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Introduction -
Infrared spectroscopy utilizes the principle of bond stretching and vibration to produce a spectrum analyzed by chemists. Organic molecules produce complex patterns and spectrums due to the large number of possible vibrations, rotations, and isotopes present in the organic molecule. With this taken into consideration diatomic molecules are the simplest molecules that could possibly experience stretching, vibration and rotation. This intuitively makes sense as a diatomic molecule can be imagined as a two balls connected by a spring. Now if this model is placed on a Cartesian coordinate system with the length of the molecule in the positive and negative x direction, one can easy imagine how the stretching of the bond can be modeled as a simple harmonic oscillator. Namely by the equation (v) = hy (v + 1/2), discrete allowed energy levels of v where v=1, 2, 3 . . and h being Plank's constant can be used to solved for energy in the harmonic oscillator model. Similarly, if one end of the molecule was held in place while the other end was flicked in the positive y direction the intuitive, and Newtonian consequence, would be that the molecule will vibrate in the positive and negative y directions until it reaches equilibrium.
The third movement one could imagine would be the entire molecule spinning as a simple rotor around the midpoint of the bond with energy levels allowed by the equation E(J) = h2J(J+1)/8π2f with J being the rotational equipment of v and I being the moment of inertia (or the point about where the rotor turns). There 3 movements rotations, vibration, and stretching are all contributing factors to spectra produced by IR and can be investigating using diatomic molecules such as HCI and DCI. When taking into consideration rotation, it is important to remember that all rotating things have an inherent moment of inertia about which the object is rotating. This concept can easily be visualized classically by spinning a top and observing how the top spine around its moment of inertia, or the central axis. However most molecules are not perfectly symmetrical like a top and will have a shifted moment of inertia depending on the mass of the two atoms bonded to each other.
In the case of HCI and DCI, by gathering data of two identical molecules aside from a proton, change in the rotational behavior can be monitored.