.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/spectro/rotational/plot_02_microwave_isotope_shift.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_spectro_rotational_plot_02_microwave_isotope_shift.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_spectro_rotational_plot_02_microwave_isotope_shift.py:


Microwave spectroscopy and the isotope shift: CO isotopologues' J=1-0 lines in GHz
===================================================================================

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 :math:`\mu_a/\mu_b`, the ratio
:func:`~chemistrykit.spectro.systems.rotational.isotope_shift_ratio`
predicts. This example computes the :math:`J=1\leftarrow0` lines of
:math:`^{12}\mathrm{C}^{16}\mathrm{O}`,
:math:`^{13}\mathrm{C}^{16}\mathrm{O}` and
:math:`^{12}\mathrm{C}^{18}\mathrm{O}` in GHz and compares them with the
measured values (115.271, 110.201 and 109.782 GHz).

.. GENERATED FROM PYTHON SOURCE LINES 21-43

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    import scipy.constants as sc

    from chemistrykit.quantum.systems.rigid_rotor import RigidRotor
    from chemistrykit.spectro.systems.rotational import isotope_shift_ratio, rotational_line_wavenumbers

    u = sc.atomic_mass
    r_co = 113.09e-12  # m, ground-state (r_0) C-O bond length, shared by all isotopologues
    isotopologues = {
        "12C16O": (12.000 * u, 15.995 * u, 115.271),
        "13C16O": (13.003 * u, 15.995 * u, 110.201),
        "12C18O": (12.000 * u, 17.999 * u, 109.782),
    }

    frequencies_ghz = {}
    for name, (m_c, m_o, measured) in isotopologues.items():
        rotor = RigidRotor.from_diatomic(mass1=m_c, mass2=m_o, bond_length=r_co)
        nu_cm = rotational_line_wavenumbers(rotor, J_max=4)
        frequencies_ghz[name] = nu_cm * 100.0 * sc.c / 1e9
        print(f"{name}: J=1<-0 predicted {frequencies_ghz[name][0]:.3f} GHz, measured {measured:.3f} GHz")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    12C16O: J=1<-0 predicted 115.269 GHz, measured 115.271 GHz
    13C16O: J=1<-0 predicted 110.189 GHz, measured 110.201 GHz
    12C18O: J=1<-0 predicted 109.768 GHz, measured 109.782 GHz




.. GENERATED FROM PYTHON SOURCE LINES 44-47

The frequency ratio for any isotopologue pair is the inverse ratio of
their reduced masses. It is the same for every line, and it matches
``isotope_shift_ratio``:

.. GENERATED FROM PYTHON SOURCE LINES 47-53

.. code-block:: Python


    ratio_13c = isotope_shift_ratio(mass1a=12.000 * u, mass2=15.995 * u, mass1b=13.003 * u)
    observed_ratio = frequencies_ghz["13C16O"] / frequencies_ghz["12C16O"]
    print(f"isotope_shift_ratio(12C->13C) = {ratio_13c:.5f}; line-by-line ratios {np.round(observed_ratio, 5)}")
    print(f"Measured ratio 110.201/115.271 = {110.201 / 115.271:.5f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    isotope_shift_ratio(12C->13C) = 0.95593; line-by-line ratios [0.95593 0.95593 0.95593 0.95593 0.95593]
    Measured ratio 110.201/115.271 = 0.95602




.. GENERATED FROM PYTHON SOURCE LINES 54-64

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(10, 4))
    colors = {"12C16O": "black", "13C16O": "tab:blue", "12C18O": "tab:red"}
    for name, freqs in frequencies_ghz.items():
        ax.vlines(freqs, 0.0, 1.0, color=colors[name], lw=2, label=name)
    ax.set_xlabel("frequency (GHz)")
    ax.set_yticks([])
    ax.set_title("CO rotational lines in the microwave: heavier isotopologues shift down")
    ax.legend()
    fig.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/spectro/rotational/images/sphx_glr_plot_02_microwave_isotope_shift_001.png
   :alt: CO rotational lines in the microwave: heavier isotopologues shift down
   :srcset: /api/gallery/spectro/rotational/images/sphx_glr_plot_02_microwave_isotope_shift_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.027 seconds)


.. _sphx_glr_download_api_gallery_spectro_rotational_plot_02_microwave_isotope_shift.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_microwave_isotope_shift.ipynb <plot_02_microwave_isotope_shift.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_microwave_isotope_shift.py <plot_02_microwave_isotope_shift.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_microwave_isotope_shift.zip <plot_02_microwave_isotope_shift.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_