.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/structure/bonding/plot_02_pauling_bond_length.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_structure_bonding_plot_02_pauling_bond_length.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_structure_bonding_plot_02_pauling_bond_length.py:


Pauling's bond-order and bond-length correlation for carbon-carbon bonds
========================================================================

Linus Pauling (1947) related the length of a bond to its order,

.. math::

    D(n) = D(1) - c\,\log_{10} n,

with :math:`D(1) = 1.54` Å the C-C single bond and :math:`c = 0.71` Å for
carbon. The single, double and triple bonds of ethane, ethylene and
acetylene lie on the curve. Read backwards, it turns a measured length
into a bond order: benzene's 1.397 Å bond and graphite's 1.42 Å bond get
orders between 1 and 2. This example uses
:func:`~chemistrykit.structure.systems.bonding.bond_length_from_order` and
:func:`~chemistrykit.structure.systems.bonding.bond_order_from_length`.

.. GENERATED FROM PYTHON SOURCE LINES 21-34

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.structure.systems.bonding import PAULING_C_C_CONSTANT, bond_length_from_order, bond_order_from_length
    from chemistrykit.structure.visualizers.structure_plots import plot_bond_order_correlation

    D1 = 1.54  # ethane C-C, angstrom
    reference = {"ethane C-C": (1, 1.54), "ethylene C=C": (2, 1.339), "acetylene C#C": (3, 1.203)}
    for name, (n, measured) in reference.items():
        predicted = bond_length_from_order(D1, n)
        print(f"{name:14s}: order {n}, predicted {predicted:.3f} A, measured {measured:.3f} A")
        assert abs(predicted - measured) < 0.02





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

 .. code-block:: none

    ethane C-C    : order 1, predicted 1.540 A, measured 1.540 A
    ethylene C=C  : order 2, predicted 1.326 A, measured 1.339 A
    acetylene C#C : order 3, predicted 1.201 A, measured 1.203 A




.. GENERATED FROM PYTHON SOURCE LINES 35-40

Now read bond orders off measured lengths. Benzene's comes out near 1.6,
close to the 1 + 2/3 of Huckel-Coulson theory. Graphite, where each
carbon shares one pi bond among three neighbours (order 4/3), comes out
near 1.5: the ordering is right, but the correlation is empirical and
only good to about 0.1 in bond order.

.. GENERATED FROM PYTHON SOURCE LINES 40-46

.. code-block:: Python


    unknown = {"benzene": 1.397, "graphite": 1.421}
    estimated = {name: bond_order_from_length(D1, length) for name, length in unknown.items()}
    for name, n in estimated.items():
        print(f"{name:9s}: {unknown[name]:.3f} A -> bond order {n:.2f}")





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

 .. code-block:: none

    benzene  : 1.397 A -> bond order 1.59
    graphite : 1.421 A -> bond order 1.47




.. GENERATED FROM PYTHON SOURCE LINES 47-57

.. code-block:: Python

    ax = plot_bond_order_correlation(
        single_bond_length=D1, bond_orders=np.linspace(0.8, 3.3, 200), c=PAULING_C_C_CONSTANT, color="gray", label=r"$D(n) = 1.54 - 0.71\log_{10} n$"
    )
    for name, (n, measured) in reference.items():
        ax.scatter([n], [measured], zorder=3, label=name)
    for name, n in estimated.items():
        ax.scatter([n], [unknown[name]], marker="s", zorder=3, label=f"{name} (from length)")
    ax.set_ylabel("C-C bond length (angstrom)")
    ax.legend(fontsize=8)
    plt.show()



.. image-sg:: /api/gallery/structure/bonding/images/sphx_glr_plot_02_pauling_bond_length_001.png
   :alt: Pauling bond-order/bond-length correlation
   :srcset: /api/gallery/structure/bonding/images/sphx_glr_plot_02_pauling_bond_length_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.040 seconds)


.. _sphx_glr_download_api_gallery_structure_bonding_plot_02_pauling_bond_length.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_pauling_bond_length.ipynb <plot_02_pauling_bond_length.ipynb>`

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

      :download:`Download Python source code: plot_02_pauling_bond_length.py <plot_02_pauling_bond_length.py>`

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

      :download:`Download zipped: plot_02_pauling_bond_length.zip <plot_02_pauling_bond_length.zip>`


.. only:: html

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

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