.. index:: pair_style thole
.. index:: pair_style lj/cut/thole/long
.. index:: pair_style lj/cut/thole/long/omp

pair_style thole command
========================

pair_style lj/cut/thole/long command
====================================

Accelerator Variants: *lj/cut/thole/long/omp*

Syntax
""""""

.. code-block:: LAMMPS

   pair_style style args

* style = *thole* or *lj/cut/thole/long* or *lj/cut/thole/long/omp*
* args = list of arguments for a particular style

.. parsed-literal::

     *thole* args = damp cutoff
       damp = global damping parameter
       cutoff = global cutoff (distance units)
     *lj/cut/thole/long* or *lj/cut/thole/long/omp* args = damp cutoff (cutoff2)
       damp = global damping parameter
       cutoff = global cutoff for LJ (and Thole if only 1 arg) (distance units)
       cutoff2 = global cutoff for Thole (optional) (distance units)

Examples
""""""""

.. code-block:: LAMMPS

   pair_style hybrid/overlay ... thole 2.6 12.0
   pair_coeff 1 1 thole 1.0
   pair_coeff 1 2 thole 1.0 2.6 10.0
   pair_coeff * 2 thole 1.0 2.6

   pair_style lj/cut/thole/long 2.6 12.0

Example input scripts available: examples/PACKAGES/drude

Description
"""""""""""

The *thole* pair styles are meant to be used with force fields that
include explicit polarization through Drude dipoles.  This link
describes how to use the :doc:`thermalized Drude oscillator model <Howto_drude>` in LAMMPS and polarizable models in LAMMPS are
discussed on the :doc:`Howto polarizable <Howto_polarizable>` doc page.

The *thole* pair style should be used as a sub-style within in the
:doc:`pair_style hybrid/overlay <pair_hybrid>` command, in conjunction with a
main pair style including Coulomb interactions, i.e. any pair style
containing *coul/cut* or *coul/long* in its style name.

The *lj/cut/thole/long* pair style is equivalent to, but more convenient that
the frequent combination *hybrid/overlay lj/cut/coul/long cutoff thole damp
cutoff2*\ . It is not only a shorthand for this pair_style combination, but
it also allows for mixing pair coefficients instead of listing them all.
The *lj/cut/thole/long* pair style is also a bit faster because it avoids an
overlay and can benefit from OMP acceleration. Moreover, it uses a more
precise approximation of the direct Coulomb interaction at short range similar
to :doc:`coul/long/cs <pair_cs>`, which stabilizes the temperature of
Drude particles.

The *thole* pair styles compute the Coulomb interaction damped at
short distances by a function

.. math::

   T_{ij}(r_{ij}) = 1 - \left( 1 +
   \frac{s_{ij} r_{ij} }{2} \right)
   \exp \left( - s_{ij} r_{ij} \right)

This function results from an adaptation to point charges
:ref:`(Noskov) <Noskov1>` of the dipole screening scheme originally proposed
by :ref:`Thole <Thole1>`. The scaling coefficient :math:`s_{ij}` is determined
by the polarizability of the atoms, :math:`\alpha_i`, and by a Thole
damping parameter :math:`a`.  This Thole damping parameter usually takes
a value of 2.6, but in certain force fields the value can depend upon
the atom types. The mixing rule for Thole damping parameters is the
arithmetic average, and for polarizabilities the geometric average
between the atom-specific values.

.. math::

   s_{ij} = \frac{ a_{ij} }{
   (\alpha_{ij})^{1/3} } = \frac{ (a_i + a_j)/2 }{
   [(\alpha_i\alpha_j)^{1/2}]^{1/3} }

The damping function is only applied to the interactions between the
point charges representing the induced dipoles on polarizable sites,
that is, charges on Drude particles, :math:`q_{D,i}`, and opposite
charges, :math:`-q_{D,i}`, located on the respective core particles
(to which each Drude particle is bonded). Therefore, Thole screening
is not applied to the full charge of the core particle :math:`q_i`, but
only to the :math:`-q_{D,i}` part of it.

The interactions between core charges are subject to the weighting
factors set by the :doc:`special_bonds <special_bonds>` command. The
interactions between Drude particles and core charges or
non-polarizable atoms are also subject to these weighting factors. The
Drude particles inherit the 1-2, 1-3 and 1-4 neighbor relations from
their respective cores.

For pair_style *thole*, the following coefficients must be defined for
each pair of atoms types via the :doc:`pair_coeff <pair_coeff>` command
as in the example above.

* :math:`\alpha` (distance units\^3)
* damp
* cutoff (distance units)

The last two coefficients are optional.  If not specified the global
Thole damping parameter or global cutoff specified in the pair_style
command are used. In order to specify a cutoff (third argument) a damp
parameter (second argument) must also be specified.

For pair style *lj/cut/thole/long*, the following coefficients must be
defined for each pair of atoms types via the :doc:`pair_coeff <pair_coeff>`
command.

* :math:`\epsilon` (energy units)
* :math:`\sigma` (length units)
* :math:`\alpha` (distance units\^3)
* damp
* LJ cutoff (distance units)

The last two coefficients are optional and default to the global values from
the *pair_style* command line.

----------

.. include:: accel_styles.rst

Mixing, shift, table, tail correction, restart, rRESPA info
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

The *thole* pair style does not support mixing.  Thus, coefficients
for all I,J pairs must be specified explicitly.

The *lj/cut/thole/long* pair style does support mixing. Mixed coefficients
are defined using

.. math::

   \alpha_{ij} = & \sqrt{\alpha_i\alpha_j} \\
   & \\
   a_{ij} = & \frac 1 2 (a_i + a_j)

Restrictions
""""""""""""

These pair styles are part of the DRUDE package. They are only
enabled if LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.

This pair_style should currently not be used with the :doc:`charmm dihedral style <dihedral_charmm>` if the latter has non-zero 1-4 weighting
factors. This is because the *thole* pair style does not know which
pairs are 1-4 partners of which dihedrals.

The *lj/cut/thole/long* pair style should be used with a :doc:`Kspace solver <kspace_style>`
like PPPM or Ewald, which is only enabled if LAMMPS was built with the kspace
package.

Related commands
""""""""""""""""

:doc:`fix drude <fix_drude>`, :doc:`fix langevin/drude <fix_langevin_drude>`, :doc:`fix drude/transform <fix_drude_transform>`, :doc:`compute temp/drude <compute_temp_drude>`
:doc:`pair_style lj/cut/coul/long <pair_lj_cut_coul>`

Default
"""""""

none

----------

.. _Noskov1:

**(Noskov)** Noskov, Lamoureux and Roux, J Phys Chem B, 109, 6705 (2005).

.. _Thole1:

**(Thole)** Chem Phys, 59, 341 (1981).
