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Update docs: angle_class2
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Richard Berger
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\documentclass[12pt]{article}
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\begin{document}
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\begin{eqnarray*}
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E & = & E_a + E_{bb} + E_{ba} \\
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E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\
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E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\
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E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)
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\end{eqnarray*}
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\end{document}
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.. index:: angle\_style class2
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.. index:: angle_style class2
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angle\_style class2 command
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===========================
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angle_style class2 command
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==========================
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angle\_style class2/kk command
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angle_style class2/kk command
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=============================
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angle_style class2/omp command
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==============================
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angle\_style class2/omp command
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===============================
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angle\_style class2/p6 command
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==============================
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angle_style class2/p6 command
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=============================
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Syntax
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""""""
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.. parsed-literal::
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.. code-block:: LAMMPS
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angle_style class2
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@ -24,44 +24,49 @@ Examples
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""""""""
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.. parsed-literal::
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.. code-block:: LAMMPS
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angle_style class2
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angle_coeff \* 75.0
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angle_coeff * 75.0
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angle_coeff 1 bb 10.5872 1.0119 1.5228
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angle_coeff \* ba 3.6551 24.895 1.0119 1.5228
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angle_coeff * ba 3.6551 24.895 1.0119 1.5228
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Description
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"""""""""""
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The *class2* angle style uses the potential
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.. image:: Eqs/angle_class2.jpg
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:align: center
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.. math::
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where Ea is the angle term, Ebb is a bond-bond term, and Eba is a
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bond-angle term. Theta0 is the equilibrium angle and r1 and r2 are
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E & = & E_a + E_{bb} + E_{ba} \\
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E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\
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E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\
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E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)
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where :math:`E_a` is the angle term, :math:`E_{bb}` is a bond-bond term, and :math:`E_{ba}` is a
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bond-angle term. :math:`\theta_0` is the equilibrium angle and :math:`r_1` and :math:`r_2` are
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the equilibrium bond lengths.
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See :ref:`(Sun) <angle-Sun>` for a description of the COMPASS class2 force field.
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Coefficients for the Ea, Ebb, and Eba formulas must be defined for
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Coefficients for the :math:`E_a`, :math:`E_{bb}`, and :math:`E_{ba}` formulas must be defined for
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each angle type via the :doc:`angle\_coeff <angle_coeff>` command as in
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the example above, or in the data file or restart files read by the
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:doc:`read\_data <read_data>` or :doc:`read\_restart <read_restart>`
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commands.
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These are the 4 coefficients for the Ea formula:
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These are the 4 coefficients for the :math:`E_a` formula:
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* theta0 (degrees)
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* K2 (energy/radian\^2)
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* K3 (energy/radian\^3)
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* K4 (energy/radian\^4)
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* :math:`\theta_0` (degrees)
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* :math:`K_2` (energy/radian\^2)
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* :math:`K_3` (energy/radian\^3)
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* :math:`K_4` (energy/radian\^4)
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Theta0 is specified in degrees, but LAMMPS converts it to radians
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internally; hence the units of the various K are in per-radian.
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:math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
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internally; hence the units of the various :math:`K` are in per-radian.
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For the Ebb formula, each line in a :doc:`angle\_coeff <angle_coeff>`
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For the :math:`E_{bb}` formula, each line in a :doc:`angle\_coeff <angle_coeff>`
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command in the input script lists 4 coefficients, the first of which
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is "bb" to indicate they are BondBond coefficients. In a data file,
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these coefficients should be listed under a "BondBond Coeffs" heading
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@ -69,11 +74,11 @@ and you must leave out the "bb", i.e. only list 3 coefficients after
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the angle type.
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* bb
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* M (energy/distance\^2)
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* r1 (distance)
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* r2 (distance)
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* :math:`M` (energy/distance\^2)
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* :math:`r_1` (distance)
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* :math:`r_2` (distance)
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For the Eba formula, each line in a :doc:`angle\_coeff <angle_coeff>`
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For the :math:`E_{ba}` formula, each line in a :doc:`angle\_coeff <angle_coeff>`
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command in the input script lists 5 coefficients, the first of which
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is "ba" to indicate they are BondAngle coefficients. In a data file,
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these coefficients should be listed under a "BondAngle Coeffs" heading
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@ -81,13 +86,13 @@ and you must leave out the "ba", i.e. only list 4 coefficients after
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the angle type.
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* ba
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* N1 (energy/distance\^2)
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* N2 (energy/distance\^2)
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* r1 (distance)
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* r2 (distance)
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* :math:`N_1` (energy/distance\^2)
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* :math:`N_2` (energy/distance\^2)
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* :math:`r_1` (distance)
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* :math:`r_2` (distance)
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The theta0 value in the Eba formula is not specified, since it is the
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same value from the Ea formula.
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The :math:`\theta_0` value in the :math:`E_{ba}` formula is not specified,
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since it is the same value from the :math:`E_a` formula.
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----------
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@ -117,17 +122,19 @@ instructions on how to use the accelerated styles effectively.
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The *class2/p6* angle style uses the *class2* potential expanded to sixth order:
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.. image:: Eqs/angle_class2_p6.jpg
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:align: center
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.. math::
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In this expanded term 6 coefficients for the Ea formula need to be set:
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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
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* theta0 (degrees)
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* K2 (energy/radian\^2)
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* K3 (energy/radian\^3)
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* K4 (energy/radian\^4)
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* K5 (energy/radian\^5)
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* K6 (energy/radian\^6)
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In this expanded term 6 coefficients for the :math:`E_a` formula need to be set:
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* :math:`\theta_0` (degrees)
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* :math:`K_2` (energy/radian\^2)
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* :math:`K_3` (energy/radian\^3)
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* :math:`K_4` (energy/radian\^4)
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* :math:`K_5` (energy/radian\^5)
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* :math:`K_6` (energy/radian\^6)
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The bond-bond and bond-angle terms remain unchanged.
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@ -160,8 +167,3 @@ Related commands
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**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Commands_all.html
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@ -1,138 +0,0 @@
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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Commands_all.html)
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:line
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angle_style class2 command :h3
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angle_style class2/kk command :h3
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angle_style class2/omp command :h3
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angle_style class2/p6 command :h3
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[Syntax:]
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angle_style class2 :pre
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[Examples:]
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angle_style class2
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angle_coeff * 75.0
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angle_coeff 1 bb 10.5872 1.0119 1.5228
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angle_coeff * ba 3.6551 24.895 1.0119 1.5228 :pre
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[Description:]
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The {class2} angle style uses the potential
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:c,image(Eqs/angle_class2.jpg)
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where Ea is the angle term, Ebb is a bond-bond term, and Eba is a
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bond-angle term. Theta0 is the equilibrium angle and r1 and r2 are
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the equilibrium bond lengths.
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See "(Sun)"_#angle-Sun for a description of the COMPASS class2 force field.
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Coefficients for the Ea, Ebb, and Eba formulas must be defined for
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each angle type via the "angle_coeff"_angle_coeff.html command as in
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the example above, or in the data file or restart files read by the
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"read_data"_read_data.html or "read_restart"_read_restart.html
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commands.
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These are the 4 coefficients for the Ea formula:
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theta0 (degrees)
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K2 (energy/radian^2)
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K3 (energy/radian^3)
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K4 (energy/radian^4) :ul
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Theta0 is specified in degrees, but LAMMPS converts it to radians
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internally; hence the units of the various K are in per-radian.
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For the Ebb formula, each line in a "angle_coeff"_angle_coeff.html
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command in the input script lists 4 coefficients, the first of which
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is "bb" to indicate they are BondBond coefficients. In a data file,
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these coefficients should be listed under a "BondBond Coeffs" heading
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and you must leave out the "bb", i.e. only list 3 coefficients after
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the angle type.
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bb
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M (energy/distance^2)
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r1 (distance)
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r2 (distance) :ul
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For the Eba formula, each line in a "angle_coeff"_angle_coeff.html
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command in the input script lists 5 coefficients, the first of which
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is "ba" to indicate they are BondAngle coefficients. In a data file,
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these coefficients should be listed under a "BondAngle Coeffs" heading
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and you must leave out the "ba", i.e. only list 4 coefficients after
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the angle type.
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ba
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N1 (energy/distance^2)
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N2 (energy/distance^2)
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r1 (distance)
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r2 (distance) :ul
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The theta0 value in the Eba formula is not specified, since it is the
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same value from the Ea formula.
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:line
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Styles with a {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are
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functionally the same as the corresponding style without the suffix.
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They have been optimized to run faster, depending on your available
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hardware, as discussed on the "Speed packages"_Speed_packages.html doc
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page. The accelerated styles take the same arguments and should
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produce the same results, except for round-off and precision issues.
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These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
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USER-OMP and OPT packages, respectively. They are only enabled if
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LAMMPS was built with those packages. See the "Build
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package"_Build_package.html doc page for more info.
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You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the "-suffix command-line
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switch"_Run_options.html when you invoke LAMMPS, or you can use the
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"suffix"_suffix.html command in your input script.
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See the "Speed packages"_Speed_packages.html doc page for more
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instructions on how to use the accelerated styles effectively.
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:line
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The {class2/p6} angle style uses the {class2} potential expanded to sixth order:
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:c,image(Eqs/angle_class2_p6.jpg)
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In this expanded term 6 coefficients for the Ea formula need to be set:
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theta0 (degrees)
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K2 (energy/radian^2)
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K3 (energy/radian^3)
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K4 (energy/radian^4)
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K5 (energy/radian^5)
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K6 (energy/radian^6) :ul
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The bond-bond and bond-angle terms remain unchanged.
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:line
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[Restrictions:]
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This angle style can only be used if LAMMPS was built with the CLASS2
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package. For the {class2/p6} style LAMMPS needs to be built with the
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USER-MOFFF package. See the "Build package"_Build_package.html doc
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page for more info.
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[Related commands:]
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"angle_coeff"_angle_coeff.html
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[Default:] none
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:line
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:link(angle-Sun)
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[(Sun)] Sun, J Phys Chem B 102, 7338-7364 (1998).
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