.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/quantum_yield/plot_03_vavilov_excitation_independence.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_photochem_quantum_yield_plot_03_vavilov_excitation_independence.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_photochem_quantum_yield_plot_03_vavilov_excitation_independence.py:


Vavilov's law: fluorescence quantum yield is independent of excitation wavelength
===================================================================================

Vavilov found (1922-1927) that a dye's fluorescence quantum yield does not
change when it is excited at shorter, more energetic wavelengths. The
reason is that ultrafast internal conversion carries any higher excited
state down to :math:`S_1` before emission, so the yield depends only on the
:math:`S_1` rate constants,
:math:`\Phi_f=k_f/(k_f+k_{ic}+k_{isc})`
(:func:`~chemistrykit.photochem.fluorescence_quantum_yield`). Below, a
model dye with an :math:`S_0\to S_1` band near 480 nm and an
:math:`S_0\to S_2` band near 330 nm is excited across its whole
absorption spectrum; :func:`~chemistrykit.photochem.kasha_emission_yields`
gives the :math:`S_1` fluorescence yield for each state reached.

.. GENERATED FROM PYTHON SOURCE LINES 19-53



.. image-sg:: /api/gallery/photochem/quantum_yield/images/sphx_glr_plot_03_vavilov_excitation_independence_001.png
   :alt: Model dye absorption: $S_0\to S_2$ (330 nm) and $S_0\to S_1$ (480 nm), Vavilov's law: flat fluorescence quantum yield
   :srcset: /api/gallery/photochem/quantum_yield/images/sphx_glr_plot_03_vavilov_excitation_independence_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Phi_f spans 0.571423 to 0.571429 across 300-520 nm (S1 value 0.571429)






|

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import fluorescence_quantum_yield, kasha_emission_yields

    kf, kic, kisc = 2.0e8, 1.0e8, 0.5e8  # S1 rate constants, 1/s
    kf2, k_ic21 = 1.0e8, 1.0e13  # S2 radiative and S2 -> S1 internal conversion
    phi_S1 = fluorescence_quantum_yield(kf, kic, kisc)

    wavelength = np.linspace(300.0, 520.0, 300)
    band_S1 = np.exp(-(((wavelength - 480.0) / 20.0) ** 2))
    band_S2 = 1.6 * np.exp(-(((wavelength - 330.0) / 18.0) ** 2))
    frac_S2 = band_S2 / (band_S1 + band_S2)  # fraction of absorptions landing in S2

    _, phi_via_S2 = kasha_emission_yields(kf2, k_ic21, kf, kic + kisc, excite="S2")
    _, phi_via_S1 = kasha_emission_yields(kf2, k_ic21, kf, kic + kisc, excite="S1")
    phi_f = frac_S2 * phi_via_S2 + (1.0 - frac_S2) * phi_via_S1

    fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(6, 6))
    ax1.plot(wavelength, band_S1 + band_S2)
    ax1.set_ylabel("Absorbance (a.u.)")
    ax1.set_title("Model dye absorption: $S_0\\to S_2$ (330 nm) and $S_0\\to S_1$ (480 nm)")
    ax2.plot(wavelength, phi_f)
    ax2.axhline(phi_S1, color="k", ls=":", label=r"$k_f/(k_f+k_{ic}+k_{isc})$")
    ax2.set_ylim(0, 1)
    ax2.set_xlabel("Excitation wavelength (nm)")
    ax2.set_ylabel(r"$\Phi_f$")
    ax2.set_title("Vavilov's law: flat fluorescence quantum yield")
    ax2.legend()
    fig.tight_layout()

    print(f"Phi_f spans {phi_f.min():.6f} to {phi_f.max():.6f} across 300-520 nm (S1 value {phi_S1:.6f})")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.062 seconds)


.. _sphx_glr_download_api_gallery_photochem_quantum_yield_plot_03_vavilov_excitation_independence.py:

.. only:: html

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

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      :download:`Download Jupyter notebook: plot_03_vavilov_excitation_independence.ipynb <plot_03_vavilov_excitation_independence.ipynb>`

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

      :download:`Download Python source code: plot_03_vavilov_excitation_independence.py <plot_03_vavilov_excitation_independence.py>`

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

      :download:`Download zipped: plot_03_vavilov_excitation_independence.zip <plot_03_vavilov_excitation_independence.zip>`


.. only:: html

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

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