Update docs: angle_mm3

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$$

  E = K (\theta - \theta_0)^2 \left[ 1 - 0.014(\theta - \theta_0) + 5.6(10)^{-5} (\theta - \theta_0)^2 - 7.0(10)^{-7} (\theta - \theta_0)^3 + 9(10)^{-10} (\theta - \theta_0)^4 \right]

$$

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.. index:: angle\_style mm3

.. index:: angle_style mm3

angle\_style mm3 command

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

angle_style mm3 command

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

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style mm3

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   angle_style mm3

   angle_coeff 1 100.0 107.0

The *mm3* angle style uses the potential that is anharmonic in the angle

as defined in :ref:`(Allinger) <mm3-allinger1989>`

.. image:: Eqs/angle_mm3.jpg

   :align: center

.. math::

where theta0 is the equilibrium value of the angle, and K is a

prefactor. The anharmonic prefactors have units deg\^(-n), for example

-0.014 deg\^(-1), 5.6(10)\^(-5) deg\^(-2), ...

   E = K (\theta - \theta_0)^2 \left[ 1 - 0.014(\theta - \theta_0) + 5.6(10)^{-5} (\theta - \theta_0)^2 - 7.0(10)^{-7} (\theta - \theta_0)^3 + 9(10)^{-10} (\theta - \theta_0)^4 \right]

where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a

prefactor. The anharmonic prefactors have units :math:`\deg^{-n}`, for example

:math:`-0.014 \deg^{-1}`, :math:`5.6 \cdot 10^{-5} \deg^{-2}`, ...

The following coefficients 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:

* K (energy/radian\^2)

* theta0 (degrees)

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

* :math:`\theta_0` (degrees)

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

internally; hence the units of K are in energy/radian\^2.

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

internally; hence the units of :math:`K` are in energy/radian\^2.

Restrictions

""""""""""""

:doc:`angle\_coeff <angle_coeff>`

**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 mm3 command :h3

[Syntax:]

angle_style mm3 :pre

[Examples:]

angle_style mm3

angle_coeff 1 100.0 107.0 :pre

[Description:]

The {mm3} angle style uses the potential that is anharmonic in the angle

as defined in "(Allinger)"_#mm3-allinger1989

:c,image(Eqs/angle_mm3.jpg)

where theta0 is the equilibrium value of the angle, and K is a

prefactor. The anharmonic prefactors have units deg^(-n), for example

-0.014 deg^(-1), 5.6(10)^(-5) deg^(-2), ...

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:

K (energy/radian^2)

theta0 (degrees) :ul

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

internally; hence the units of K are in energy/radian^2.

[Restrictions:]

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

USER_YAFF package.  See the "Build package"_Build_package.html doc

page for more info.

[Related commands:]

"angle_coeff"_angle_coeff.html

[Default:] none

:line