131 lines
3.9 KiB
ReStructuredText
131 lines
3.9 KiB
ReStructuredText
.. index:: pair_style cosine/squared
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pair_style cosine/squared 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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pair_style cosine/squared cutoff
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* cutoff = global cutoff for cosine-squared interactions (distance units)
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.. code-block:: LAMMPS
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pair_coeff I J eps sigma
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pair_coeff I J eps sigma cutoff
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pair_coeff I J eps sigma wca
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pair_coeff I J eps sigma cutoff wca
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* I, J = a particle type
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* eps = interaction strength, i.e. the depth of the potential minimum (energy units)
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* sigma = distance of the potential minimum from 0
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* cutoff = the cutoff distance for this pair type, if different from global (distance units)
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* wca = if specified a Weeks-Chandler-Andersen potential (with eps strength and minimum at sigma) is added, otherwise not
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Examples
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""""""""
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.. code-block:: LAMMPS
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pair_style cosine/squared 3.0
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pair_coeff * * 1.0 1.3
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pair_coeff 1 3 1.0 1.3 2.0
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pair_coeff 1 3 1.0 1.3 wca
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pair_coeff 1 3 1.0 1.3 2.0 wca
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Description
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"""""""""""
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Style *cosine/squared* computes a potential of the form
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.. math::
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E =
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\begin{cases}
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-\epsilon& \quad r < \sigma \\
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-\epsilon\cos\left(\frac{\pi\left(r - \sigma\right)}{2\left(r_c - \sigma\right)}\right)^2&\quad \sigma \leq r < r_c \\
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0& \quad r \geq r_c
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\end{cases}
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between two point particles, where (:math:`\sigma, -\epsilon`) is the
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location of the (rightmost) minimum of the potential, as explained in
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the syntax section above.
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This potential was first used in :ref:`(Cooke) <CKD>` for a coarse-grained lipid
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membrane model. It is generally very useful as a non-specific
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interaction potential because it is fully adjustable in depth and width
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while joining the minimum at (sigma, -epsilon) and zero at (cutoff, 0)
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smoothly, requiring no shifting and causing no related artifacts, tail
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energy calculations etc. This evidently requires *cutoff* to be larger
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than *sigma*\ .
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If the *wca* option is used then a Weeks-Chandler-Andersen potential
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:ref:`(Weeks) <WCA>` is added to the above specified cosine-squared potential,
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specifically the following:
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.. math::
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E = \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
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2\left(\frac{\sigma}{r}\right)^6 + 1\right]
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, \quad r < \sigma
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In this case, and this case only, the :math:`\sigma` parameter can be equal to
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*cutoff* (:math:`\sigma =` cutoff) which will result in ONLY the WCA potential
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being used (and print a warning), so the minimum will be attained at
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(sigma, 0). This is a convenience feature that enables a purely
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repulsive potential to be used without a need to define an additional
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pair style and use the hybrid styles.
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The energy and force of this pair style for parameters epsilon = 1.0,
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sigma = 1.0, cutoff = 2.5, with and without the WCA potential, are shown
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in the graphs below:
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.. image:: JPG/pair_cosine_squared_graphs.jpg
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:align: center
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----------
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Mixing, shift, table, tail correction, restart, rRESPA info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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Mixing is not supported for this style.
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The *shift*, *table* and *tail* options are not relevant for this style.
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This pair style writes its information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands do not need
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to be specified in an input script that reads a restart file.
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These pair styles can only be used via the *pair* keyword of the
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:doc:`run_style respa <run_style>` command. They do not support the
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*inner*, *middle*, *outer* keywords.
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----------
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Restrictions
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""""""""""""
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The *cosine/squared* style is part of the EXTRA-PAIR package. It is only
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enabled if LAMMPS is build with that package. See the :doc:`Build package <Build_package>` page for more info.
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Related commands
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""""""""""""""""
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:doc:`pair_coeff <pair_coeff>`,
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:doc:`pair_style lj/cut <pair_lj>`
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Default
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"""""""
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none
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.. _CKD:
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**(Cooke)** "Cooke, Kremer and Deserno, Phys. Rev. E, 72, 011506 (2005)"
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.. _WCA:
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**(Weeks)** "Weeks, Chandler and Andersen, J. Chem. Phys., 54, 5237 (1971)"
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