Q-branch transitions

Figure Bl.4.9. Top rotation-tunnelling hyperfine structure in one of the flipping inodes of (020)3 near 3 THz. The small splittings seen in the Q-branch transitions are induced by the bound-free hydrogen atom tiiimelling by the water monomers. Bottom the low-frequency torsional mode structure of the water duner spectrum, includmg a detailed comparison of theoretical calculations of the dynamics with those observed experimentally [ ]. The symbols next to the arrows depict the parallel (A k= 0) versus perpendicular (A = 1) nature of the selection rules in the pseudorotation manifold.

The absorption that is "missing" from the figure below lying slightly below 2900 em is the Q-branch transition for whieh E = E it is absent beeause the seleetion rules forbid it. 

Figure 8. Computed temperature sensitivity of the CARS spectrum of Ht at 1% concentration. Q-branch transitions are identified.

Figure 9. CARS spectra of Ht in a flat Hi-air diffusion flame at several temperatures determined from the identified Q-branch transitions...

Fig. 3 Computer-generated stick diagrams of the absorption spectrum of the V2 fundamental band of Hj at four different temperatures. Note the large number of lines at ca. 2500 cm and Q branch transitions with the band origin at 2521.3 cm . ...

Fig. 2.1. Far infrared spectrum of oxetanone-3. The Q-branch transitions are shown on the background of overlapped P and R transitions. P = 22 torr, pathlength = 30 cm. Absorption is plotted upward in this spectrum.

Fig. 4.2. Far-infrared spectrum of thietanone-3. The Q-branch transitions, showing considerable rotational degradation, are observed on the unresolved, overlapped P and R branch transitions.

Fig. 4.8. Raman spectrum of methylenecyclo-butane. The observed maxima are Q branch transitions of the totally symmetric Av = 2 ring puckering transition (Reproduced from Durig, J. R., Shing, A. C., Carreira, L. A.,...

Fig. 4.11. Raman spectra of gaseous cyclobutane and cyclobutane-ds- The observed Q-branch transitions are the Av = 2 ring-puckering transitions.

The seven observed Q-branch transitions for 3-oxabicyclo(3.1.0]hexane were fitted92) to a similar function with 9C2 = 26.8 B. The 6—7 transition was the last observed Q-branch. The 7-8 and 8-9 transitions were predicted to be the lowest frequencies, being almost identical, and succeeding transitions were indicated to increase in frequency. On the other hand, the potential function reported by Carreira and Lord89) for 6-oxabicyclo[3.1.0]hexane (cyclopentene oxide) had a second, very... 

Constants for deuterated phosphanes are presented In Table 7. The constants of PHJD (prolate asymmetric top) and PHDa (oblate asymmetric top) result from an analysis of their rotational spectra (see Table 15, p. 187) through Watson s [25] asymmetric rotor Hamiltonian in its S reduction [2]. Linear combinations of rotational constants of PHgD (A-C, 2B-A-C) were obtained by fitting them to Q-branch transitions [34]. 

Q-branch transitions (AJ = 0) and some R-branch transitions (AJ = +1) were identified in the rotational spectra of PHDg (Cs symmetry oblate asymmetric top) and PHJD (Csi prolate asymmetric top). Transitions, number of lines (n), and the corresponding frequency range are given in Table 15. The rotational levels are denoted by Jk KcO i the table J, Kg, K ) Kg and K are the K values for the given level for the limiting cases of prolate and oblate symmetric top, respectively [16, 17]. 

If rotational constants in both vibrational states are equal then all Q branch transitions occur at the same wavelength, the band origin. For a fundamental vibration of a perpendicular vibration with unequal rotational constants in the two vibrational levels and introducing centrifugal distortion... 

II Z, with the lasers propagating along X and the phototube along Y, are used. The polarization ratio R is defined as the ratio of the fluorescence intensity in case (a) to that in case (b). R is measured as function of J for Q branch transitions, because here lies along and larger polarization effects are expected. For P oj R transitions, is perpen-... 

The vibration-rotation spectrum can be understood on the basis of a partial energy level diagram for the lowest vibrational and rotational levels (Fig. 3.9). The upper and lower level quantum numbers are denoted by (v J ) and (v"J ), respectively. Transitions for which AJ— -h 1, AJ = — 1, and A J = 0 (the latter occurring only in states with nonzero orbital angular momentum along the molecular axis) are called R-, P-, and Q-branch transitions. The transition frequencies are derived from... 

B Lavorel, R Chaux, R Saint-Loup, H Berger. Self-density frequency shift measurements of Raman Na Q-branch transitions. Opt Commun 62 25-28, 1987. 

We now have sufficient information to draw the fundamental absorption band for HCl. The changes in quantum number which occur when the HCl band is observed are Ay = -h 1 and A7 = 1. Energy transitions for which A/ = 0 are called Q-branch transitions and usually do not occur for diatomic molecules such as HCl. (There are several exceptions, such as NO, for which A J = 0 transitions can occur. This is explained in terms of the odd electron present in NO.) The transitions where A/ = +1 are R-branch and those where A/ = — 1 are P-branch transitions. Thus, the concept of P-, Q-, and R-branches described earlier is related to the change in... 

For other parallel bands of symmetric rotors, the subbands may add differently, giving a total band in which the Q-branch transitions are distributed in the P- and R-branches. For such a band, only the P- and R-branches are seen, and the band center is a minimum. The P- and R-branches may have somewhat uneven intensity distributions since the regions where both Qq and Qp, or Qq and Qp, lines occur may be more intense than the regions where there are only Qp and Qp lines. 

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