.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/jablonski/plot_04_kasha_rule_emission_from_s1.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_jablonski_plot_04_kasha_rule_emission_from_s1.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_photochem_jablonski_plot_04_kasha_rule_emission_from_s1.py:


Kasha's rule: emission comes from the lowest excited state
============================================================

Kasha (1950) stated that emission comes almost entirely from the lowest
excited state of a given multiplicity (:math:`S_1` for fluorescence),
because internal conversion from higher states such as :math:`S_2` takes
picoseconds or less, much faster than emission. With
:func:`~chemistrykit.photochem.kasha_emission_yields`, a molecule excited
to :math:`S_2` sends only a tiny fraction of its emission from
:math:`S_2`; the exception is a molecule like azulene, whose large
:math:`S_2`-:math:`S_1` gap slows internal conversion enough for
:math:`S_2` emission to compete.

.. GENERATED FROM PYTHON SOURCE LINES 17-36

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import kasha_emission_yields

    kf2, kf1, knr1 = 1.0e8, 1.0e8, 1.0e8  # 1/s
    k_ic21 = np.logspace(7, 14, 200)  # S2 -> S1 internal conversion rate, 1/s
    phi2, phi1 = np.array([kasha_emission_yields(kf2, k, kf1, knr1) for k in k_ic21]).T

    fig, ax = plt.subplots()
    ax.semilogx(k_ic21, phi1 / (phi1 + phi2), label=r"share of emission from $S_1$")
    ax.semilogx(k_ic21, phi2 / (phi1 + phi2), label=r"share of emission from $S_2$")
    ax.axvspan(1e12, 1e14, color="0.9", label="typical $S_2\\to S_1$ internal conversion")
    ax.set_xlabel(r"$k_{ic}(S_2\to S_1)$ (s$^{-1}$)")
    ax.set_ylabel("Fraction of emitted photons")
    ax.set_title("Kasha's rule: fast internal conversion funnels emission to $S_1$")
    ax.legend(loc="center left")
    fig.tight_layout()




.. image-sg:: /api/gallery/photochem/jablonski/images/sphx_glr_plot_04_kasha_rule_emission_from_s1_001.png
   :alt: Kasha's rule: fast internal conversion funnels emission to $S_1$
   :srcset: /api/gallery/photochem/jablonski/images/sphx_glr_plot_04_kasha_rule_emission_from_s1_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 37-42

.. code-block:: Python

    for label, k in (("typical dye", 1e13), ("azulene-like (slow S2 -> S1)", 1e9)):
        p2, p1 = kasha_emission_yields(kf2, k, kf1, knr1)
        print(f"{label:30s}: Phi(S2 emission) = {p2:.2e}, Phi(S1 emission) = {p1:.3f}")

    plt.show()




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

 .. code-block:: none

    typical dye                   : Phi(S2 emission) = 1.00e-05, Phi(S1 emission) = 0.500
    azulene-like (slow S2 -> S1)  : Phi(S2 emission) = 9.09e-02, Phi(S1 emission) = 0.455





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

   **Total running time of the script:** (0 minutes 0.080 seconds)


.. _sphx_glr_download_api_gallery_photochem_jablonski_plot_04_kasha_rule_emission_from_s1.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_04_kasha_rule_emission_from_s1.ipynb <plot_04_kasha_rule_emission_from_s1.ipynb>`

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

      :download:`Download Python source code: plot_04_kasha_rule_emission_from_s1.py <plot_04_kasha_rule_emission_from_s1.py>`

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

      :download:`Download zipped: plot_04_kasha_rule_emission_from_s1.zip <plot_04_kasha_rule_emission_from_s1.zip>`


.. only:: html

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

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