.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/electron_transfer/plot_01_rehm_weller_quenching.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_electron_transfer_plot_01_rehm_weller_quenching.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_photochem_electron_transfer_plot_01_rehm_weller_quenching.py:


Rehm-Weller equation: electron-transfer quenching vs. driving force
=====================================================================

Rehm and Weller (1970) measured how fast many donor-acceptor pairs quench
fluorescence by electron transfer in acetonitrile and found that the
quenching rate constant depends on a single quantity, the
electron-transfer free energy
:math:`\Delta G_{ET}=E_{ox}(D)-E_{red}(A)-E_{00}+w`
(:func:`~chemistrykit.photochem.rehm_weller_free_energy`). Their empirical
curve (:func:`~chemistrykit.photochem.rehm_weller_quenching_rate`) is
diffusion-limited for exergonic transfer and falls off exponentially for
endergonic transfer; it does not show the Marcus inverted region at very
negative :math:`\Delta G_{ET}`.

.. GENERATED FROM PYTHON SOURCE LINES 18-47



.. image-sg:: /api/gallery/photochem/electron_transfer/images/sphx_glr_plot_01_rehm_weller_quenching_001.png
   :alt: Rehm-Weller: quenching rate vs. electron-transfer free energy
   :srcset: /api/gallery/photochem/electron_transfer/images/sphx_glr_plot_01_rehm_weller_quenching_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    E_ox = 0.8 V: dG_ET = -0.56 eV, kq = 1.32e+10 1/(M s)
    E_ox = 1.0 V: dG_ET = -0.36 eV, kq = 1.18e+10 1/(M s)
    E_ox = 1.2 V: dG_ET = -0.16 eV, kq = 6.86e+09 1/(M s)
    E_ox = 1.4 V: dG_ET = +0.04 eV, kq = 5.11e+08 1/(M s)
    E_ox = 1.6 V: dG_ET = +0.24 eV, kq = 1.21e+06 1/(M s)
    E_ox = 1.8 V: dG_ET = +0.44 eV, kq = 7.60e+02 1/(M s)






|

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import rehm_weller_free_energy, rehm_weller_quenching_rate

    dG = np.linspace(-2.0, 1.0, 400)
    kq = rehm_weller_quenching_rate(dG)

    # A series of hypothetical donors quenching an excited acceptor with
    # E00 = 2.9 eV and E_red = -1.6 V (vs. SCE).
    E_ox = np.array([0.8, 1.0, 1.2, 1.4, 1.6, 1.8])
    dG_pairs = np.array([rehm_weller_free_energy(E, -1.6, 2.9, work_term=-0.06) for E in E_ox])
    rng = np.random.default_rng(7)
    kq_meas = rehm_weller_quenching_rate(dG_pairs) * np.exp(rng.normal(0.0, 0.1, E_ox.size))

    fig, ax = plt.subplots()
    ax.semilogy(dG, kq, label="Rehm-Weller equation")
    ax.semilogy(dG_pairs, kq_meas, "o", label="donor series")
    ax.axhline(2.0e10 / 1.25, color="k", ls=":", label="diffusion plateau")
    ax.set_xlabel(r"$\Delta G_{ET}$ (eV)")
    ax.set_ylabel(r"$k_q$ (M$^{-1}$ s$^{-1}$)")
    ax.set_title("Rehm-Weller: quenching rate vs. electron-transfer free energy")
    ax.legend()
    fig.tight_layout()

    for E, g, k in zip(E_ox, dG_pairs, kq_meas):
        print(f"E_ox = {E:.1f} V: dG_ET = {g:+.2f} eV, kq = {k:.2e} 1/(M s)")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.059 seconds)


.. _sphx_glr_download_api_gallery_photochem_electron_transfer_plot_01_rehm_weller_quenching.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_rehm_weller_quenching.ipynb <plot_01_rehm_weller_quenching.ipynb>`

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

      :download:`Download Python source code: plot_01_rehm_weller_quenching.py <plot_01_rehm_weller_quenching.py>`

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

      :download:`Download zipped: plot_01_rehm_weller_quenching.zip <plot_01_rehm_weller_quenching.zip>`


.. only:: html

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

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