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15: Spectroscopy

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    The tools of time-dependent perturbation theory can be applied to transitions among electronic, vibrational, and rotational states of molecules.

    • 15.1: Rotational Transitions
      In microwave spectroscopy, the energy of the radiation lies in the range of fractions of a \(cm^{-1} \text{ through several } cm^{-1}\); such energies are adequate to excite rotational motions of molecules but are not high enough to excite any but the weakest vibrations (e.g., those of weakly bound Van der Waals complexes). In rotational transitions, the electronic and vibrational states are thus left unchanged by the excitation process.
    • 15.2: Vibration-Rotation Transitions
      When the initial and final electronic states are identical, but the respective vibrational and rotational states are not, one is dealing with transitions between vibration-rotation states of the molecule. These transitions are studied in infrared (IR) spectroscopy using light of energy in the 30 cm\(^{-1} \text{ (far IR) to 5000 cm}^{-1}\) range. The electric dipole matrix element analysis still begins with the electronic dipole moment integral.
    • 15.3: Electronic-Vibration-Rotation Transitions
      Molecular point-group symmetry can often be used to determine whether a particular transition's dipole matrix element will vanish and, as a result, the electronic transition will be "forbidden" and thus predicted to have zero intensity. If the direct product of the symmetries of the initial and final electronic states do not match the symmetry of the electric dipole operator (which has the symmetry of its x, y, and z components) the matrix element will vanish.
    • 15.4: Time Correlation Function Expressions for Transition Rates
      The first-order "golden-rule" expression for the rates of photon-induced transitions can be recast into a form in which certain specific physical models are easily introduced, By using so-called equilibrium averaged time correlation functions, it is possible to obtain rate expressions appropriate to a large number of molecules that exist in a distribution of initial states (e.g., for molecules that occupy many possible rotational and perhaps several vibrational levels at room temperature).

    Thumbnail: Analysis of white light by dispersing it with a prism is an example of spectroscopy. (CC BY-SA 3.0; D-Kuru).

    This page titled 15: Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jack Simons via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.