Update docs: angle_class2

\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}

  E & = & E_a + E_{bb} + E_{ba} \\

  E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\

  E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\

  E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)

\end{eqnarray*}

\end{document}

 No newline at end of file

.. index:: angle\_style class2

.. index:: angle_style class2

angle\_style class2 command

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

angle_style class2 command

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

angle\_style class2/kk command

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

angle\_style class2/omp command

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

angle_style class2/kk command

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

angle\_style class2/p6 command

angle_style class2/omp command

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

angle_style class2/p6 command

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

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style class2

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style class2

   angle_coeff \* 75.0

   angle_coeff * 75.0

   angle_coeff 1 bb 10.5872 1.0119 1.5228

   angle_coeff \* ba 3.6551 24.895 1.0119 1.5228

   angle_coeff * ba 3.6551 24.895 1.0119 1.5228

Description

"""""""""""

The *class2* angle style uses the potential

.. image:: Eqs/angle_class2.jpg

   :align: center

.. math::

   E & = & E_a + E_{bb} + E_{ba} \\

   E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\

   E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\

   E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)

where Ea is the angle term, Ebb is a bond-bond term, and Eba is a

bond-angle term.  Theta0 is the equilibrium angle and r1 and r2 are

where :math:`E_a` is the angle term, :math:`E_{bb}` is a bond-bond term, and :math:`E_{ba}` is a

bond-angle term.  :math:`\theta_0` is the equilibrium angle and :math:`r_1` and :math:`r_2` are

the equilibrium bond lengths.

See :ref:`(Sun) <angle-Sun>` for a description of the COMPASS class2 force field.

Coefficients for the Ea, Ebb, and Eba formulas must be defined for

Coefficients for the :math:`E_a`, :math:`E_{bb}`, and :math:`E_{ba}` formulas must be defined for

each angle type via the :doc:`angle\_coeff <angle_coeff>` command as in

the example above, or in the data file or restart files read by the

:doc:`read\_data <read_data>` or :doc:`read\_restart <read_restart>`

commands.

These are the 4 coefficients for the Ea formula:

These are the 4 coefficients for the :math:`E_a` formula:

* theta0 (degrees)

* K2 (energy/radian\^2)

* K3 (energy/radian\^3)

* K4 (energy/radian\^4)

* :math:`\theta_0` (degrees)

* :math:`K_2` (energy/radian\^2)

* :math:`K_3` (energy/radian\^3)

* :math:`K_4` (energy/radian\^4)

Theta0 is specified in degrees, but LAMMPS converts it to radians

internally; hence the units of the various K are in per-radian.

:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians

internally; hence the units of the various :math:`K` are in per-radian.

For the Ebb formula, each line in a :doc:`angle\_coeff <angle_coeff>`

For the :math:`E_{bb}` formula, each line in a :doc:`angle\_coeff <angle_coeff>`

command in the input script lists 4 coefficients, the first of which

is "bb" to indicate they are BondBond coefficients.  In a data file,

these coefficients should be listed under a "BondBond Coeffs" heading

the angle type.

* bb

* M (energy/distance\^2)

* r1 (distance)

* r2 (distance)

* :math:`M` (energy/distance\^2)

* :math:`r_1` (distance)

* :math:`r_2` (distance)

For the Eba formula, each line in a :doc:`angle\_coeff <angle_coeff>`

For the :math:`E_{ba}` formula, each line in a :doc:`angle\_coeff <angle_coeff>`

command in the input script lists 5 coefficients, the first of which

is "ba" to indicate they are BondAngle coefficients.  In a data file,

these coefficients should be listed under a "BondAngle Coeffs" heading

the angle type.

* ba

* N1 (energy/distance\^2)

* N2 (energy/distance\^2)

* r1 (distance)

* r2 (distance)

* :math:`N_1` (energy/distance\^2)

* :math:`N_2` (energy/distance\^2)

* :math:`r_1` (distance)

* :math:`r_2` (distance)

The theta0 value in the Eba formula is not specified, since it is the

same value from the Ea formula.

The :math:`\theta_0` value in the :math:`E_{ba}` formula is not specified,

since it is the same value from the :math:`E_a` formula.

----------

The *class2/p6* angle style uses the *class2* potential expanded to sixth order:

.. image:: Eqs/angle_class2_p6.jpg

   :align: center

.. math::

In this expanded term 6 coefficients for the Ea formula need to be set:

   E_{a} = K_2\left(\theta - \theta_0\right)^2 + K_3\left(\theta - \theta_0\right)^3 + K_4\left(\theta - \theta_0\right)^4 + K_5\left(\theta - \theta_0\right)^5 + K_6\left(\theta - \theta_0\right)^6

* theta0 (degrees)

* K2 (energy/radian\^2)

* K3 (energy/radian\^3)

* K4 (energy/radian\^4)

* K5 (energy/radian\^5)

* K6 (energy/radian\^6)

In this expanded term 6 coefficients for the :math:`E_a` formula need to be set:

* :math:`\theta_0` (degrees)

* :math:`K_2` (energy/radian\^2)

* :math:`K_3` (energy/radian\^3)

* :math:`K_4` (energy/radian\^4)

* :math:`K_5` (energy/radian\^5)

* :math:`K_6` (energy/radian\^6)

The bond-bond and bond-angle terms remain unchanged.

**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).

.. _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 class2 command :h3

angle_style class2/kk command :h3

angle_style class2/omp command :h3

angle_style class2/p6 command :h3

[Syntax:]

angle_style class2 :pre

[Examples:]

angle_style class2

angle_coeff * 75.0

angle_coeff 1 bb 10.5872 1.0119 1.5228

angle_coeff * ba 3.6551 24.895 1.0119 1.5228 :pre

[Description:]

The {class2} angle style uses the potential

:c,image(Eqs/angle_class2.jpg)

where Ea is the angle term, Ebb is a bond-bond term, and Eba is a

bond-angle term.  Theta0 is the equilibrium angle and r1 and r2 are

the equilibrium bond lengths.

See "(Sun)"_#angle-Sun for a description of the COMPASS class2 force field.

Coefficients for the Ea, Ebb, and Eba formulas 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.

These are the 4 coefficients for the Ea formula:

theta0 (degrees)

K2 (energy/radian^2)

K3 (energy/radian^3)

K4 (energy/radian^4) :ul

Theta0 is specified in degrees, but LAMMPS converts it to radians

internally; hence the units of the various K are in per-radian.

For the Ebb formula, each line in a "angle_coeff"_angle_coeff.html

command in the input script lists 4 coefficients, the first of which

is "bb" to indicate they are BondBond coefficients.  In a data file,

these coefficients should be listed under a "BondBond Coeffs" heading

and you must leave out the "bb", i.e. only list 3 coefficients after

the angle type.

bb

M (energy/distance^2)

r1 (distance)

r2 (distance) :ul

For the Eba formula, each line in a "angle_coeff"_angle_coeff.html

command in the input script lists 5 coefficients, the first of which

is "ba" to indicate they are BondAngle coefficients.  In a data file,

these coefficients should be listed under a "BondAngle Coeffs" heading

and you must leave out the "ba", i.e. only list 4 coefficients after

the angle type.

ba

N1 (energy/distance^2)

N2 (energy/distance^2)

r1 (distance)

r2 (distance) :ul

The theta0 value in the Eba formula is not specified, since it is the

same value from the Ea formula.

: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

The {class2/p6} angle style uses the {class2} potential expanded to sixth order:

:c,image(Eqs/angle_class2_p6.jpg)

In this expanded term 6 coefficients for the Ea formula need to be set:

theta0 (degrees)

K2 (energy/radian^2)

K3 (energy/radian^3)

K4 (energy/radian^4)

K5 (energy/radian^5)

K6 (energy/radian^6) :ul

The bond-bond and bond-angle terms remain unchanged.

:line

[Restrictions:]

This angle style can only be used if LAMMPS was built with the CLASS2

package.  For the {class2/p6} style LAMMPS needs to be built with the

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

page for more info.

[Related commands:]

"angle_coeff"_angle_coeff.html

[Default:] none

:line

:link(angle-Sun)

[(Sun)] Sun, J Phys Chem B 102, 7338-7364 (1998).