128 lines
3.8 KiB
ReStructuredText
128 lines
3.8 KiB
ReStructuredText
.. index:: improper_style class2
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improper_style class2 command
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=============================
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improper_style class2/omp command
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=================================
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improper_style class2/kk command
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================================
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Syntax
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""""""
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.. code-block:: LAMMPS
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improper_style class2
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Examples
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""""""""
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.. code-block:: LAMMPS
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improper_style class2
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improper_coeff 1 100.0 0
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improper_coeff * aa 0.0 0.0 0.0 115.06 130.01 115.06
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Description
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"""""""""""
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The *class2* improper style uses the potential
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.. math::
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E = & E_i + E_{aa} \\
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E_i = & K [ \frac{\chi_{ijkl} + \chi_{kjli} + \chi_{ljik}}{3} - \chi_0 ]^2 \\
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E_{aa} = & M_1 (\theta_{ijk} - \theta_1) (\theta_{kjl} - \theta_3) + \\
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& M_2 (\theta_{ijk} - \theta_1) (\theta_{ijl} - \theta_2) + \\
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& M_3 (\theta_{ijl} - \theta_2) (\theta_{kjl} - \theta_3)
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where :math:`E_i` is the improper term and :math:`E_{aa}` is an
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angle-angle term. The 3 :math:`\chi` terms in :math:`E_i` are an
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average over 3 out-of-plane angles.
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The 4 atoms in an improper quadruplet (listed in the data file read by
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the :doc:`read_data <read_data>` command) are ordered I,J,K,L.
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:math:`\chi_{ijkl}` refers to the angle between the plane of I,J,K and
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the plane of J,K,L, and the bond JK lies in both planes. Similarly for
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:math:`\chi_{kjli}` and :math:`\chi_{ljik}`.
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Note that atom J appears in the common bonds (JI, JK, JL) of all 3 X
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terms. Thus J (the second atom in the quadruplet) is the atom of
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symmetry in the 3 :math:`\chi` angles.
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The subscripts on the various :math:`\theta`\ s refer to different
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combinations of 3 atoms (I,J,K,L) used to form a particular angle.
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E.g. :math:`\theta_{ijl}` is the angle formed by atoms I,J,L with J
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in the middle. :math:`\theta_1`, :math:`\theta_2`, :math:`\theta_3`
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are the equilibrium positions of those angles. Again,
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atom J (the second atom in the quadruplet) is the atom of symmetry in the
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theta angles, since it is always the center atom.
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Since atom J is the atom of symmetry, normally the bonds J-I, J-K, J-L
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would exist for an improper to be defined between the 4 atoms, but
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this is not required.
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See :ref:`(Sun) <improper-Sun>` for a description of the COMPASS class2 force field.
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Coefficients for the :math:`E_i` and :math:`E_{aa}` formulas must be
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defined for each
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improper type via the :doc:`improper_coeff <improper_coeff>` command as
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in 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 2 coefficients for the :math:`E_i` formula:
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* :math:`K` (energy)
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* :math:`\chi_0` (degrees)
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:math:`\chi_0` is specified in degrees, but LAMMPS converts it to
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radians internally; hence :math:`K` is effectively energy per
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radian\^2.
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For the :math:`E_{aa}` formula, each line in a :doc:`improper_coeff
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<improper_coeff>` command in the input script lists 7 coefficients,
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the first of which is *aa* to indicate they are AngleAngle
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coefficients. In a data file, these coefficients should be listed
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under a *AngleAngle Coeffs* heading and you must leave out the *aa*,
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i.e. only list 6 coefficients after the improper type.
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* *aa*
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* :math:`M_1` (energy)
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* :math:`M_2` (energy)
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* :math:`M_3` (energy)
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* :math:`\theta_1` (degrees)
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* :math:`\theta_2` (degrees)
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* :math:`\theta_3` (degrees)
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The :math:`\theta` values are specified in degrees, but LAMMPS
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converts them to radians internally; hence the hence the various
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:math:`M` are effectively energy per radian\^2.
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----------
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.. include:: accel_styles.rst
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----------
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Restrictions
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""""""""""""
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This improper style can only be used if LAMMPS was built with the
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CLASS2 package. See the :doc:`Build package <Build_package>` doc
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page for more info.
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Related commands
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""""""""""""""""
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:doc:`improper_coeff <improper_coeff>`
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**Default:** none
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----------
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.. _improper-Sun:
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**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).
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