.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/spectro/nmr/plot_03_karplus_vicinal_coupling.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_spectro_nmr_plot_03_karplus_vicinal_coupling.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_spectro_nmr_plot_03_karplus_vicinal_coupling.py:


The Karplus relation: vicinal 3J(H,H) coupling as a function of dihedral angle
===============================================================================

Karplus (1959) used valence-bond theory to show that the three-bond
(vicinal) H-C-C-H coupling constant depends on the dihedral angle
:math:`\phi`. It is large for eclipsed (0 degrees) and anti
(180 degrees) protons and nearly zero near 90 degrees. This lets a
measured :math:`^3J` report molecular conformation. This example plots
Karplus's 1959 curve from
:func:`~chemistrykit.spectro.systems.nmr.karplus_coupling`, reads off
the axial-axial and axial-equatorial couplings of a cyclohexane chair,
and shows the resulting doublet splittings.

.. GENERATED FROM PYTHON SOURCE LINES 17-34

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.spectro.systems.nmr import first_order_multiplet, karplus_coupling
    from chemistrykit.spectro.visualizers.spectro_plots import plot_broadened_spectrum

    phi = np.linspace(0.0, 180.0, 361)
    j_1959 = karplus_coupling(phi)

    # In an ideal cyclohexane chair, axial-axial vicinal protons are anti
    # (~180 degrees); axial-equatorial and equatorial-equatorial are gauche (~60 degrees).
    j_ax_ax = karplus_coupling(180.0)
    j_ax_eq = karplus_coupling(60.0)
    print(f"3J(axial-axial, 180 deg)  = {j_ax_ax:.2f} Hz")
    print(f"3J(axial-equatorial, 60 deg) = {j_ax_eq:.2f} Hz")
    print(f"3J at 90 deg = {karplus_coupling(90.0):.2f} Hz (minimum)")





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

 .. code-block:: none

    3J(axial-axial, 180 deg)  = 9.22 Hz
    3J(axial-equatorial, 60 deg) = 1.85 Hz
    3J at 90 deg = -0.28 Hz (minimum)




.. GENERATED FROM PYTHON SOURCE LINES 35-44

.. code-block:: Python

    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(11, 4))
    ax1.plot(phi, j_1959, color="tab:blue")
    for angle, label in ((60.0, "gauche (ax-eq)"), (180.0, "anti (ax-ax)")):
        ax1.plot(angle, karplus_coupling(angle), "o", color="tab:red")
        ax1.annotate(label, (angle, karplus_coupling(angle)), xytext=(-60, 10), textcoords="offset points", fontsize=9)
    ax1.set_xlabel(r"H-C-C-H dihedral angle $\phi$ (degrees)")
    ax1.set_ylabel(r"$^3J$ (Hz)")
    ax1.set_title("Karplus (1959) curve")




.. image-sg:: /api/gallery/spectro/nmr/images/sphx_glr_plot_03_karplus_vicinal_coupling_001.png
   :alt: Karplus (1959) curve
   :srcset: /api/gallery/spectro/nmr/images/sphx_glr_plot_03_karplus_vicinal_coupling_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Karplus (1959) curve')



.. GENERATED FROM PYTHON SOURCE LINES 45-47

The same proton coupled to one anti neighbour vs. one gauche
neighbour: a wide doublet vs. a narrow one.

.. GENERATED FROM PYTHON SOURCE LINES 47-59

.. code-block:: Python


    x = np.linspace(3.45, 3.55, 3000)
    wide = first_order_multiplet(chemical_shift_ppm=3.5, j_coupling_hz=j_ax_ax, n_neighbors=1, spectrometer_frequency_mhz=400.0)
    narrow = first_order_multiplet(chemical_shift_ppm=3.5, j_coupling_hz=j_ax_eq, n_neighbors=1, spectrometer_frequency_mhz=400.0)
    plot_broadened_spectrum(wide, x, ax=ax2, shape="lorentzian", fwhm=0.002, color="tab:red", label=f"anti: J = {j_ax_ax:.1f} Hz")
    plot_broadened_spectrum(narrow, x, ax=ax2, shape="lorentzian", fwhm=0.002, color="tab:green", label=f"gauche: J = {j_ax_eq:.1f} Hz")
    ax2.invert_xaxis()
    ax2.set_xlabel("chemical shift (ppm)")
    ax2.set_title("Doublet splitting reports the dihedral angle")
    ax2.legend()
    fig.tight_layout()
    plt.show()








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

   **Total running time of the script:** (0 minutes 0.083 seconds)


.. _sphx_glr_download_api_gallery_spectro_nmr_plot_03_karplus_vicinal_coupling.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_03_karplus_vicinal_coupling.ipynb <plot_03_karplus_vicinal_coupling.ipynb>`

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

      :download:`Download Python source code: plot_03_karplus_vicinal_coupling.py <plot_03_karplus_vicinal_coupling.py>`

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.. only:: html

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

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