# Rotation-Vibration Transitions of a Parallel Band of a Symmetric Rotor

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This Demonstration shows the energy level transitions associated with the lines observed in the rotationally resolved infrared spectrum of a parallel band of a symmetric rotor. A symmetric rotor possesses a greater-than-two-fold rotation axis (symmetry element) and as a result there is an inherent degeneracy of the vibrational energy levels. This degeneracy, along with the Coriolis splitting of the vibrational levels, has been neglected in this Demonstration for clarity. The observed transitions are between non-degenerate vibrational energy levels and the fundamental vibrational transition is coupled with rotational transitions in which , .

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Contributed by: Whitney R. Hess and Lisa M. Goss (March 2011)

(Idaho State University)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In this Demonstration, lower state constants are indicated by a superscript double prime (″) and excited state constants are indicated by a superscript prime (′).

The spectrum in the bottom graphic is simulated at a temperature of 50 Kelvin and it is assumed that the centrifugal distortion constants (, , and ) and the anharmonicity constant () are negligible. However, the interaction of rotation and vibration is considered by using unequal values for the lower and excited state rotational constants and (). To simulate the spectrum, , and were used.

For the top graphic, the axis in the energy level diagram is arbitrary. The arrows indicating transitions and the energy levels corresponding to each value are spread out only for clarity.

The transitions are labeled according to the designation , where *, **, **, *and are as follows:

: transitions with are designated with a superscript Q, and all transitions in a parallel band fall into this category

: P, Q, or R depending on whether , respectively

: the value of is indicated by the subscript

: the value of is enclosed in the parentheses

For example, indicates the line corresponding to the transition in the Q branch within the sub-band.

Snapshots 1, 2, 3, and 4: full spectrum, P branch, Q branch, R branch views, respectively

References

[1] P. Atkins and J. de Paula, *Physical Chemistry*, New York: Oxford University Press, 2006.

[2] G. Herzberg, *Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules*, Princeton, NJ: D. Van Nostrand Company, Inc., 1945.

## Permanent Citation