.. index:: pair_style coul/diel

pair_style coul/diel command
============================

pair_style coul/diel/omp command
================================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style coul/diel cutoff

cutoff = global cutoff (distance units)

Examples
""""""""

.. code-block:: LAMMPS

   pair_style coul/diel 3.5
   pair_coeff 1 4 78. 1.375 0.112

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

Style *coul/diel* computes a Coulomb correction for implicit solvent
ion interactions in which the dielectric permittivity is distance dependent.
The dielectric permittivity epsilon_D(r) connects to limiting regimes:
One limit is defined by a small dielectric permittivity (close to vacuum)
at or close to contact separation between the ions. At larger separations
the dielectric permittivity reaches a bulk value used in the regular Coulomb
interaction coul/long or coul/cut.
The transition is modeled by a hyperbolic function which is incorporated
in the Coulomb correction term for small ion separations as follows

.. math::

   E  = & \frac{Cq_iq_j}{\epsilon r} \left( \frac{\epsilon}{\epsilon_D(r)}-1\right)                       \qquad r < r_c \\
   \epsilon_D(r)  = & \frac{5.2+\epsilon}{2} +  \frac{\epsilon-5.2}{2}\tanh\left(\frac{r-r_{me}}{\sigma_e}\right)

where :math:`r_{me}` is the inflection point of :math:`\epsilon_D(r)` and :math:`\sigma_e` is a slope
defining length scale. C is the same Coulomb conversion factor as in the
pair_styles coul/cut, coul/long, and coul/debye. In this way the Coulomb
interaction between ions is corrected at small distances r. The lower
limit of epsilon_D(r->0)=5.2 due to dielectric saturation :ref:`(Stiles) <Stiles>`
while the Coulomb interaction reaches its bulk limit by setting
:math:`\epsilon_D(r \to \infty) = \epsilon`, the bulk value of the solvent which is 78
for water at 298K.

Examples of the use of this type of Coulomb interaction include implicit
solvent simulations of salt ions
:ref:`(Lenart) <Lenart1>` and of ionic surfactants :ref:`(Jusufi) <Jusufi1>`.
Note that this potential is only reasonable for implicit solvent simulations
and in combination with coul/cut or coul/long. It is also usually combined
with gauss/cut, see :ref:`(Lenart) <Lenart1>` or :ref:`(Jusufi) <Jusufi1>`.

The following coefficients must be defined for each pair of atom
types via the :doc:`pair_coeff <pair_coeff>` command as in the example
above, or in the data file or restart files read by the
:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
commands:

* :math:`\epsilon` (no units)
* :math:`r_{me}` (distance units)
* :math:`\sigma_e` (distance units)

The global cutoff (:math:`r_c`) specified in the pair_style command is used.

----------

**Mixing, shift, table, tail correction, restart, rRESPA info**\ :

This pair style does not support parameter mixing. Coefficients must
be given explicitly for each type of particle pairs.

This pair style supports the :doc:`pair_modify <pair_modify>` shift
option for the energy of the Gauss-potential portion of the pair
interaction.

The :doc:`pair_modify <pair_modify>` table option is not relevant
for this pair style.

This pair style does not support the :doc:`pair_modify <pair_modify>`
tail option for adding long-range tail corrections to energy and
pressure.

This pair style can only be used via the *pair* keyword of the
:doc:`run_style respa <run_style>` command.  It does not support the
*inner*\ , *middle*\ , *outer* keywords.

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

This style is part of the "USER-MISC" package.  It is only enabled if
LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` doc page for more info.

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

:doc:`pair_coeff <pair_coeff>`
:doc:`pair_style gauss/cut <pair_gauss>`

**Default:** none

----------

.. _Stiles:

**(Stiles)** Stiles , Hubbard, and Kayser, J Chem Phys, 77,
6189 (1982).

.. _Lenart1:

**(Lenart)** Lenart , Jusufi, and Panagiotopoulos, J Chem Phys, 126,
044509 (2007).

.. _Jusufi1:

**(Jusufi)** Jusufi, Hynninen, and Panagiotopoulos, J Phys Chem B, 112,
13783 (2008).
