# Rotation-Vibration Transitions for a Perpendicular Band of a Symmetric Rotor

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This Demonstration shows the rotation-vibration energy level transitions that correspond to the lines observed in a rotationally resolved infrared spectrum of a perpendicular band of a symmetric rotor. The inherent degeneracy of the vibrational levels (since a symmetric rotor possesses a greater-than-twofold rotation axis) has been neglected in order to maintain clarity in this Demonstration. The transitions occur between nondegenerate vibrational energy levels, and the fundamental vibrational transition is accompanied by rotational transitions in which .

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

(Idaho State University)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

In this Demonstration, a superscript double prime (″) indicates lower state constants and quantum numbers and a superscript prime (′) indicates excited state constants and quantum numbers.

The spectrum in the bottom graphic is simulated at a temperature of 50 Kelvin and with the assumptions that the centrifugal distortion constants and anharmonicity are negligible. Unequal values for the lower and excited state rotational constants and were used in order to account for the interaction of rotation and vibration . The values of and were used to simulate the spectrum.

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

The transition labels are written as , where *, **, **, *and are as follows:

: transitions with ("positive" sub-bands) are designated with a superscript and transitions with ("negative" sub-bands) are designated with a superscript ;

: , , or 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 branch within the "negative" sub-band.

Snapshots 1 and 2: full spectrum (does not utilize the Manipulate functionality) and sub-band views, respectively

Snapshot 3: using the axis lower and upper boundary controls will zoom in on a region of the spectrum and if a transition of interest is outside of the chosen range, the message "transition out of axis range" will appear

Snapshot 4: the separation between the "positive" and "negative" sub-bands becomes larger as a result of the greater difference in the transition energies between the sub-bands as increases

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