Understanding the Gap in a HCl Absorption Spectrum

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SUMMARY

The discussion focuses on the gap observed in the HCl absorption spectrum, specifically identified as the Q branch, which is a forbidden region for linear molecules. Participants clarify that the vibrational spectra consist of three parts: the P branch (with a -1 change in rotational quantum number), the Q branch (with no change), and the R branch (with a +1 change). The gap arises because the Q branch does not allow transitions for linear molecules, leading to a symmetrical line in the spectrum. Additionally, the energy level spacing between the P and R branches is not uniform due to the non-ideal behavior of molecules compared to perfect harmonic oscillators.

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  • Understanding of molecular spectroscopy concepts
  • Familiarity with rotational quantum numbers
  • Knowledge of vibrational energy levels in diatomic molecules
  • Basic principles of quantum mechanics
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http://www.cartage.org.lb/en/themes/Sciences/Physics/MolecularPhysics/MolecularSpectra/Rotation/Rotation.htm
 
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Hi PJ, thanks for the link. But can you be more specific as to which bit of the article you're referring to? Or do I have to go through the math for the explanation? Thanks.
 
From the article, I gather that the "gap" is the Q branch, which is the forbidden region. But why?
 
See reference (http://en.wikipedia.org/wiki/Rovibrational_coupling)

Vibrational spectra can be broken into 3 parts.

P branch; -1 change in rotational quantum number (J).
Q branch; no change in rotational quantum number.
R branch; +1 change in rotational quantum number.

The Q-branch is forbidden for linear (straight-line) molecules, hence the gap in the center of the spectrum. In the 1st approximation, the spacing between the energy levels in the P and R branch should be equal, assuming a perfect harmonic oscillator. Molecules are not, in general, perfect harmonic oscillators however, and so the energy spacing tends to decrease with increasing change in rotational quantum number.

Claude.
 

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