these lines succeeded, for instance, in the case of H2O, in elucidating the rotational spectrum in excited vibrational states 356). Through comparison of wavelengths and intensities of many lines in H2O , H2 0 and DjO isotopic effects could be studied in these excited vibrational levels 357,358) Perturbations of rotational levels by Coriolis resonance which mixes different levels could be cleared up through the assignment and wavelength measurement of some DCN and HCN laser lines 359). 

Here, oohx also passes through two new, lower order A/ = 1 Coriolis resonances near oohx = 3t >bend . 

Since the perturbations turn on at slightly lower Vj than the onset of changes in fine-structure parameters [5], it seems likely that the perturbations in (0, 32, 0) are due mostly to new oohx 4oobend anharmonic resonances and the rapid changes in fine-structure parameters at (0, 36,0) due mostly to new oohx = 3oobend Coriolis resonances. 

Two vibronic states which happen to occur at nearly the same energy will perturb one another if certain conditions are fulfilled. The interacting states may be derived from different electronic states, but in polyatomic spectra are often merely different vibrational states of the same electronic states. The perturbations, which are either homogeneous (AK = 0) (e.g. Fermi resonance) or heterogeneous (AK = 1) (Coriolis resonance) (Mulliken, 1937) are then analogous to the perturbations observed in infrared and Raman spectra. Such perturbations are commonplace in electronic bands where the completely unperturbed band is the exception rather than the rule. 

Despite the complication which resonances introduce into the analysis of a spectrum and the theoretical treatment of the hamiltonian, when they can be analysed they often give valuable information on the force field which cannot be obtained directly in the absence of a resonance. We consider briefly the two commonest types of resonance interaction, Fermi (or anharmonic) resonance and Coriolis resonance, to illustrate this point. 

Coriolis Resonance. The hamiltonian (54) contains cross terms in the angular momenta of the type ... 

The observed a values are of course generally an important source of information on the cubic anharmonic force field. However, in the presence of a Coriolis resonance the particular a values involved are dominated by the harmonic Coriolis contribution arising from equation (66), and analysis of a Coriolis resonance essentially gives information on the constant or... 

Methane as the prototype of spherical tops was the subject of a great number of investigations, of which only some can be mentioned here. At high resolution the structure of rovibrational bands becomes very complicated due to tensorial splittings. Moreover Fermi and Coriolis resonances lead to interactions between fundamentals and overtone and combination bands of CH4 therefore theoretical models for the dyade 1/2 and 1 4 (Champion, 1977) and the pentade i/j, i/3, 2j> 2, 1 2 + and 21/4 (Lolck et al., 1982 and Poussigue et al., 1982) have been developed and sets of molecular con.stants were determined by adjustment to all available experimental high resolution IR and Raman... 

The case of strong Coriolis resonance (e. g. if must be treated... 

In high-barrier cases quite often the splitting of a pair of nearly degenerate levels can be determined by treatment of the Coriolis resonances between the levels (see below). These splittings may be used to scale the energy levels however, even though they are very well determined, this... 

Coriolis resonance between 03 = 1, 07 = 1, and 09 = 1 constrained to ground state value... 

Coriolis resonance parameters constrained to ab initio values... 

The vibration-rotation spectra and/or the rotational spectra in excited vibrational states provide the af constants and, when all the a/ constants are determined, the equilibrium rotational constants can be obtained by extrapolation. This method has often been hampered by anharmonic or harmonic resonance interactions in excited vibrational states, such as Fermi resonances arising from cubic and higher anharmonic force constants in the vibrational potential, or by Coriolis resonances. Equihbrium rotational constants have so far been determined only for a limited number of simple molecules. To be even more precise, one has further to consider the contributions of electrons to the moments of inertia, and to correct for the small effects of centrifugal distortion which arise from transformation of the original Hamiltonian to eliminate indeterminacy terms [11]. Higher-order time-independent effects such as the breakdown of the Bom-Oppenheimer separation between the electronic and nuclear motions have been discussed so far only for diatomic molecules [12]. 

In the discussion that follows, it will be shown that V3 and V5 are coupled by a rotational resonance interaction which changes the rotational structure of V3 from that expected for an A band. The rotational structure of the V5 band is strongly perturbed by a rotational resonance interaction with the fundamental and so the line structure of V5 is determined by the interaction between V5 and v. This interaction between V5 and is of the Coriolis resonance type. 

On the high-frequency side of V4 is the combination band V2 -I- V5. The two bands overlap, so that again only Rr and Rq lines can be identified. The V2 + V5 combination band can be analyzed in the manner described for the V4 band A j(B + C ), and Vq values can be determined, assuming that the symmetric rotor model is applicable. The V2 + V5 band is quite intense, in fact about one-fourth as intense as the fundamental V4. This suggests that some sort of interaction is occurring however, since no anomalous spacing of the positions is found, the interaction is probably not a Coriolis resonance. 

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