.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/spectro/electronic/plot_01_franck_condon.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_electronic_plot_01_franck_condon.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_spectro_electronic_plot_01_franck_condon.py:


Franck-Condon vibronic progressions in a UV-Vis absorption band
====================================================================

Builds a vibronic progression from the Huang-Rhys displacement
parameter, verifies the Franck-Condon factors' normalization (they must
sum to 1 -- the required correctness check for any Franck-Condon
calculation), and shows how a larger excited-state displacement shifts
the most-intense vibronic peak to higher `v'`.

.. GENERATED FROM PYTHON SOURCE LINES 13-28

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.spectro.systems.electronic import franck_condon_progression, franck_condon_spectrum, huang_rhys_factor
    from chemistrykit.spectro.visualizers.spectro_plots import plot_broadened_spectrum, plot_stick_spectrum

    # A displaced excited-state potential energy surface, characterized by
    # the Huang-Rhys parameter S.
    S = huang_rhys_factor(displacement=3.0e-11, mass=1.6e-27, angular_frequency=4.0e13)
    print(f"Huang-Rhys parameter S = {S:.3f}")

    progression = franck_condon_progression(v_max=25, S=S)
    print(f"Sum of Franck-Condon factors (should be ~1): {np.sum(progression):.6f}")
    print(f"Most probable transition: 0 -> {int(np.argmax(progression))} (S = {S:.2f})")





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

 .. code-block:: none

    Huang-Rhys parameter S = 0.273
    Sum of Franck-Condon factors (should be ~1): 1.000000
    Most probable transition: 0 -> 0 (S = 0.27)




.. GENERATED FROM PYTHON SOURCE LINES 29-32

Building the full vibronic spectrum -- stick positions at the
electronic origin plus v' quanta of excited-state vibrational spacing,
stick heights the Franck-Condon factors:

.. GENERATED FROM PYTHON SOURCE LINES 32-47

.. code-block:: Python


    spectrum = franck_condon_spectrum(origin_wavenumber=22000.0, vibrational_wavenumber=1400.0, S=S, v_max=12)

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4))
    plot_stick_spectrum(spectrum, ax=ax1, color="darkviolet")
    ax1.set_xlabel("wavenumber (cm^-1)")
    ax1.set_title(f"Vibronic stick spectrum (S={S:.2f})")

    x = np.linspace(spectrum.positions[0] - 500.0, spectrum.positions[-1] + 500.0, 2000)
    plot_broadened_spectrum(spectrum, x, ax=ax2, shape="gaussian", fwhm=250.0, color="indigo")
    ax2.set_xlabel("wavenumber (cm^-1)")
    ax2.set_title("Simulated absorption band")

    fig.tight_layout()




.. image-sg:: /api/gallery/spectro/electronic/images/sphx_glr_plot_01_franck_condon_001.png
   :alt: Vibronic stick spectrum (S=0.27), Simulated absorption band
   :srcset: /api/gallery/spectro/electronic/images/sphx_glr_plot_01_franck_condon_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 48-52

A larger displacement (bigger S) shifts the peak of the vibronic
envelope to higher v' and broadens the whole progression -- the
textbook signature of a large geometry change upon electronic
excitation:

.. GENERATED FROM PYTHON SOURCE LINES 52-63

.. code-block:: Python


    fig2, ax3 = plt.subplots(figsize=(7, 4))
    for S_value in (0.5, 2.0, 5.0):
        prog = franck_condon_progression(v_max=20, S=S_value)
        ax3.plot(np.arange(len(prog)), prog, "o-", label=f"S={S_value}")
    ax3.set_xlabel("v'")
    ax3.set_ylabel("Franck-Condon factor")
    ax3.set_title("Vibronic progression shape vs. displacement")
    ax3.legend()
    fig2.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/spectro/electronic/images/sphx_glr_plot_01_franck_condon_002.png
   :alt: Vibronic progression shape vs. displacement
   :srcset: /api/gallery/spectro/electronic/images/sphx_glr_plot_01_franck_condon_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.115 seconds)


.. _sphx_glr_download_api_gallery_spectro_electronic_plot_01_franck_condon.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_franck_condon.ipynb <plot_01_franck_condon.ipynb>`

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

      :download:`Download Python source code: plot_01_franck_condon.py <plot_01_franck_condon.py>`

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

      :download:`Download zipped: plot_01_franck_condon.zip <plot_01_franck_condon.zip>`


.. only:: html

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

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