.. index:: dihedral_style class2
.. index:: dihedral_style class2/omp
.. index:: dihedral_style class2/kk

dihedral_style class2 command
=============================

Accelerator Variants: *class2/omp*, *class2/kk*

Syntax
""""""

.. code-block:: LAMMPS

   dihedral_style class2

Examples
""""""""

.. code-block:: LAMMPS

   dihedral_style class2
   dihedral_coeff 1 100 75 100 70 80 60
   dihedral_coeff * mbt 3.5945 0.1704 -0.5490 1.5228
   dihedral_coeff * ebt 0.3417 0.3264 -0.9036 0.1368 0.0 -0.8080 1.0119 1.1010
   dihedral_coeff 2 at 0.0 -0.1850 -0.7963 -2.0220 0.0 -0.3991 110.2453 105.1270
   dihedral_coeff * aat -13.5271 110.2453 105.1270
   dihedral_coeff * bb13 0.0 1.0119 1.1010

Description
"""""""""""

The *class2* dihedral style uses the potential

.. math::

   E        = & E_d + E_{mbt} + E_{ebt} + E_{at} + E_{aat} + E_{bb13} \\
   E_d      = & \sum_{n=1}^{3} K_n [ 1 - \cos (n \phi - \phi_n) ] \\
   E_{mbt}  = & (r_{jk} - r_2) [ A_1 \cos (\phi) + A_2 \cos (2\phi) + A_3 \cos (3\phi) ] \\
   E_{ebt}  = & (r_{ij} - r_1) [ B_1 \cos (\phi) + B_2 \cos (2\phi) + B_3 \cos (3\phi) ] + \\
              & (r_{kl} - r_3) [ C_1 \cos (\phi) + C_2 \cos (2\phi) + C_3 \cos (3\phi) ] \\
   E_{at}   = & (\theta_{ijk} - \theta_1) [ D_1 \cos (\phi) + D_2 \cos (2\phi) + D_3 \cos (3\phi) ] + \\
              & (\theta_{jkl} - \theta_2) [ E_1 \cos (\phi) + E_2 \cos (2\phi) + E_3 \cos (3\phi) ] \\
   E_{aat}  = & M (\theta_{ijk} - \theta_1) (\theta_{jkl} - \theta_2) \cos (\phi) \\
   E_{bb13} = & N (r_{ij} - r_1) (r_{kl} - r_3)

where :math:`E_d` is the dihedral term, :math:`E_{mbt}` is a middle-bond-torsion term,
:math:`E_{ebt}` is an end-bond-torsion term, :math:`E_{at}` is an angle-torsion term, :math:`E_{aat}`
is an angle-angle-torsion term, and :math:`E_{bb13}` is a bond-bond-13 term.

:math:`\theta_1` and :math:`\theta_2` are equilibrium angles and :math:`r_1`, :math:`r_2`, and
:math:`r_3` are equilibrium bond lengths.

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

Coefficients for the :math:`E_d`, :math:`E_{mbt}`, :math:`E_{ebt}`,
:math:`E_{at}`, :math:`E_{aat}`, and :math:`E_{bb13}` formulas must be
defined for each dihedral type via the :doc:`dihedral_coeff <dihedral_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 6 coefficients for the :math:`E_d` formula:

* :math:`K_1` (energy)
* :math:`\phi_1` (degrees)
* :math:`K_2` (energy)
* :math:`\phi_2` (degrees)
* :math:`K_3` (energy)
* :math:`phi_3` (degrees)

For the :math:`E_{mbt}` formula, each line in a
:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists
5 coefficients, the first of which is *mbt* to indicate they are
MiddleBondTorsion coefficients.  In a data file, these coefficients
should be listed under a *MiddleBondTorsion Coeffs* heading and you
must leave out the *mbt*, i.e. only list 4 coefficients after the
dihedral type.

* *mbt*
* :math:`A_1` (energy/distance)
* :math:`A_2` (energy/distance)
* :math:`A_3` (energy/distance)
* :math:`r_2` (distance)

For the :math:`E_{ebt}` formula, each line in a
:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists
9 coefficients, the first of which is *ebt* to indicate they are
EndBondTorsion coefficients.  In a data file, these coefficients
should be listed under a *EndBondTorsion Coeffs* heading and you must
leave out the *ebt*, i.e. only list 8 coefficients after the dihedral
type.

* *ebt*
* :math:`B_1` (energy/distance)
* :math:`B_2` (energy/distance)
* :math:`B_3` (energy/distance)
* :math:`C_1` (energy/distance)
* :math:`C_2` (energy/distance)
* :math:`C_3` (energy/distance)
* :math:`r_1` (distance)
* :math:`r_3` (distance)

For the :math:`E_{at}` formula, each line in a
:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists
9 coefficients, the first of which is *at* to indicate they are
AngleTorsion coefficients.  In a data file, these coefficients should
be listed under a *AngleTorsion Coeffs* heading and you must leave out
the *at*, i.e. only list 8 coefficients after the dihedral type.

* *at*
* :math:`D_1` (energy)
* :math:`D_2` (energy)
* :math:`D_3` (energy)
* :math:`E_1` (energy)
* :math:`E_2` (energy)
* :math:`E_3` (energy)
* :math:`\theta_1` (degrees)
* :math:`\theta_2` (degrees)

:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but
LAMMPS converts them to radians internally; hence the various
:math:`D` and :math:`E` are effectively energy per radian.

For the :math:`E_{aat}` formula, each line in a :doc:`dihedral_coeff
<dihedral_coeff>` command in the input script lists 4 coefficients,
the first of which is *aat* to indicate they are AngleAngleTorsion
coefficients.  In a data file, these coefficients should be listed
under a *AngleAngleTorsion Coeffs* heading and you must leave out the
*aat*, i.e. only list 3 coefficients after the dihedral type.

* *aat*
* :math:`M` (energy)
* :math:`\theta_1` (degrees)
* :math:`\theta_2` (degrees)

:math:`\theta_1` and :math:`\theta_2` are specified in degrees, but
LAMMPS converts them to radians internally; hence :math:`M` is
effectively energy per radian\^2.

For the :math:`E_{bb13}` formula, each line in a
:doc:`dihedral_coeff <dihedral_coeff>` command in the input script lists
4 coefficients, the first of which is *bb13* to indicate they are
BondBond13 coefficients.  In a data file, these coefficients should be
listed under a *BondBond13 Coeffs* heading and you must leave out the
*bb13*, i.e. only list 3 coefficients after the dihedral type.

* *bb13*
* :math:`N` (energy/distance\^2)
* :math:`r_1` (distance)
* :math:`r_3` (distance)

----------

.. include:: accel_styles.rst

----------

Restrictions
""""""""""""

This dihedral style can only be used if LAMMPS was built with the
CLASS2 package.  See the :doc:`Build package <Build_package>` doc
page for more info.

Related commands
""""""""""""""""

:doc:`dihedral_coeff <dihedral_coeff>`

Default
"""""""

none

----------

.. _dihedral-Sun:

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