Lennard-Jones potential
=======================

The Lennard-Jones (LJ) potential is an intermolecular pair potential. It models soft repulsive and
attractive (van der Waals) interactions, and it describes electronically neutral atoms or molecules.
It is a simple yet realistic model to describe intermolecular interactions: two particles repel each
other at a very close distance, attract each other at moderate distance, and do not interact at infinite
distance.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Lennard-Jones_potential#Overview>`__.

.. py:currentmodule:: symplyphysics.laws.chemistry.potential_energy_models.lennard_jones_potential

.. py:data:: potential

    :attr:`~symplyphysics.symbols.classical_mechanics.potential_energy` of the configuration.

Symbol:
    :code:`U`

Latex:
    :math:`U`

Dimension:
    :code:`energy`


.. py:data:: dispersion_energy

    Depth of the potential well, also referred to as *dispersion energy*. See :attr:`~symplyphysics.symbols.basic.energy`.

Symbol:
    :code:`e`

Latex:
    :math:`\varepsilon`

Dimension:
    :code:`energy`


.. py:data:: particle_size

    Distance (see :attr:`~symplyphysics.symbols.classical_mechanics.radius`) at which potential is zero, also referred to as *particle size*.

Symbol:
    :code:`sigma`

Latex:
    :math:`\sigma`

Dimension:
    :code:`length`


.. py:data:: distance

    :attr:`~symplyphysics.symbols.classical_mechanics.euclidean_distance` between the centers of the particles.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`U = 4 * e * ((sigma / r)^12 - (sigma / r)^6)`


    Latex:
        .. math::
            U = 4 \varepsilon \left(\left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right)