Update docs: angle_cosine_shift_exp

\documentstyle[12pt]{article}

\begin{document}

$$

E=-U_{min} 

\frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1}

\quad\mbox{with}\quad

U(\theta,\theta_0)

=-0.5 \left(1+\cos(\theta-\theta_0) \right)

$$

\end{document}

.. index:: angle\_style cosine/shift/exp

.. index:: angle_style cosine/shift/exp

angle\_style cosine/shift/exp command

=====================================

angle_style cosine/shift/exp command

====================================

angle\_style cosine/shift/exp/omp command

=========================================

angle_style cosine/shift/exp/omp command

========================================

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style cosine/shift/exp

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style cosine/shift/exp

   angle_coeff \* 10.0 45.0 2.0

   angle_coeff * 10.0 45.0 2.0

Description

"""""""""""

The *cosine/shift/exp* angle style uses the potential

.. image:: Eqs/angle_cosine_shift_exp.jpg

   :align: center

.. math::

where Umin, theta, and a are defined for each angle type.

   E = -U_{\text{min}} \frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1} \quad \text{with} \quad U(\theta,\theta_0) = -0.5 \left(1+\cos(\theta-\theta_0) \right)

The potential is bounded between [-Umin:0] and the minimum is

located at the angle theta0. The a parameter can be both positive or

where :math:`U_{\text{min}}`, :math:`\theta`, and :math:`a` are defined for each angle type.

The potential is bounded between :math:`[-U_{\text{min}}, 0]` and the minimum is

located at the angle :math:`\theta_0`. The a parameter can be both positive or

negative and is used to control the spring constant at the

equilibrium.

The spring constant is given by k = A exp(A) Umin / [2 (Exp(a)-1)].

For a > 3, k/Umin = a/2 to better than 5% relative error. For negative

values of the a parameter, the spring constant is essentially zero,

The spring constant is given by :math:`k = A \exp(A) U_{\text{min}} / [2 (\exp(a)-1)]`.

For :math:`a > 3`, :math:`\frac{k}{U_{\text{min}}} = \frac{a}{2}` to better than 5% relative error. For negative

values of the :math:`a` parameter, the spring constant is essentially zero,

and anharmonic terms takes over. The potential is furthermore well

behaved in the limit a -> 0, where it has been implemented to linear

order in a for a < 0.001. In this limit the potential reduces to the

behaved in the limit :math:`a \rightarrow 0`, where it has been implemented to linear

order in :math:`a` for :math:`a < 0.001`. In this limit the potential reduces to the

cosineshifted potential.

The following coefficients must be defined for each angle type via the

the data file or restart files read by the :doc:`read\_data <read_data>`

or :doc:`read\_restart <read_restart>` commands:

* umin (energy)

* theta (angle)

* A (real number)

* :math:`U_min` (energy)

* :math:`\theta` (angle)

* :math:`A` (real number)

----------

:doc:`dihedral\_cosine\_shift\_exp <dihedral_cosine_shift_exp>`

**Default:** none

.. _lws: http://lammps.sandia.gov

.. _ld: Manual.html

.. _lc: Commands_all.html

"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)

:link(ld,Manual.html)

:link(lc,Commands_all.html)

:line

angle_style cosine/shift/exp command :h3

angle_style cosine/shift/exp/omp command :h3

[Syntax:]

angle_style cosine/shift/exp :pre

[Examples:]

angle_style cosine/shift/exp

angle_coeff * 10.0 45.0 2.0 :pre

[Description:]

The {cosine/shift/exp} angle style uses the potential

:c,image(Eqs/angle_cosine_shift_exp.jpg)

where Umin, theta, and a are defined for each angle type.

The potential is bounded between \[-Umin:0\] and the minimum is

located at the angle theta0. The a parameter can be both positive or

negative and is used to control the spring constant at the

equilibrium.

The spring constant is given by k = A exp(A) Umin / \[2 (Exp(a)-1)\].

For a > 3, k/Umin = a/2 to better than 5% relative error. For negative

values of the a parameter, the spring constant is essentially zero,

and anharmonic terms takes over. The potential is furthermore well

behaved in the limit a -> 0, where it has been implemented to linear

order in a for a < 0.001. In this limit the potential reduces to the

cosineshifted potential.

The following coefficients must be defined for each angle type via the

"angle_coeff"_angle_coeff.html command as in the example above, or in

the data file or restart files read by the "read_data"_read_data.html

or "read_restart"_read_restart.html commands:

umin (energy)

theta (angle)

A (real number) :ul

:line

Styles with a {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are

functionally the same as the corresponding style without the suffix.

They have been optimized to run faster, depending on your available

hardware, as discussed on the "Speed packages"_Speed_packages.html doc

page.  The accelerated styles take the same arguments and should

produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,

USER-OMP and OPT packages, respectively.  They are only enabled if

LAMMPS was built with those packages.  See the "Build

package"_Build_package.html doc page for more info.

You can specify the accelerated styles explicitly in your input script

by including their suffix, or you can use the "-suffix command-line

switch"_Run_options.html when you invoke LAMMPS, or you can use the

"suffix"_suffix.html command in your input script.

See the "Speed packages"_Speed_packages.html doc page for more

instructions on how to use the accelerated styles effectively.

:line

[Restrictions:]

This angle style can only be used if LAMMPS was built with the

USER-MISC package.  See the "Build package"_Build_package.html doc

page for more info.

[Related commands:]

"angle_coeff"_angle_coeff.html,

"angle_cosine_shift"_angle_cosine_shift.html,

"dihedral_cosine_shift_exp"_dihedral_cosine_shift_exp.html

[Default:] none