"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Commands_all.html)

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pair_style cosine/squared command :h3

[Syntax:]

pair_style cosine/squared cutoff :pre

cutoff = global cutoff for cosine-squared interactions (distance units) :ul

pair_coeff i j eps sigma
pair_coeff i j eps sigma cutoff
pair_coeff i j eps sigma wca
pair_coeff i j eps sigma cutoff wca :pre

i,j = a particle type
eps = interaction strength, i.e. the depth of the potential minimum (energy units)
sigma = distance of the potential minimum from 0
cutoff = the cutoff distance for this pair type, if different from global (distance units)
wca = if specified a Weeks-Chandler-Andersen potential (with eps strength and minimum at sigma) is added, otherwise not :ul

[Examples:]

pair_style cosine/squared 3.0
pair_coeff * * 1.0 1.3
pair_coeff 1 3 1.0 1.3 2.0
pair_coeff 1 3 1.0 1.3 wca
pair_coeff 1 3 1.0 1.3 2.0 wca :pre

[Description:]

Style {cosine/squared} computes a potential of the form

:c,image(Eqs/pair_cosine_squared.jpg)

between two point particles, where (sigma, -epsilon) is the location of
the (rightmost) minimum of the potential, as explained in the syntax
section above.

This potential was first used in (Cooke)_#CKD for a coarse-grained lipid
membrane model.  It is generally very useful as a non-specific
interaction potential because it is fully adjustable in depth and width
while joining the minimum at (sigma, -epsilon) and zero at (cutoff, 0)
smoothly, requiring no shifting and causing no related artifacts, tail
energy calculations etc. This evidently requires {cutoff} to be larger
than {sigma}.

If the {wca} option is used then a Weeks-Chandler-Andersen potential
(Weeks)_#WCA is added to the above specified cosine-squared potential,
specifically the following:

:c,image(Eqs/pair_cosine_squared_wca.jpg)

In this case, and this case only, the {sigma} parameter can be equal to
{cutoff} (sigma = cutoff) which will result in ONLY the WCA potential
being used (and print a warning), so the minimum will be attained at
(sigma, 0). This is a convenience feature that enables a purely
repulsive potential to be used without a need to define an additional
pair style and use the hybrid styles.

The energy and force of this pair style for parameters epsilon = 1.0,
sigma = 1.0, cutoff = 2.5, with and without the WCA potential, are shown
in the graphs below:

:c,image(JPG/pair_cosine_squared_graphs.jpg)

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[Mixing, shift, table, tail correction, restart, rRESPA info]:

Mixing is not supported for this style.

The {shift}, {table} and {tail} options are not relevant for this style.

This pair style writes its information to "binary restart
files"_restart.html, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.

These pair styles can only be used via the {pair} keyword of the
"run_style respa"_run_style.html command.  They do not support the
{inner}, {middle}, {outer} keywords.

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[Restrictions:]

The {cosine/squared} style is part of the "USER-MISC" package. It is only
enabled if LAMMPS is build with that package.  See the "Build
package"_Build_package.html doc page for more info.

[Related commands:]

"pair_coeff"_pair_coeff.html,
"pair_style lj/cut"_pair_lj.html

[Default:] none

:link(CKD)
[(Cooke)] "Cooke, Kremer and Deserno, Phys. Rev. E, 72, 011506 (2005)"

:link(WCA)
[(Weeks)] "Weeks, Chandler and Andersen, J. Chem. Phys., 54, 5237 (1971)"
