Update docs: angle_cosine_periodic

\documentstyle[12pt]{article}

\begin{document}

$$

E=C\left[ 1-B(-1)^ncos\left( n\theta\right) \right]  

$$

\end{document}

.. index:: angle\_style cosine/periodic

.. index:: angle_style cosine/periodic

angle\_style cosine/periodic command

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

angle_style cosine/periodic command

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

angle\_style cosine/periodic/omp command

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

angle_style cosine/periodic/omp command

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

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style cosine/periodic

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style cosine/periodic

   angle_coeff \* 75.0 1 6

   angle_coeff * 75.0 1 6

Description

"""""""""""

The *cosine/periodic* angle style uses the following potential, which

is commonly used in the :doc:`DREIDING <Howto_bioFF>` force field,

particularly for organometallic systems where *n* = 4 might be used

for an octahedral complex and *n* = 3 might be used for a trigonal

particularly for organometallic systems where :math:`n` = 4 might be used

for an octahedral complex and :math:`n` = 3 might be used for a trigonal

center:

.. image:: Eqs/angle_cosine_periodic.jpg

   :align: center

.. math::

where C, B and n are coefficients defined for each angle type.

   E = C \left[ 1 - B(-1)^n\cos\left( n\theta\right) \right]

where :math:`C`, :math:`B` and :math:`n` are coefficients defined for each angle type.

See :ref:`(Mayo) <cosine-Mayo>` for a description of the DREIDING force field

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

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

* C (energy)

* B = 1 or -1

* n = 1, 2, 3, 4, 5 or 6 for periodicity

* :math:`C` (energy)

* :math:`B` = 1 or -1

* :math:`n` = 1, 2, 3, 4, 5 or 6 for periodicity

Note that the prefactor C is specified and not the overall force

constant K = C / n\^2.  When B = 1, it leads to a minimum for the

linear geometry.  When B = -1, it leads to a maximum for the linear

Note that the prefactor :math:`C` is specified and not the overall force

constant :math:`K = \frac{C}{n^2}`.  When :math:`B = 1`, it leads to a minimum for the

linear geometry.  When :math:`B = -1`, it leads to a maximum for the linear

geometry.

**(Mayo)** Mayo, Olfason, Goddard III, J Phys Chem, 94, 8897-8909

(1990).

.. _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/periodic command :h3

angle_style cosine/periodic/omp command :h3

[Syntax:]

angle_style cosine/periodic :pre

[Examples:]

angle_style cosine/periodic

angle_coeff * 75.0 1 6 :pre

[Description:]

The {cosine/periodic} angle style uses the following potential, which

is commonly used in the "DREIDING"_Howto_bioFF.html force field,

particularly for organometallic systems where {n} = 4 might be used

for an octahedral complex and {n} = 3 might be used for a trigonal

center:

:c,image(Eqs/angle_cosine_periodic.jpg)

where C, B and n are coefficients defined for each angle type.

See "(Mayo)"_#cosine-Mayo for a description of the DREIDING force field

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:

C (energy)

B = 1 or -1

n = 1, 2, 3, 4, 5 or 6 for periodicity :ul

Note that the prefactor C is specified and not the overall force

constant K = C / n^2.  When B = 1, it leads to a minimum for the

linear geometry.  When B = -1, it leads to a maximum for the linear

geometry.

: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

MOLECULE package.  See the "Build package"_Build_package.html doc page

for more info.

[Related commands:]

"angle_coeff"_angle_coeff.html

[Default:] none

:line

:link(cosine-Mayo)

[(Mayo)] Mayo, Olfason, Goddard III, J Phys Chem, 94, 8897-8909

(1990).