.. _sphx_glr_api_gallery_spectro_nmr:

NMR spectroscopy
-----------------

Nuclear magnetic resonance: Larmor frequencies and the chemical shift,
first-order spin-spin coupling multiplets (the n+1 rule and a doublet of
triplets), the Karplus dihedral-angle dependence of vicinal couplings,
and Fourier-transform NMR from a free-induction decay.


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    <div class="sphx-glr-thumbcontainer" tooltip="Indirect spin-spin coupling carried through the bonding electrons (Ramsey and Purcell, 1952) splits an NMR resonance into a multiplet. The splitting is J Hz regardless of field strength. In the first-order limit, n equivalent spin-1/2 neighbours give n+1 lines with Pascal&#x27;s-triangle intensities. This example simulates ethanol&#x27;s -CH3 triplet and -CH2- quartet, then a doublet of triplets from two inequivalent coupling partners with different J values.">

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  .. image:: /api/gallery/spectro/nmr/images/thumb/sphx_glr_plot_01_nmr_multiplets_thumb.png
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  :doc:`/api/gallery/spectro/nmr/plot_01_nmr_multiplets`

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      <div class="sphx-glr-thumbnail-title">Spin-spin (J) coupling and the n+1 rule: ethanol's triplet/quartet and a doublet of triplets</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Bloch and Purcell (1946) showed that nuclei in a static field B_0 absorb radio-frequency energy sharply at the Larmor frequency \nu_0=\gamma B_0/(2\pi). The effect became a chemical tool when it was found that a nucleus&#x27;s surrounding electrons shield it slightly, so the exact resonance frequency depends on its chemical environment. This example computes ^1\mathrm{H} and ^{13}\mathrm{C} Larmor frequencies against field strength. It then places three proton environments of methyl acetate-like shielding on the frequency axis at two field strengths and shows that converting to ppm with chemical_shift_ppm makes the spectrum field-independent.">

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  .. image:: /api/gallery/spectro/nmr/images/thumb/sphx_glr_plot_02_nmr_resonance_chemical_shift_thumb.png
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  :doc:`/api/gallery/spectro/nmr/plot_02_nmr_resonance_chemical_shift`

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      <div class="sphx-glr-thumbnail-title">Nuclear magnetic resonance: Larmor frequencies and the field-independent chemical shift</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Karplus (1959) used valence-bond theory to show that the three-bond (vicinal) H-C-C-H coupling constant depends on the dihedral angle \phi. It is large for eclipsed (0 degrees) and anti (180 degrees) protons and nearly zero near 90 degrees. This lets a measured ^3J report molecular conformation. This example plots Karplus&#x27;s 1959 curve from karplus_coupling, reads off the axial-axial and axial-equatorial couplings of a cyclohexane chair, and shows the resulting doublet splittings.">

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  .. image:: /api/gallery/spectro/nmr/images/thumb/sphx_glr_plot_03_karplus_vicinal_coupling_thumb.png
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  :doc:`/api/gallery/spectro/nmr/plot_03_karplus_vicinal_coupling`

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      <div class="sphx-glr-thumbnail-title">The Karplus relation: vicinal 3J(H,H) coupling as a function of dihedral angle</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Ernst and Anderson (1966) replaced the slow frequency sweep of continuous-wave NMR with a single short radio-frequency pulse. The pulse excites all resonances at once. The resulting free-induction decay (FID) is a sum of decaying oscillations, one per resonance, and its Fourier transform gives the whole spectrum. Because each FID takes about as long as a single scan and many can be averaged, the method is far more sensitive. This example simulates a noisy FID for three resonances with free_induction_decay, transforms it with fid_to_spectrum, and shows signal averaging: signal-to-noise grows as \sqrt{N} over N co-added scans.">

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  .. image:: /api/gallery/spectro/nmr/images/thumb/sphx_glr_plot_04_fourier_transform_nmr_thumb.png
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  :doc:`/api/gallery/spectro/nmr/plot_04_fourier_transform_nmr`

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      <div class="sphx-glr-thumbnail-title">Fourier-transform NMR: from a free-induction decay to a spectrum</div>
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.. toctree::
   :hidden:

   /api/gallery/spectro/nmr/plot_01_nmr_multiplets
   /api/gallery/spectro/nmr/plot_02_nmr_resonance_chemical_shift
   /api/gallery/spectro/nmr/plot_03_karplus_vicinal_coupling
   /api/gallery/spectro/nmr/plot_04_fourier_transform_nmr