.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/spectro/vibrational/plot_01_harmonic_vs_morse.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_vibrational_plot_01_harmonic_vs_morse.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_spectro_vibrational_plot_01_harmonic_vs_morse.py:


Harmonic vs. Morse IR band positions, and recovering anharmonicity from overtones
====================================================================================

Predicts HCl's fundamental IR absorption from a harmonic oscillator,
compares it against the exact (anharmonic) Morse-potential fundamental
and first overtone, then inverts the observed :math:`0\to1`/:math:`0\to2`
band positions to recover the spectroscopic constants
:math:`\omega_e`/:math:`\omega_ex_e` -- exactly the way real
anharmonicity constants are measured from an observed overtone spectrum.

.. GENERATED FROM PYTHON SOURCE LINES 14-34

.. code-block:: Python

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

    from chemistrykit.quantum.systems.harmonic_oscillator import MorseOscillator
    from chemistrykit.spectro.core.base_system import Spectrum
    from chemistrykit.spectro.systems.vibrational import anharmonicity_from_overtones, harmonic_fundamental_wavenumber, morse_transition_wavenumbers
    from chemistrykit.spectro.visualizers.spectro_plots import plot_stick_spectrum

    mu = (1.008 * 34.97) / (1.008 + 34.97) * sc.atomic_mass  # HCl-like reduced mass
    k = 480.0  # N/m
    De = 7.24e-19  # J, HCl-like dissociation energy

    harmonic_nu = harmonic_fundamental_wavenumber(force_constant=k, reduced_mass=mu)
    print(f"Harmonic fundamental: {harmonic_nu:.1f} cm^-1")

    morse = MorseOscillator(mass=mu, force_constant=k, dissociation_energy=De)
    nu01, nu02, nu03 = morse_transition_wavenumbers(morse, v_max=3)
    print(f"Morse fundamental (0->1): {nu01:.1f} cm^-1")
    print(f"Morse first overtone (0->2): {nu02:.1f} cm^-1 (would be {2 * nu01:.1f} cm^-1 if purely harmonic)")





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

 .. code-block:: none

    Harmonic fundamental: 2883.6 cm^-1
    Morse fundamental (0->1): 2769.5 cm^-1
    Morse first overtone (0->2): 5425.0 cm^-1 (would be 5539.1 cm^-1 if purely harmonic)




.. GENERATED FROM PYTHON SOURCE LINES 35-38

Recovering the spectroscopic constants from just these two observed
band positions -- exactly, no fitting -- and confirming they predict
the (unused, held-out) third overtone correctly:

.. GENERATED FROM PYTHON SOURCE LINES 38-45

.. code-block:: Python


    omega_e, omega_e_xe = anharmonicity_from_overtones(nu01, nu02)
    print(f"Recovered omega_e = {omega_e:.1f} cm^-1, omega_e*xe = {omega_e_xe:.2f} cm^-1")

    predicted_nu03 = 3.0 * omega_e - 12.0 * omega_e_xe
    print(f"Predicted 0->3 overtone: {predicted_nu03:.1f} cm^-1 (actual: {nu03:.1f} cm^-1)")





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

 .. code-block:: none

    Recovered omega_e = 2883.6 cm^-1, omega_e*xe = 57.04 cm^-1
    Predicted 0->3 overtone: 7966.4 cm^-1 (actual: 7966.4 cm^-1)




.. GENERATED FROM PYTHON SOURCE LINES 46-51

.. code-block:: Python

    spectrum = Spectrum(positions=[nu01, nu02, nu03], intensities=[1.0, 0.15, 0.02], labels=["0->1", "0->2", "0->3"])
    ax = plot_stick_spectrum(spectrum, color="darkorange")
    ax.set_xlabel("wavenumber (cm^-1)")
    ax.set_title("Morse-oscillator overtone progression (decreasing spacing)")
    plt.show()



.. image-sg:: /api/gallery/spectro/vibrational/images/sphx_glr_plot_01_harmonic_vs_morse_001.png
   :alt: Morse-oscillator overtone progression (decreasing spacing)
   :srcset: /api/gallery/spectro/vibrational/images/sphx_glr_plot_01_harmonic_vs_morse_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.025 seconds)


.. _sphx_glr_download_api_gallery_spectro_vibrational_plot_01_harmonic_vs_morse.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_harmonic_vs_morse.ipynb <plot_01_harmonic_vs_morse.ipynb>`

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

      :download:`Download Python source code: plot_01_harmonic_vs_morse.py <plot_01_harmonic_vs_morse.py>`

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

      :download:`Download zipped: plot_01_harmonic_vs_morse.zip <plot_01_harmonic_vs_morse.zip>`


.. only:: html

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

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