.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/energy_transfer/plot_02_dexter_exchange_transfer.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_energy_transfer_plot_02_dexter_exchange_transfer.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_photochem_energy_transfer_plot_02_dexter_exchange_transfer.py:


Dexter exchange energy transfer: exponential fall-off with distance
=====================================================================

Dexter (1953) described a second energy-transfer mechanism in which the
donor and acceptor swap electrons, which needs their orbitals to overlap.
Its rate, :math:`k_{ET}=KJ\exp(-2r/L)`
(:func:`~chemistrykit.photochem.dexter_rate`), therefore dies off
exponentially within a few Å of contact, and because electron exchange
conserves total spin it can move triplet energy (triplet sensitization),
which dipole-dipole Förster coupling cannot. The log-scale plot shows the
straight line of an exponential law, with the slope set by :math:`L`.

.. GENERATED FROM PYTHON SOURCE LINES 16-34

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import dexter_rate

    r = np.linspace(0.0, 15.0, 300)  # edge-to-edge distance, Angstrom
    K, J = 1.0e13, 1.0  # s^-1, normalized overlap
    fig, ax = plt.subplots()
    for L in (1.0, 2.0, 3.0):
        ax.semilogy(r, dexter_rate(r, K, J, L), label=f"$L$ = {L:.0f} Å")
    ax.axhline(1.0e5, color="k", ls=":", label=r"triplet decay rate ~$10^5$ s$^{-1}$")
    ax.set_ylim(1e-2, 2e13)
    ax.set_xlabel("Donor-acceptor edge-to-edge distance $r$ (Å)")
    ax.set_ylabel(r"$k_{ET}$ (s$^{-1}$)")
    ax.set_title(r"Dexter exchange transfer: $k_{ET}=KJ\,e^{-2r/L}$")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/photochem/energy_transfer/images/sphx_glr_plot_02_dexter_exchange_transfer_001.png
   :alt: Dexter exchange transfer: $k_{ET}=KJ\,e^{-2r/L}$
   :srcset: /api/gallery/photochem/energy_transfer/images/sphx_glr_plot_02_dexter_exchange_transfer_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 35-36

Distance at which exchange transfer still outcompetes a 10 us triplet.

.. GENERATED FROM PYTHON SOURCE LINES 36-41

.. code-block:: Python

    for L in (1.0, 2.0, 3.0):
        r_max = 0.5 * L * np.log(K * J / 1.0e5)
        print(f"L = {L:.0f} A: triplet-triplet transfer dominates out to r = {r_max:.1f} A")

    plt.show()




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

 .. code-block:: none

    L = 1 A: triplet-triplet transfer dominates out to r = 9.2 A
    L = 2 A: triplet-triplet transfer dominates out to r = 18.4 A
    L = 3 A: triplet-triplet transfer dominates out to r = 27.6 A





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

   **Total running time of the script:** (0 minutes 0.055 seconds)


.. _sphx_glr_download_api_gallery_photochem_energy_transfer_plot_02_dexter_exchange_transfer.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_02_dexter_exchange_transfer.ipynb <plot_02_dexter_exchange_transfer.ipynb>`

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

      :download:`Download Python source code: plot_02_dexter_exchange_transfer.py <plot_02_dexter_exchange_transfer.py>`

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

      :download:`Download zipped: plot_02_dexter_exchange_transfer.zip <plot_02_dexter_exchange_transfer.zip>`


.. only:: html

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

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