.. _sphx_glr_api_gallery_spectro_vibrational:

Vibrational spectra
---------------------

Harmonic vs. Morse-potential IR band positions and anharmonicity
constants; Wilson GF-matrix normal modes for CO2 and H2O; the Raman/IR
mutual exclusion rule for CO2; and the doubly degenerate bend of a
linear triatomic.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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

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    <div class="sphx-glr-thumbcontainer" tooltip="Predicts HCl&#x27;s fundamental IR absorption from a harmonic oscillator, compares it against the exact (anharmonic) Morse-potential fundamental and first overtone, then inverts the observed 0\to1/0\to2 band positions to recover the spectroscopic constants \omega_e/\omega_ex_e -- exactly the way real anharmonicity constants are measured from an observed overtone spectrum.">

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  .. image:: /api/gallery/spectro/vibrational/images/thumb/sphx_glr_plot_01_harmonic_vs_morse_thumb.png
    :alt:

  :doc:`/api/gallery/spectro/vibrational/plot_01_harmonic_vs_morse`

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      <div class="sphx-glr-thumbnail-title">Harmonic vs. Morse IR band positions, and recovering anharmonicity from overtones</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example uses Wilson&#x27;s GF-matrix method to calculate normal modes for a linear triatomic (CO2) and a bent one (H2O) with TriatomicNormalModes. The molecule&#x27;s geometry and masses give the kinetic-energy matrix G=BM^{-1}B^T, where B is the Wilson B-matrix. A diagonal valence force field gives the potential-energy matrix F. Solving the eigenvalue problem GFL=L\Lambda, with \lambda_k=(2\pi c\tilde\nu_k)^2, gives the normal-mode wavenumbers. Changing only the bend entry of F shifts the bend frequency, while the stretches barely move.">

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  .. image:: /api/gallery/spectro/vibrational/images/thumb/sphx_glr_plot_02_triatomic_normal_modes_thumb.png
    :alt:

  :doc:`/api/gallery/spectro/vibrational/plot_02_triatomic_normal_modes`

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      <div class="sphx-glr-thumbnail-title">Wilson's GF-matrix method: CO2 and H2O normal-mode frequencies from the G and F matrices</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Raman and Krishnan (1928) found that a small fraction of scattered light is shifted in frequency by a molecule&#x27;s vibrational wavenumbers. A mode is Raman-active if it changes the molecule&#x27;s polarizability. It is infrared-active if it changes the dipole moment. For a centrosymmetric molecule such as CO2, no mode is active in both spectra.">

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  .. image:: /api/gallery/spectro/vibrational/images/thumb/sphx_glr_plot_03_raman_ir_mutual_exclusion_thumb.png
    :alt:

  :doc:`/api/gallery/spectro/vibrational/plot_03_raman_ir_mutual_exclusion`

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      <div class="sphx-glr-thumbnail-title">Raman scattering vs. infrared absorption: the mutual exclusion rule for CO2</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Herzberg&#x27;s Infrared and Raman Spectra of Polyatomic Molecules (1945) set out the rules for counting and labelling vibrations of polyatomic molecules. A nonlinear molecule of N atoms has 3N-6 vibrations. A linear molecule has 3N-5, because rotation about its axis does not count as a degree of freedom. For CO2 this means four vibrations: the symmetric stretch, the antisymmetric stretch, and a doubly degenerate bend (in-plane and out-of-plane bending have the same frequency by cylindrical symmetry). This example compares linear CO2 with bent H2O using TriatomicNormalModes, whose is_linear flag marks the bend as a degenerate pair.">

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  .. image:: /api/gallery/spectro/vibrational/images/thumb/sphx_glr_plot_04_linear_bend_degeneracy_thumb.png
    :alt:

  :doc:`/api/gallery/spectro/vibrational/plot_04_linear_bend_degeneracy`

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      <div class="sphx-glr-thumbnail-title">Herzberg's linear-molecule rules: CO2's doubly degenerate bend and 3N-5 vibrations</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/spectro/vibrational/plot_01_harmonic_vs_morse
   /api/gallery/spectro/vibrational/plot_02_triatomic_normal_modes
   /api/gallery/spectro/vibrational/plot_03_raman_ir_mutual_exclusion
   /api/gallery/spectro/vibrational/plot_04_linear_bend_degeneracy