.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/spectro/nmr/plot_01_nmr_multiplets.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_01_nmr_multiplets.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_spectro_nmr_plot_01_nmr_multiplets.py:


Spin-spin (J) coupling and the n+1 rule: ethanol's triplet/quartet and a doublet of triplets
=============================================================================================

Indirect spin-spin coupling carried through the bonding electrons
(Ramsey and Purcell, 1952) splits an NMR resonance into a multiplet. The
splitting is :math:`J` Hz regardless of field strength. In the
first-order limit, :math:`n` equivalent spin-1/2 neighbours give
:math:`n+1` lines with Pascal's-triangle intensities. This example
simulates ethanol's -CH3 triplet and -CH2- quartet, then a doublet of
triplets from two inequivalent coupling partners with different
:math:`J` values.

.. GENERATED FROM PYTHON SOURCE LINES 16-29

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

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

    freq_mhz = 400.0
    ch3 = first_order_multiplet(chemical_shift_ppm=1.2, j_coupling_hz=7.0, n_neighbors=2, spectrometer_frequency_mhz=freq_mhz)  # split by CH2's 2 H's -> triplet
    ch2 = first_order_multiplet(chemical_shift_ppm=3.7, j_coupling_hz=7.0, n_neighbors=3, spectrometer_frequency_mhz=freq_mhz)  # split by CH3's 3 H's -> quartet

    print(f"CH3 triplet positions (ppm): {np.round(ch3.positions, 4)}, intensities: {ch3.intensities}")
    print(f"CH2 quartet positions (ppm): {np.round(ch2.positions, 4)}, intensities: {ch2.intensities}")





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

 .. code-block:: none

    CH3 triplet positions (ppm): [1.1825 1.2    1.2175], intensities: [1. 2. 1.]
    CH2 quartet positions (ppm): [3.6738 3.6912 3.7088 3.7262], intensities: [1. 3. 3. 1.]




.. GENERATED FROM PYTHON SOURCE LINES 30-39

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    plot_stick_spectrum(ch3, ax=axes[0], color="steelblue")
    axes[0].set_title("Ethanol -CH3 (triplet)")
    axes[0].set_xlabel("chemical shift (ppm)")
    plot_stick_spectrum(ch2, ax=axes[1], color="crimson")
    axes[1].set_title("Ethanol -CH2- (quartet)")
    axes[1].set_xlabel("chemical shift (ppm)")
    fig.tight_layout()




.. image-sg:: /api/gallery/spectro/nmr/images/sphx_glr_plot_01_nmr_multiplets_001.png
   :alt: Ethanol -CH3 (triplet), Ethanol -CH2- (quartet)
   :srcset: /api/gallery/spectro/nmr/images/sphx_glr_plot_01_nmr_multiplets_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 40-43

A genuine doublet of triplets: one neighbor with J1=12 Hz, two
equivalent neighbors with J2=5 Hz -- 6 distinct lines, total relative
intensity conserved at (1+1)*(1+2+1)=8:

.. GENERATED FROM PYTHON SOURCE LINES 43-56

.. code-block:: Python


    dt = multi_coupling_multiplet(chemical_shift_ppm=5.5, couplings=[(12.0, 1), (5.0, 2)], spectrometer_frequency_mhz=freq_mhz)
    print(f"\nDoublet-of-triplets: {len(dt.positions)} lines, total intensity {np.sum(dt.intensities):.1f}")
    print(f"Positions (ppm): {np.round(dt.positions, 4)}")
    print(f"Intensities: {dt.intensities}")

    fig2, ax2 = plt.subplots(figsize=(7, 4))
    x = np.linspace(dt.positions[0] - 0.02, dt.positions[-1] + 0.02, 3000)
    plot_broadened_spectrum(dt, x, ax=ax2, shape="lorentzian", fwhm=0.002, color="darkgreen")
    ax2.set_xlabel("chemical shift (ppm)")
    ax2.set_title("Doublet of triplets (J1=12 Hz, J2=5 Hz)")
    fig2.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/spectro/nmr/images/sphx_glr_plot_01_nmr_multiplets_002.png
   :alt: Doublet of triplets (J1=12 Hz, J2=5 Hz)
   :srcset: /api/gallery/spectro/nmr/images/sphx_glr_plot_01_nmr_multiplets_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Doublet-of-triplets: 6 lines, total intensity 8.0
    Positions (ppm): [5.4725 5.485  5.4975 5.5025 5.515  5.5275]
    Intensities: [1. 2. 1. 1. 2. 1.]





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

   **Total running time of the script:** (0 minutes 0.096 seconds)


.. _sphx_glr_download_api_gallery_spectro_nmr_plot_01_nmr_multiplets.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_nmr_multiplets.ipynb <plot_01_nmr_multiplets.ipynb>`

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

      :download:`Download Python source code: plot_01_nmr_multiplets.py <plot_01_nmr_multiplets.py>`

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

      :download:`Download zipped: plot_01_nmr_multiplets.zip <plot_01_nmr_multiplets.zip>`


.. only:: html

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

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