Lower and Upper State Rotational Combination Differences

In the beginning, no B-values were known Presently, it would be very unusual, if the carrier (the molecule responsible) of the spectrum is known, for neither B nor B to be known. If B (and D ) is known, then one has a set of extremely accurate, a priori known rotational combination differences (see Fig. 1.5) 

These combination differences can be used to find the correct absolute numbering of the Fortrat parabola. The Fortrat equation 

If the initial absolute numbering of the Fortrat parabola is incorrect (the relative numbering is assumed to be correct, but could easily be corrupted by inadequate precision in the wavenumber calibration of the measured spectrum), as it almost certainly will be, the set of a priori known A2F values will not match the set of trial combination differences computed from the Fortrat equation. It is necessary to examine a series of trial absolute numberings of the Fortrat equation, shifting m in integer steps, until the known combination differences match those derived from the Fortrat equation, either 

One reason for not knowing either B or B could be that the identity of the carrier of the spectrum is uncertain. Even when the carrier is known, there might be several likely candidates for the upper or lower electronic-vibrational state. When several likely candidates exist for one of the electronic-vibrational states involved in the transition, an a priori known (or predicted by ab initio calculation) range of (B,D) values for the candidate state may be used, in 

---

Figure 1.5 Lower and Upper State Rotational Combination Differences.

---