How does a harmonic oscillator model have the same frequency

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SUMMARY

The discussion centers on the complexities of modeling vibrational frequencies in molecules using harmonic oscillators, particularly in the context of infrared (IR) spectroscopy. It is established that while vibrational frequency is primarily determined by reduced mass, the vibrational energy levels are not uniformly spaced due to anharmonicity. Additionally, for polyatomic molecules like carbon dioxide, a single harmonic oscillator model is insufficient; coupled oscillators must be employed to accurately represent the vibrational behavior. The presence of rotation-vibrational coupling further complicates the analysis, leading to varied spectral features despite identical frequencies.

PREREQUISITES
  • Understanding of vibrational frequency and reduced mass
  • Familiarity with harmonic and anharmonic oscillators
  • Knowledge of coupled oscillators in molecular modeling
  • Basic principles of infrared spectroscopy
NEXT STEPS
  • Study the concept of anharmonicity in vibrational energy levels
  • Research coupled oscillators and their application in molecular modeling
  • Learn about rotation-vibrational coupling effects in polyatomic molecules
  • Explore advanced IR spectroscopy techniques and their interpretations
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Chemistry students, molecular physicists, and researchers in spectroscopy who are looking to deepen their understanding of vibrational modeling and IR spectral analysis.

Fruit Water
I'm currently studying IR but my mind is having trouble tying everything together.
While I see that vibrational frequency is determined really by just reduced mass, I can see from the equation that vib equation is the same throughout energy levels and so does energy (bc that basically depends on reduced mass and frequency). However, I've seen IR and there's all sorts of crazy spikes and loops and I'm confused on how that ties it together? Like something can have the same frequency but the spikes will be all different? I've tried reading about IR from different sources and something just isn't clicking. I'd seriously appreciate it if someone can clear this up for me!
 
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You can't model a molecule with many atoms by just using a single harmonic oscillator. For something as simple as carbon dioxide you already have to use a model with coupled oscillators. Another problem is anharmonicity (vibrational energy levels not being equally spaced at high excited states) and rotation-vibrational coupling (higher rotational states having a larger expectation value of internuclear distance because of "centrifugal" effect).
 

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