87 lines
2.5 KiB
ReStructuredText
87 lines
2.5 KiB
ReStructuredText
.. index:: improper_style ring
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.. index:: improper_style ring/omp
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improper_style ring command
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===========================
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Accelerator Variants: *ring/omp*
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Syntax
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""""""
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.. code-block:: LAMMPS
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improper_style ring
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Examples
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""""""""
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.. code-block:: LAMMPS
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improper_style ring
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improper_coeff 1 8000 70.5
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Description
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"""""""""""
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The *ring* improper style uses the potential
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.. math::
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E = &\frac{1}{6} K \left(\Delta_{ijl} + \Delta_{ijk} + \Delta_{kjl} \right)^6 \\
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\Delta_{ijl} = & \cos{\theta_{ijl} - \cos{\theta_0}} \\
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\Delta_{ijk} = & \cos{\theta_{ijk} - \cos{\theta_0}} \\
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\Delta_{kjl} = & \cos{\theta_{kjl} - \cos{\theta_0}}
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where :math:`K` is a prefactor, :math:`\theta` is the angle formed by
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the atoms specified by (i,j,k,l) indices and :math:`\theta_0` its
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equilibrium value.
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If the 4 atoms in an improper quadruplet (listed in the data file read
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by the :doc:`read_data <read_data>` command) are ordered i,j,k,l then
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:math:`\theta_{ijl}` is the angle between atoms i,j and l,
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:math:`\theta_{ijk}` is the angle between atoms i,j and k,
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:math:`\theta_{kjl}` is the angle between atoms j,k, and l.
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The "ring" improper style implements the improper potential introduced
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by Destree et al., in Equation (9) of :ref:`(Destree) <Destree>`. This
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potential does not affect small amplitude vibrations but is used in an
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ad-hoc way to prevent the onset of accidentally large amplitude
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fluctuations leading to the occurrence of a planar conformation of the
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three bonds i-j, j-k and j-l, an intermediate conformation toward the
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chiral inversion of a methine carbon. In the "Impropers" section of
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data file four atoms: i, j, k and l are specified with i,j and l lying
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on the backbone of the chain and k specifying the chirality of j.
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The following coefficients must be defined for each improper type via
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the :doc:`improper_coeff <improper_coeff>` command as in the example
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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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* :math:`K` (energy)
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* :math:`\theta_0` (degrees)
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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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MOLECULE 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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.. _Destree:
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**(Destree)** M. Destree, F. Laupretre, A. Lyulin, and J.-P. Ryckaert,
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J Chem Phys, 112, 9632 (2000).
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