P and R branches

Figure 6.27 The IJSq, 77 — infrared band of acetylene. (The unusual vertical scale allows both the very intense Q branch and the weak P and R branches to be shown conveniently)...

The effective value of B, for the lower components of the doubled levels, can be obtained from the P and R branches by the same method of combination differences used for a type of band and, for the upper components, from the Q branch. From these two quantities and may be calculated. 

From the following wavenumbers of the P and R branches of the 1-0 infrared vibrational band of H Cl obtain values for the rotational constants Bq, Bi and B, the band centre coq, the vibration-rotation interaction constant a and the intemuclear distance r. Given that the band centre of the 2-0 band is at 4128.6 cm determine cOg and, using this value, the force constant k. 

The method of combination differences applied to the P and R branches gives the lower state rotational constants B", or B" and D", just as in a A transition, from Equation (6.29) or Equation (6.32). These branches also give rotational constants B, or B and D, relating to the upper components of the 77 state, from Equation (6.30) or Equation (6.33). The constants B, or B and D, relating to the lower components of the state, may be obtained from the Q branch. The value of q can be obtained from B and B. ... 

Each of the lasing vibrational transitions has associated rotational fine structure, discussed for linear molecules in Section 6.2.4.1. The Sgli transition is — Ig with associated P and R branches, for which AJ = — 1 and +1, respectively, similar to the 3q band of HCN in Figure 6.25. The 3q22 band is, again, with a P and R branch. 

The IR spectra of linear molecules at low pressure do not contain a Q-branch at all. The intensity increases with 1/tj in the central part of this spectrum exclusively due to the exchange between P- and R-branches (Fig. 6.4). The secular simplification is inapplicable in this case. In order to describe the rise of intensity in a gap of the IR spectrum with increase of density, one has to know the exact solution of the problem, e.g. (6.45H6.47). Using it, one can calculate... 

The detection probability for a given trajectory depends on the fragment orientation (its Mj value) and the nature of the probe transition. All of these images were obtained via the two-photon Ilg XAS) transition. Five rotational branches are thus possible O, P, Q, R and S. The amplitudes for each of these two-photon transitions can be obtained from a sum of paired, Mj-dependent, one-photon amplitudes.37 The O branch, for example, consists of a contribution from a parallel P-type transition to a 7A virtual state, followed by a perpendicular P-type transition to the final 1ffs Rydberg (which is assumed to be ionized promptly). The product of those two transition amplitudes must be summed with another product in which the first transition is perpendicular and the second is parallel. The P and R branches consist of four contributions each and the Q branch has six such terms in its transition amplitude. The required one-photon amplitudes are taken from Ref. 37. 

Here a third selection rule applies for linear molecules, transitions corresponding to vibrations along the main axis are allowed if Aj = 1. The A/=0 transition is only allowed for vibrations perpendicular to the main axis. Note that because of this selection rule the purely vibrational transition (called Q branch) appears in the gas phase spectrum of C(X but is absent in that of CO. In both cases, two branches of rotational side bands appear (called P and R branch) (see Fig. 8.3 for gas phase CO). 

It should be noted that the spacings between the experimentally observed peaks in HC1 are not constant as would be expected based on the above P- and R- branch formulas. This is because the moment of inertia appropriate for the v = 1 vibrational level is different than that of the v = 0 level. These effects of vibration-rotation coupling can be modeled by allowing the v = 0 and v = 1 levels to have rotational energies written as... 

A certain triatomic molecule shows three strong IR bands, each having a simple rotational structure. One band has P, Q, and R branches, while the other two have only P and R branches. Is the molecule linear or bent ... 

If one or both electronic states are not 2 states, then it turns out that we usually can have A7 = 0 also, giving a Q branch, in addition to P and R branches ... 

From the selection rules given in Section 6.5, we see that nonlinear-symmetric-top and asymmetric-top bands show Q branches, as well as P and R branches. Detailed consideration of the band shapes is omitted.7... 

Figure 17. Density dependence of the band maximum position of the 3vs mode (vm) in pure C02 at temperatures between 298 and 500 K (with vg = 6972.6 cm" ). Below the critical density (0.45 g cm-3), P and R branches were observed, and vm is taken as the arithmetic mean of the P and R branch maxima. Points on the lower left represent hot bands. Reproduced from Ref. 77a with permission from Verlag der Zeitschrift fur Naturforschung.

As before the subbands right and left from were interpreted as (vt + v ) combination bands and the fine structure as a series of hot bands of the (v, + n vp — n"vp) type. The hot bands are parallel bands with strong P and R branches and very weak Q branches. Since the H-bond shortens in the v = 1 state of vlt B > B" and the band heads are in the P branch. Many close-lying rotational lines accumulate around the band head so that what we observe is essentially a series of P branches each one belonging to a hot band. The latter form a sequence in the vibrational quantum number of the bridge bending vibration vp. 

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