Update docs: bond_mm3

\documentclass[12pt]{article}

\begin{document}

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$$

  E = K (r - r_0)^2 \left[ 1 - 2.55(r-r_0) + (7/12) 2.55^2(r-r_0)^2 \right]

$$

\end{document}

.. index:: bond\_style mm3

.. index:: bond_style mm3

bond\_style mm3 command

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

bond_style mm3 command

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

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   bond_style mm3

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   bond_style mm3

   bond_coeff 1 100.0 107.0

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

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

.. image:: Eqs/bond_mm3.jpg

   :align: center

.. math::

where r0 is the equilibrium value of the bond, and K is a

   E = K (r - r_0)^2 \left[ 1 - 2.55(r-r_0) + (7/12) 2.55^2(r-r_0)^2 \right]

where :math:`r_0` is the equilibrium value of the bond, and :math:`K` is a

prefactor. The anharmonic prefactors have units angstrom\^(-n):

-2.55 angstrom\^(-1) and (7/12)2.55\^2 angstrom\^(-2). The code takes

care of the necessary unit conversion for these factors internally.

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

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

* K (energy/distance\^2)

* r0 (distance)

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

* :math:`r_0` (distance)

Restrictions

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

**(Allinger)** Allinger, Yuh, Lii, JACS, 111(23), 8551-8566

(1989),

.. _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

bond_style mm3 command :h3

[Syntax:]

bond_style mm3 :pre

[Examples:]

bond_style mm3

bond_coeff 1 100.0 107.0 :pre

[Description:]

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

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

:c,image(Eqs/bond_mm3.jpg)

where r0 is the equilibrium value of the bond, and K is a

prefactor. The anharmonic prefactors have units angstrom^(-n):

-2.55 angstrom^(-1) and (7/12)2.55^2 angstrom^(-2). The code takes

care of the necessary unit conversion for these factors internally.

Note that the MM3 papers contains an error in Eq (1):

(7/12)2.55 should be replaced with (7/12)2.55^2

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

"bond_coeff"_bond_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/distance^2)

r0 (distance) :ul

[Restrictions:]

This bond 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:]

"bond_coeff"_bond_coeff.html

[Default:] none

:line

:link(mm3-allinger1989)

[(Allinger)] Allinger, Yuh, Lii, JACS, 111(23), 8551-8566

(1989),