.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/crystal/lattice_energy/plot_02_kapustinskii.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_crystal_lattice_energy_plot_02_kapustinskii.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_crystal_lattice_energy_plot_02_kapustinskii.py:


Kapustinskii equation: lattice energy without a crystal structure
===================================================================

Kapustinskii (1956) replaced the structure-specific Madelung constant with
a near-universal constant per ion, so
:class:`~chemistrykit.crystal.systems.lattice_energy.KapustinskiiLatticeEnergy`
needs only the number of ions per formula unit, the charges, and the
ionic radii. On rock-salt halides it tracks the structure-based
Born-Lande value; it also handles salts of other structures (fluorite
CaF2) where no Madelung constant is supplied at all.

.. GENERATED FROM PYTHON SOURCE LINES 15-38

.. code-block:: Python

    import matplotlib.pyplot as plt

    from chemistrykit.crystal.systems.lattice_energy import BornLandeLatticeEnergy, KapustinskiiLatticeEnergy
    from chemistrykit.crystal.utils.reference_data import SHANNON_IONIC_RADII_PM as R
    from chemistrykit.crystal.utils.reference_data import average_born_exponent

    rock_salt = {
        # name: (cation, anion, r0 in pm, cation config, anion config)
        "LiF": ("Li+", "F-", 201.0, "He", "Ne"),
        "NaCl": ("Na+", "Cl-", 282.0, "Ne", "Ar"),
        "KCl": ("K+", "Cl-", 315.0, "Ar", "Ar"),
        "KBr": ("K+", "Br-", 330.0, "Ar", "Kr"),
        "RbI": ("Rb+", "I-", 367.0, "Kr", "Xe"),
    }
    kap, bl = [], []
    for name, (cat, an, r0, c1, c2) in rock_salt.items():
        U_k = KapustinskiiLatticeEnergy(2, 1, 1, R[cat], R[an]).lattice_energy() / 1000.0
        U_b = BornLandeLatticeEnergy(1, 1, r0 * 1e-12, average_born_exponent(c1, c2)).lattice_energy() / 1000.0
        kap.append(U_k)
        bl.append(U_b)
        print(f"{name:5s} Kapustinskii {U_k:7.1f}   Born-Lande {U_b:7.1f} kJ/mol   ({(U_k - U_b) / U_b:+.1%})")
        assert abs(U_k - U_b) / abs(U_b) < 0.08





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

 .. code-block:: none

    LiF   Kapustinskii  -960.8   Born-Lande -1006.6 kJ/mol   (-4.6%)
    NaCl  Kapustinskii  -746.2   Born-Lande  -753.4 kJ/mol   (-0.9%)
    KCl   Kapustinskii  -672.4   Born-Lande  -685.1 kJ/mol   (-1.9%)
    KBr   Kapustinskii  -645.7   Born-Lande  -658.3 kJ/mol   (-1.9%)
    RbI   Kapustinskii  -586.5   Born-Lande  -601.4 kJ/mol   (-2.5%)




.. GENERATED FROM PYTHON SOURCE LINES 39-42

Structures Kapustinskii needs no Madelung constant for: doubly charged
MgO (rock salt) and three-ion CaF2 (fluorite). Approximate experimental
values: MgO about -3800 kJ/mol, CaF2 about -2630 kJ/mol.

.. GENERATED FROM PYTHON SOURCE LINES 42-47

.. code-block:: Python

    U_mgo = KapustinskiiLatticeEnergy(2, 2, 2, R["Mg2+"], R["O2-"]).lattice_energy() / 1000.0
    U_caf2 = KapustinskiiLatticeEnergy(3, 2, 1, R["Ca2+"], R["F-"]).lattice_energy() / 1000.0
    print(f"\nMgO  (Kapustinskii): {U_mgo:7.1f} kJ/mol")
    print(f"CaF2 (Kapustinskii): {U_caf2:7.1f} kJ/mol")





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

 .. code-block:: none


    MgO  (Kapustinskii): -3799.3 kJ/mol
    CaF2 (Kapustinskii): -2638.1 kJ/mol




.. GENERATED FROM PYTHON SOURCE LINES 48-60

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(5.5, 5))
    ax.scatter(bl, kap)
    for name, x, y in zip(rock_salt, bl, kap, strict=True):
        ax.annotate(name, (x, y), textcoords="offset points", xytext=(5, -10))
    lims = [min(bl + kap) - 50, max(bl + kap) + 50]
    ax.plot(lims, lims, "k--", lw=0.8, label="perfect agreement")
    ax.set_xlabel("Born-Lande U (kJ/mol, needs structure)")
    ax.set_ylabel("Kapustinskii U (kJ/mol, radii only)")
    ax.set_title("Kapustinskii's structure-free estimate")
    ax.legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/crystal/lattice_energy/images/sphx_glr_plot_02_kapustinskii_001.png
   :alt: Kapustinskii's structure-free estimate
   :srcset: /api/gallery/crystal/lattice_energy/images/sphx_glr_plot_02_kapustinskii_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.042 seconds)


.. _sphx_glr_download_api_gallery_crystal_lattice_energy_plot_02_kapustinskii.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_kapustinskii.ipynb <plot_02_kapustinskii.ipynb>`

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

      :download:`Download Python source code: plot_02_kapustinskii.py <plot_02_kapustinskii.py>`

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

      :download:`Download zipped: plot_02_kapustinskii.zip <plot_02_kapustinskii.zip>`


.. only:: html

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

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