:orphan:

.. _example_gallery:

==================
Simulation Gallery
==================

In this section, we use the **mrsimulator** tools to create spin systems and
simulate spectrum with practical/experimental applications. These examples illustrate

- building spin systems (uncoupled and weakly-coupled),
- building NMR methods,
- simulating spectrum, and
- processing spectrum (e.g. adding line-broadening).

For applications related to least-squares fitting, see the
:ref:`fitting_examples`.



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    <div class="sphx-glr-thumbnails">


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    </div>


1D NMR simulation (small molecules/crystalline solids)
------------------------------------------------------

The following examples are the NMR spectrum simulation of small molecules and crystalline
solids for the following methods:

- Bloch decay method (:py:class:`~mrsimulator.method.lib.BlochDecaySpectrum`),
- Central transition selective Bloch decay method (:py:class:`~mrsimulator.method.lib.BlochDecayCTSpectrum`).
- Generic one-dimensional method (:py:class:`~mrsimulator.method.lib.Method1D`).



.. raw:: html

    <div class="sphx-glr-thumbnails">


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="²⁹Si (I=1/2) spinning sideband simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_0_Wollastonite_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_0_Wollastonite.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wollastonite, ²⁹Si (I=1/2)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Simulating spectra of custom isotopes.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_10_custom_isotope_general_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_10_custom_isotope_general.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Using Custom Isotopes</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Simulating spectra of custom isotopes">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_11_custom_isotope_selective_excitation_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_11_custom_isotope_selective_excitation.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Selective Excitations using Custom Isotopes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The alpha-carbon resonance of glycine, 13C (I=1/2), attached to 14N (I=1). The 14N quadrupolar ...">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_12_quad_dipolar_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_12_quad_dipolar.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Influence of 14N on 13C NMR MAS spectra of glycine</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="³³S (I=3/2) quadrupolar spectrum simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_1_PotassiumSulfate_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_1_PotassiumSulfate.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Potassium Sulfate, ³³S (I=3/2)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="¹⁷O (I=5/2) quadrupolar spectrum simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_2_Coesite_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_2_Coesite.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Coesite, ¹⁷O (I=5/2)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹⁷O (I=5/2) quadrupolar static spectrum simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_3_quad_csa_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_3_quad_csa.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Non-coincidental Quad and CSA, ¹⁷O (I=5/2)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="²⁷Al (I=5/2) quadrupolar spectrum simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_4_satellite_transition_sim_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_4_satellite_transition_sim.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arbitrary spin transition (single-quantum)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="³³S (I=5/2) quadrupolar spectrum simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_5_multi-quantum_spectrum_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_5_multi-quantum_spectrum.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Arbitrary spin transition (multi-quantum)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹³C-¹H static dipolar coupling simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_6_dipolar_coupled_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_6_dipolar_coupled.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Coupled spin-1/2 (Static dipolar spectrum)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹³C-¹H sideband simulation">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_7_CAS_dipolar_J_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_7_CAS_dipolar_J.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Coupled spin-1/2 (CSA + heteronuclear dipolar + J-couplings)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Writing custom methods using the Event objects.">

.. only:: html

  .. image:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_9_custom_method_Hahnecho_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(crystalline)_plot_9_custom_method_Hahnecho.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Writing Custom methods (HahnEcho)</div>
    </div>


.. raw:: html

    </div>


1D NMR simulation (macromolecules/amorphous solids)
---------------------------------------------------

The following examples are the NMR spectrum simulation of macromolecules and amorphous
materials for the following methods:

- Bloch decay method (:py:class:`~mrsimulator.method.lib.BlochDecaySpectrum`),
- Central transition selective Bloch decay method (:py:class:`~mrsimulator.method.lib.BlochDecayCTSpectrum`).

For NMR simulation of amorphous solids, we also show examples of simulating spectrum
using user-defined model or using commonly accepted models such as Czjzek or extended
Czjzek distribution.



.. raw:: html

    <div class="sphx-glr-thumbnails">


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹³C/¹⁵N (I=1/2) spinning sideband simulation.">

.. only:: html

  .. image:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_0_protein_GB1_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(macro_amorphous)_plot_0_protein_GB1.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Protein GB1, ¹³C and ¹⁵N (I=1/2)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="²⁹Si (I=1/2) simulation of amorphous material.">

.. only:: html

  .. image:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_3_amorphous_like_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(macro_amorphous)_plot_3_amorphous_like.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Amorphous material, ²⁹Si (I=1/2)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="²⁷Al (I=5/2) simulation of amorphous material.">

.. only:: html

  .. image:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_4_amorphous_like_quad_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(macro_amorphous)_plot_4_amorphous_like_quad.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Amorphous material, ²⁷Al (I=5/2)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we illustrate the simulation of spectrum originating from a Czjzek distributio...">

.. only:: html

  .. image:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_5_czjzek_distribution_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(macro_amorphous)_plot_5_czjzek_distribution.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Czjzek distribution (Shielding and Quadrupolar)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we illustrate the simulation of spectrum originating from an extended Czjzek d...">

.. only:: html

  .. image:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_6_extended_czjzek_thumb.png
    :alt:

  :ref:`sphx_glr_examples_1D_simulation(macro_amorphous)_plot_6_extended_czjzek.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Extended Czjzek distribution (Shielding and Quadrupolar)</div>
    </div>


.. raw:: html

    </div>


2D NMR simulation (Crystalline solids)
--------------------------------------

The following examples are the NMR spectrum simulation for crystalline solids. The
examples include the illustrations for the following methods:

- Triple-quantum variable-angle spinning (i.e., 3Q-MAS) using the specialized
  :func:`~mrsimulator.method.lib.ThreeQ_VAS` method.
- Satellite-transition variable-angle spinning (i.e., ST-MAS) using the specialized
  :func:`~mrsimulator.method.lib.ST1_VAS` method.
- Switched Angle Spinning (SAS) using the generic :func:`~mrsimulator.method.Method` object.
- MAS-detected Dynamic Angle Spinning (DAS) using the generic :func:`~mrsimulator.method.Method` object.
- Correlation of Anisotropies Separated Through Echo Refocusing (COASTER) using the generic
  :func:`~mrsimulator.method.Method` object.
- Phase Adjusted Spinning Sidebands (PASS and QPASS) and Magic-Angle Turning (MAT and QMAT) using the
  specialized :func:`~mrsimulator.method.lib.SSB2D` method.



.. raw:: html

    <div class="sphx-glr-thumbnails">


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) triple-quantum magic-angle spinning (3Q-MAS) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_0_MQMAS_RbNO3_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_0_MQMAS_RbNO3.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RbNO₃, ⁸⁷Rb (I=3/2) 3QMAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="²⁷Al (I=5/2) triple-quantum magic-angle spinning (3Q-MAS) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_1_MQMAS_albite_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_1_MQMAS_albite.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Albite, ²⁷Al (I=5/2) 3QMAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) satellite-transition off magic-angle spinning simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_1_STMAS_RbNO3_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_1_STMAS_RbNO3.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RbNO₃, ⁸⁷Rb (I=3/2) STMAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) Switched-angle spinning (SAS) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_2_SAS_Rb2SO4_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_2_SAS_Rb2SO4.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Rb₂SO₄, ⁸⁷Rb (I=3/2) SAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Co59 (I=7/2) satellite-transition magic-angle spinning simulation. (Quad-coupling cross terms)">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_2_STMAS_quad_coupling_cross_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_2_STMAS_quad_coupling_cross.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Co59 (I=7/2) STMAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Co59 (I=7/2) satellite-transition magic-angle spinning simulation. (Quad-csa cross terms)">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_2_STMAS_quad_shield_cross_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_2_STMAS_quad_shield_cross.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Co59 (I=7/2) STMAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) Switched-angle spinning (SAS) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_3_SAS_Rb2CrO4_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_3_SAS_Rb2CrO4.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Rb₂CrO₄, ⁸⁷Rb (I=3/2) SAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹⁷O (I=5/2) 3QMAS simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_4_3QMAS_Coesite_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_4_3QMAS_Coesite.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Coesite, ¹⁷O (I=5/2) 3QMAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹⁷O (I=5/2) Dynamic-angle spinning (DAS) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_4_DAS_Coesite_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_4_DAS_Coesite.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Coesite, ¹⁷O (I=5/2) DAS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) Correlation of anisotropies separated through echo refocusing (COASTER) simulation...">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_5_COASTER_Rb2CrO4_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_5_COASTER_Rb2CrO4.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Rb₂CrO₄, ⁸⁷Rb (I=3/2) COASTER</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="¹³C (I=1/2) 2D Phase-adjusted spinning sideband (PASS) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_6_PASS_itraconazole_drug_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_6_PASS_itraconazole_drug.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Itraconazole, ¹³C (I=1/2) PASS</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) Quadrupolar Magic-angle turning (QMAT) simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_7_QSSB_Rb2SO4_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_7_QSSB_Rb2SO4.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Rb₂SO₄, ⁸⁷Rb (I=3/2) QMAT</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="²⁹Si (I=1/2) magic angle flipping.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_8_MAF_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_8_MAF.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wollastonite, ²⁹Si (I=1/2), MAF</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="²H (I=1) 2D NMR CSA-Quad 1st order correlation spectrum simulation.">

.. only:: html

  .. image:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_9_shifting-d_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(crystalline)_plot_9_shifting-d.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCl₂.2D₂O, ²H (I=1) Shifting-d echo</div>
    </div>


.. raw:: html

    </div>

2D NMR simulation (Disordered/Amorphous solids)
-----------------------------------------------

The following examples are the NMR spectrum simulation for amorphous solids. The
examples include the illustrations for the following methods:

- Triple-quantum variable-angle spinning (:func:`~mrsimulator.method.lib.ThreeQ_VAS`)

.. - Double hop Dynamic angle spinning (DAS)



.. raw:: html

    <div class="sphx-glr-thumbnails">


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="⁸⁷Rb (I=3/2) 3QMAS simulation with site disorder.">

.. only:: html

  .. image:: /examples/2D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_0_crystalline_disorder_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(macro_amorphous)_plot_0_crystalline_disorder.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Simulating site disorder (crystalline)</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="²⁷Al (I=5/2) 3QMAS simulation of amorphous material.">

.. only:: html

  .. image:: /examples/2D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_1_I=2.5_thumb.png
    :alt:

  :ref:`sphx_glr_examples_2D_simulation(macro_amorphous)_plot_1_I=2.5.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Czjzek distribution, ²⁷Al (I=5/2) 3QMAS</div>
    </div>


.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /examples/1D_simulation(crystalline)/index.rst
   /examples/1D_simulation(macro_amorphous)/index.rst
   /examples/2D_simulation(crystalline)/index.rst
   /examples/2D_simulation(macro_amorphous)/index.rst


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: examples_python.zip </examples/examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: examples_jupyter.zip </examples/examples_jupyter.zip>`


.. only:: html

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

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