:orphan:



.. _sphx_glr_examples:

.. _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`.


.. raw:: html

    <div class="sphx-glr-clear"></div>



.. _sphx_glr_examples_1D_simulation(crystalline):


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-thumbcontainer" tooltip="²⁹Si (I=1/2) spinning sideband simulation.">

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_0_Wollastonite_thumb.png
     :alt: Wollastonite, ²⁹Si (I=1/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_0_Wollastonite

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_1_PotassiumSulfate_thumb.png
     :alt: Potassium Sulfate, ³³S (I=3/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_1_PotassiumSulfate

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_2_Coesite_thumb.png
     :alt: Coesite, ¹⁷O (I=5/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_2_Coesite

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_3_quad_csa_thumb.png
     :alt: Non-coincidental Quad and CSA, ¹⁷O (I=5/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_3_quad_csa

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_4_satellite_transition_sim_thumb.png
     :alt: Arbitrary spin transition (single-quantum)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_4_satellite_transition_sim

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_5_multi-quantum_spectrum_thumb.png
     :alt: Arbitrary spin transition (multi-quantum)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_5_multi-quantum_spectrum

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_6_dipolar_coupled_thumb.png
     :alt: Coupled spin-1/2 (Static dipolar spectrum)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_6_dipolar_coupled

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_7_CAS_dipolar_J_thumb.png
     :alt: Coupled spin-1/2 (CSA + heteronuclear dipolar + J-couplings)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_7_CAS_dipolar_J

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(crystalline)/images/thumb/sphx_glr_plot_9_custom_method_Hahnecho_thumb.png
     :alt: Writing Custom methods (HahnEcho)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(crystalline)/plot_9_custom_method_Hahnecho
.. raw:: html

    <div class="sphx-glr-clear"></div>



.. _sphx_glr_examples_1D_simulation(macro_amorphous):


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

.. only:: html

 .. figure:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_0_protein_GB1_thumb.png
     :alt: Protein GB1, ¹³C and ¹⁵N (I=1/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(macro_amorphous)/plot_0_protein_GB1

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_3_amorphous_like_thumb.png
     :alt: Amorphous material, ²⁹Si (I=1/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(macro_amorphous)/plot_3_amorphous_like

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_4_amorphous_like_quad_thumb.png
     :alt: Amorphous material, ²⁷Al (I=5/2)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(macro_amorphous)/plot_4_amorphous_like_quad

.. raw:: html

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

.. only:: html

 .. figure:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_5_czjzek_distribution_thumb.png
     :alt: Czjzek distribution (Shielding and Quadrupolar)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(macro_amorphous)/plot_5_czjzek_distribution

.. 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

 .. figure:: /examples/1D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_6_extended_czjzek_thumb.png
     :alt: Extended Czjzek distribution (Shielding and Quadrupolar)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/1D_simulation(macro_amorphous)/plot_6_extended_czjzek
.. raw:: html

    <div class="sphx-glr-clear"></div>



.. _sphx_glr_examples_2D_simulation(crystalline):


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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_0_MQMAS_RbNO3_thumb.png
     :alt: RbNO₃, ⁸⁷Rb (I=3/2) 3QMAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_0_MQMAS_RbNO3

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_1_MQMAS_albite_thumb.png
     :alt: Albite, ²⁷Al (I=5/2) 3QMAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_1_MQMAS_albite

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_1_STMAS_RbNO3_thumb.png
     :alt: RbNO₃, ⁸⁷Rb (I=3/2) STMAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_1_STMAS_RbNO3

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_2_SAS_Rb2SO4_thumb.png
     :alt: Rb₂SO₄, ⁸⁷Rb (I=3/2) SAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_2_SAS_Rb2SO4

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_3_SAS_Rb2CrO4_thumb.png
     :alt: Rb₂CrO₄, ⁸⁷Rb (I=3/2) SAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_3_SAS_Rb2CrO4

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_4_3QMAS_Coesite_thumb.png
     :alt: Coesite, ¹⁷O (I=5/2) 3QMAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_4_3QMAS_Coesite

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_4_DAS_Coesite_thumb.png
     :alt: Coesite, ¹⁷O (I=5/2) DAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_4_DAS_Coesite

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_5_COASTER_Rb2CrO4_thumb.png
     :alt: Rb₂CrO₄, ⁸⁷Rb (I=3/2) COASTER

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_5_COASTER_Rb2CrO4

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_6_PASS_itraconazole_drug_thumb.png
     :alt: Itraconazole, ¹³C (I=1/2) PASS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_6_PASS_itraconazole_drug

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_7_QSSB_Rb2SO4_thumb.png
     :alt: Rb₂SO₄, ⁸⁷Rb (I=3/2) QMAT

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_7_QSSB_Rb2SO4

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_8_MAF_thumb.png
     :alt: Wollastonite, ²⁹Si (I=1/2), MAF

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_8_MAF

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(crystalline)/images/thumb/sphx_glr_plot_9_shifting-d_thumb.png
     :alt: MCl₂.2D₂O, ²H (I=1) Shifting-d echo

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(crystalline)/plot_9_shifting-d
.. raw:: html

    <div class="sphx-glr-clear"></div>



.. _sphx_glr_examples_2D_simulation(macro_amorphous):

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

.. only:: html

 .. figure:: /examples/2D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_0_crystalline_disorder_thumb.png
     :alt: Simulating site disorder (crystalline)

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(macro_amorphous)/plot_0_crystalline_disorder

.. raw:: html

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

.. only:: html

 .. figure:: /examples/2D_simulation(macro_amorphous)/images/thumb/sphx_glr_plot_1_I=2.5_thumb.png
     :alt: Czjzek distribution, ²⁷Al (I=5/2) 3QMAS

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

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /examples/2D_simulation(macro_amorphous)/plot_1_I=2.5
.. raw:: html

    <div class="sphx-glr-clear"></div>



.. only :: html

 .. container:: sphx-glr-footer
    :class: 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>`_