Rotational Structure Fortrat Parabola

The second differences may be measured directly from the spectrum without any knowledge whether J increases or decreases as one follows a branch toward higher frequency. Thus one immediately obtains a good estimate for B — B neglecting contributions from D and D . The line intensities usually vary smoothly along a rotational branch because collisions cause rotational populations to approach Boltzmann equilibrium rapidly and rotational linestrength factors (see Section 6.1 and Whiting, et ai, 1980) are approximately linear in J. 

The bandhead conveys useful qualitative and quantitative information, but it may also conceal the low-J regions of the R, Q, and P branches. The qualitative information comes directly from the crude shape of a band. If a band has its head in the R branch, the band will appear to terminate abruptly on the high-frequency (blue) side and the rotational branches will extend, with increasing line spacings toward low-frequency (red). Such a band is said to be red 

The formation of bandheads exacts a significant price in terms of the effort needed to establish the absolute J, J rotational assignments of all rotational lines in a vibrational band of an electronic transition. Valuable species identification, geometric structure, electronic structure, and dynamical information is locked up in the details of a band, and the only key to the lock is a rotational analysis. 

provided that a sufficient number of line frequencies in each branch fragment are measured accurately enough (in the vast majority of pattern recognition situations, accurate measurements are essential for distinguishing between genuine and spurious patterns) it is often possible to unify all lines in the R and P branches into a single Fortrat parabola, as shown in Fig. 1.4. 

Unfortunately, the absolute rotational numbering cannot be established without additional information unless the low-J region is sufficiently well resolved to reveal a gap between the lowest-./ first R and P lines, e.g. respectively R(0) 

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