.. _sphx_glr_api_gallery_spectro_rotational:

Rotational spectra
-------------------

Rigid-rotor rotational spectra built on ``chemistrykit.quantum``'s rigid
rotor: quantized levels, evenly spaced transition wavenumbers and
Boltzmann line intensities, and microwave isotope shifts of CO
isotopologues.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Dennison (1926) gave the quantum-mechanical rotational energy levels E_J=\hbar^2J(J+1)/(2I). With the \Delta J=+1 selection rule, these levels produce absorption lines at 2B(J+1), which are evenly spaced by 2B. This example builds an HCl-like rigid rotor from chemistrykit.quantum, prints its level energies and line positions, checks the constant 2B spacing, and adds the Boltzmann-population intensity pattern seen in a real far-infrared or microwave spectrum.">

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  .. image:: /api/gallery/spectro/rotational/images/thumb/sphx_glr_plot_01_rotational_spectrum_thumb.png
    :alt:

  :doc:`/api/gallery/spectro/rotational/plot_01_rotational_spectrum`

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      <div class="sphx-glr-thumbnail-title">Dennison's quantized rigid rotor: HCl rotational lines spaced by 2B, with Boltzmann intensities</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Rotational lines of light molecules lie in the microwave region, which became routinely accessible after Cleeton and Williams (1934) and postwar microwave spectroscopy by Townes and others. Microwave frequencies can be measured very precisely, so isotope shifts are easy to see. Isotopic substitution leaves the bond length unchanged but changes the reduced mass, so every line of the heavier isotopologue moves down by \mu_a/\mu_b, the ratio isotope_shift_ratio predicts. This example computes the J=1\leftarrow0 lines of ^{12}\mathrm{C}^{16}\mathrm{O}, ^{13}\mathrm{C}^{16}\mathrm{O} and ^{12}\mathrm{C}^{18}\mathrm{O} in GHz and compares them with the measured values (115.271, 110.201 and 109.782 GHz).">

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  .. image:: /api/gallery/spectro/rotational/images/thumb/sphx_glr_plot_02_microwave_isotope_shift_thumb.png
    :alt:

  :doc:`/api/gallery/spectro/rotational/plot_02_microwave_isotope_shift`

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      <div class="sphx-glr-thumbnail-title">Microwave spectroscopy and the isotope shift: CO isotopologues' J=1-0 lines in GHz</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/spectro/rotational/plot_01_rotational_spectrum
   /api/gallery/spectro/rotational/plot_02_microwave_isotope_shift