.. _sphx_glr_api_gallery_md_pair_potentials:

Pair potentials
----------------

The Lennard-Jones 12-6 potential, Morse vs. harmonic bond potentials and
the classical vibration of a two-body diatomic oscillator, the Buckingham
exp-6 potential, and a small bonded molecule vibrating under coupled
harmonic bond-stretch and angle-bend terms.


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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="The harmonic bond potential (~chemistrykit.md.systems.pair_potentials.HarmonicBond) is the small-oscillation limit of the anharmonic Morse potential -- they agree near the equilibrium separation but diverge away from it (Morse correctly flattens out toward a finite dissociation energy; harmonic does not). DiatomicOscillator integrates the classical two-body bond-vibration problem via the shared velocity-Verlet integrator, for either potential.">

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  .. image:: /api/gallery/md/pair_potentials/images/thumb/sphx_glr_plot_01_morse_vs_harmonic_thumb.png
    :alt:

  :doc:`/api/gallery/md/pair_potentials/plot_01_morse_vs_harmonic`

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      <div class="sphx-glr-thumbnail-title">Morse vs. harmonic bond potentials, and diatomic bond vibration</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="HarmonicMolecule builds a small molecular-mechanics &quot;force field&quot; out of nothing but harmonic bond (~chemistrykit.md.systems.pair_potentials.HarmonicBond) and harmonic angle-bend (~chemistrykit.md.systems.pair_potentials.HarmonicAngle) terms -- the classical, spring-and-hinge picture of molecular structure that founded molecular mechanics. A bent, water-like triatomic (one heavy vertex atom, two light outer atoms, equilibrium angle 104.5 degrees) is displaced away from its equilibrium geometry and left to vibrate under velocity-Verlet integration alone (no thermostat): both bond lengths and the bond angle oscillate indefinitely about their equilibrium values, and the total energy is conserved to within integration error.">

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  .. image:: /api/gallery/md/pair_potentials/images/thumb/sphx_glr_plot_02_harmonic_molecule_thumb.png
    :alt:

  :doc:`/api/gallery/md/pair_potentials/plot_02_harmonic_molecule`

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      <div class="sphx-glr-thumbnail-title">A bent triatomic molecule: coupled bond-stretch and angle-bend vibrations</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="The Buckingham (exp-6) potential replaces the Lennard-Jones r^{-12} repulsive wall with an exponential -- closer to the true quantum-mechanical electron-overlap repulsion -- while keeping the same r^{-6} dispersion attraction. Matched to a Lennard-Jones potential&#x27;s well depth, position, and long-range tail, the two agree closely everywhere near and beyond the minimum. But the exponential repulsion is eventually overwhelmed by the unbounded -C/r^6 attractive term at short enough range, so the Buckingham potential has a second, spurious turnover well inside the true minimum: past that point it falls back toward -\infty as r\to0 instead of diverging to +\infty the way Lennard-Jones&#x27;s pure r^{-12} repulsion does.">

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  .. image:: /api/gallery/md/pair_potentials/images/thumb/sphx_glr_plot_03_buckingham_vs_lj_thumb.png
    :alt:

  :doc:`/api/gallery/md/pair_potentials/plot_03_buckingham_vs_lj`

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      <div class="sphx-glr-thumbnail-title">Buckingham vs. Lennard-Jones: exponential repulsion and its inner turnover</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Lennard-Jones&#x27;s 1924 pair potential combines a steep r^{-12} repulsion with the r^{-6} London-dispersion attraction:">

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  .. image:: /api/gallery/md/pair_potentials/images/thumb/sphx_glr_plot_04_lennard_jones_potential_thumb.png
    :alt:

  :doc:`/api/gallery/md/pair_potentials/plot_04_lennard_jones_potential`

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      <div class="sphx-glr-thumbnail-title">The Lennard-Jones 12-6 potential: repulsion, dispersion, and the minimum</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/md/pair_potentials/plot_01_morse_vs_harmonic
   /api/gallery/md/pair_potentials/plot_02_harmonic_molecule
   /api/gallery/md/pair_potentials/plot_03_buckingham_vs_lj
   /api/gallery/md/pair_potentials/plot_04_lennard_jones_potential