:mod:`atsim.potentials.potentialforms`
======================================

.. py:module:: atsim.potentials.potentialforms

.. autoapi-nested-parse::

   Functions representing different potential forms.

   The functions contained herein are function factories returning
   a function that takes separation as its sole argument.

   See :ref:`list-of-potential-forms` for descriptions of these potential forms.



Module Contents
---------------


Functions
~~~~~~~~~

.. autoapisummary::

   atsim.potentials.potentialforms.potential
   atsim.potentials.potentialforms.is_potential
   atsim.potentials.potentialforms.buck4


.. function:: potential(func)

   Decorator for callables that should be tagged as potential-forms or potential-functions


.. function:: is_potential(obj)

   Identifies if an object is a potential-form or potential-function


.. function:: buck4(A, rho, C, r_detach, r_min, r_attach)

   Returns a potential form describing the four-range Buckingham potential.

   The potential form is:

   .. math::

     V(r_{ij}) = 
     \begin{cases}
       A \exp(-r_{ij}/\rho)                                                 , & 0 \leq r_{ij} \leq  r_\text{detach}\\
       a_0 + a_1 r_{ij} +a_2 r_{ij}^2+a_3 r_{ij}^3+a_4 r_{ij}^4+a_5 r_{ij}^5, & r_\text{detach} < r_{ij} < r_\text{min}\\
       b_0 +b_1 *r_{ij}+b_2*r_{ij}^2+b_3*r_{ij}^3                           , & r_\text{min} \leq r_{ij} < r_\text{attach}\\
       -\frac{C}{r_{ij}^6}                                                  , & r_{ij} \geq r_\text{attach}\\
     \end{cases}

   In other words this is a Buckingham potential in which the Born-Mayer component acts at small separations and the disprsion
   term acts at larger separation. These two parts are linked by a fifth then third order polynomial (with a minimum formed in the spline
   at :math:`r_  ext{min}`).

   The spline parameters are subject to the constraints that :math:`V(r_{ij})`, first and second derivatives must be equal at the boundary points
   and the function must have a stationary point at `r_min`.

   .. seealso::

     * :class:`atsim.potentials.Buck4_Spline`
     * :class:`atsim.potentials.Buck4_SplinePotential`

   .. note::

     Due to the complexity of calculating the spline-coefficients this potential form does not have an equivalent in the atsim.potentials.potentialfunctions
     module.


   :param A: A potential parameter.
   :param rho: potential parameter.
   :param C: C parameter.
   :param r_detach: Separation where spline starts.
   :param r_min: Location of stationary point.
   :param r_attach: End of splined region.

   :return: Splined potential.


.. data:: buck
   

   

.. data:: bornmayer
   

   

.. data:: coul
   

   

.. data:: constant
   

   

.. data:: exponential
   

   

.. data:: hbnd
   

   

.. data:: lj
   

   

.. data:: morse
   

   

.. data:: polynomial
   

   

.. data:: sqrt
   

   

.. data:: tang_toennies
   

   

.. data:: zbl
   

   

.. data:: zero
   

   

.. data:: exp_spline