This Demonstration shows the rotationally resolved infrared spectrum of a perpendicular band of a symmetric rotor. It uses a top-down approach, with each level of options deconstructing the spectrum and revealing more details about its structure. You can view the full spectrum or choose to view the sub-bands in order to unlock the other control options and further deconstruct the sub-bands. It is also possible to zoom into any region of the spectrum by using the

axis lower-limit and upper-limit boundary controls.

The vibrational energy levels for a symmetric rotor possess an inherent degeneracy because there are more than two rotation axes. This degeneracy and Coriolis splitting of the degenerate vibrational energy levels is not addressed in this Demonstration. Instead, transitions for this spectrum occur between nondegenerate vibrational energy levels. Symmetric rotors possess two axes with equal moments of inertia and a principal axis with a unique moment of inertia. When the change in the dipole moment is perpendicular to the principal axis, a perpendicular band spectrum results. For a perpendicular band, the vibrational selection rules are

(where

for an absorbance spectrum) and the rotational selection rules are

and

,

for all values of

*,* with the further restriction that

. If the complete perpendicular band spectrum is deconstructed, it appears as a superposition of sub-bands, with each sub-band consisting of a

branch (

,

, smaller wavenumbers),

branch (

,

, middle branch), and

branch (

,

, larger wavenumbers). Since

, the series of sub-bands corresponding to

are termed the "positive" sub-bands and the series of sub-bands corresponding to

are termed the "negative" sub-bands. The rotational quantum number

and therefore there is no

negative sub-band. As a result of the restriction that

, there is a decreasing number of lines observed at the beginning of each branch with increasing

. The observed line intensities reflect a dependence on the rotational quantum numbers

and

, as well as a dependence on the thermal population of the lower state rotational energy levels.

* *Within the positive and negative sub-bands, greater intensity is observed for the lines in which

.