.. index:: pair_style lj/cut/dipole/cut
.. index:: pair_style lj/cut/dipole/cut/gpu
.. index:: pair_style lj/cut/dipole/cut/omp
.. index:: pair_style lj/sf/dipole/sf
.. index:: pair_style lj/sf/dipole/sf/gpu
.. index:: pair_style lj/sf/dipole/sf/omp
.. index:: pair_style lj/cut/dipole/long
.. index:: pair_style lj/cut/dipole/long/gpu
.. index:: pair_style lj/long/dipole/long

pair_style lj/cut/dipole/cut command
====================================

Accelerator Variants: *lj/cut/dipole/cut/gpu*, *lj/cut/dipole/cut/omp*

pair_style lj/sf/dipole/sf command
==================================

Accelerator Variants: *lj/sf/dipole/sf/gpu*, *lj/sf/dipole/sf/omp*

pair_style lj/cut/dipole/long command
=====================================

Accelerator Variants: *lj/cut/dipole/long/gpu*

pair_style lj/long/dipole/long command
======================================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style lj/cut/dipole/cut cutoff (cutoff2)
   pair_style lj/sf/dipole/sf cutoff (cutoff2)
   pair_style lj/cut/dipole/long cutoff (cutoff2)
   pair_style lj/long/dipole/long flag_lj flag_coul cutoff (cutoff2)

* cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)
* cutoff2 = global cutoff for Coulombic and dipole (optional) (distance units)
* flag_lj = *long* or *cut* or *off*

  .. parsed-literal::

       *long* = use long-range damping on dispersion 1/r\^6 term
       *cut* = use a cutoff on dispersion 1/r\^6 term
       *off* = omit disperion 1/r\^6 term entirely

* flag_coul = *long* or *off*

  .. parsed-literal::

       *long* = use long-range damping on Coulombic 1/r and point-dipole terms
       *off* = omit Coulombic and point-dipole terms entirely

Examples
""""""""

.. code-block:: LAMMPS

   pair_style lj/cut/dipole/cut 10.0
   pair_coeff * * 1.0 1.0
   pair_coeff 2 3 1.0 1.0 2.5 4.0

   pair_style lj/sf/dipole/sf 9.0
   pair_coeff * * 1.0 1.0
   pair_coeff 2 3 1.0 1.0 2.5 4.0 scale 0.5
   pair_coeff 2 3 1.0 1.0 2.5 4.0

   pair_style lj/cut/dipole/long 10.0
   pair_coeff * * 1.0 1.0
   pair_coeff 2 3 1.0 1.0 2.5 4.0

   pair_style lj/long/dipole/long long long 3.5 10.0
   pair_coeff * * 1.0 1.0
   pair_coeff 2 3 1.0 1.0 2.5 4.0

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

Style *lj/cut/dipole/cut* computes interactions between pairs of particles
that each have a charge and/or a point dipole moment.  In addition to
the usual Lennard-Jones interaction between the particles (Elj) the
charge-charge (Eqq), charge-dipole (Eqp), and dipole-dipole (Epp)
interactions are computed by these formulas for the energy (E), force
(F), and torque (T) between particles I and J.

.. math::

   E_{LJ}  = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
                        \left(\frac{\sigma}{r}\right)^6 \right] \\
   E_{qq}  = & \frac{q_i q_j}{r} \\
   E_{qp}  = & \frac{q}{r^3} (p \bullet \vec{r}) \\
   E_{pp}  = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) -
             \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r}) \\
             & \\
   F_{qq}  = & \frac{q_i q_j}{r^3} \vec{r} \\
   F_{qp}  = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5}
             (\vec{p} \bullet \vec{r}) \vec{r} \\
   F_{pp}  = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} -
             \frac{15}{r^7} (\vec{p_i} \bullet \vec{r})
             (\vec{p_j} \bullet \vec{r}) \vec{r} +
             \frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} +
             (\vec{p_i} \bullet \vec{r}) \vec{p_j} \right] \\
             & \\
   T_{pq} = T_{ij}  = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\
   T_{qp} = T_{ji}  = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\
   T_{pp} = T_{ij}  = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) +
                      \frac{3}{r^5} (\vec{p_j} \bullet \vec{r})
                      (\vec{p_i} \times \vec{r}) \\
   T_{pp} = T_{ji}  = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) +
                      \frac{3}{r^5} (\vec{p_i} \bullet \vec{r})
                      (\vec{p_j} \times \vec{r})

where :math:`q_i` and :math:`q_j` are the charges on the two particles,
:math:`\vec{p_i}` and :math:`\vec{p_j}` are the dipole moment vectors of
the two particles, r is their separation distance, and the vector r =
Ri - Rj is the separation vector between the two particles.  Note that
Eqq and Fqq are simply Coulombic energy and force, Fij = -Fji as
symmetric forces, and Tij != -Tji since the torques do not act
symmetrically.  These formulas are discussed in :ref:`(Allen) <Allen2>`
and in :ref:`(Toukmaji) <Toukmaji2>`.

Also note, that in the code, all of these terms (except Elj) have a
:math:`C/\epsilon` prefactor, the same as the Coulombic term in the LJ +
Coulombic pair styles discussed :doc:`here <pair_lj>`.  C is an
energy-conversion constant and epsilon is the dielectric constant
which can be set by the :doc:`dielectric <dielectric>` command.  The
same is true of the equations that follow for other dipole pair
styles.

Style *lj/sf/dipole/sf* computes "shifted-force" interactions between
pairs of particles that each have a charge and/or a point dipole
moment. In general, a shifted-force potential is a (slightly) modified
potential containing extra terms that make both the energy and its
derivative go to zero at the cutoff distance; this removes
(cutoff-related) problems in energy conservation and any numerical
instability in the equations of motion :ref:`(Allen) <Allen2>`. Shifted-force
interactions for the Lennard-Jones (E_LJ), charge-charge (Eqq),
charge-dipole (Eqp), dipole-charge (Epq) and dipole-dipole (Epp)
potentials are computed by these formulas for the energy (E), force
(F), and torque (T) between particles I and J:

.. math::

   E_{LJ}  = &  4\epsilon \left\{ \left[ \left( \frac{\sigma}{r} \right)^{\!12} -
  \left( \frac{\sigma}{r} \right)^{\!6}  \right] +
  \left[ 6\left( \frac{\sigma}{r_c} \right)^{\!12} -
  3\left(\frac{\sigma}{r_c}\right)^{\!6}\right]\left(\frac{r}{r_c}\right)^{\!2}
  - 7\left( \frac{\sigma}{r_c} \right)^{\!12} +
  4\left( \frac{\sigma}{r_c} \right)^{\!6}\right\} \\
  E_{qq}  = & \frac{q_i q_j}{r}\left(1-\frac{r}{r_c}\right)^{\!2} \\
  E_{pq}  = & E_{ji} = -\frac{q}{r^3} \left[ 1 -
  3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
  E_{qp}  = & E_{ij} = \frac{q}{r^3} \left[ 1 -
  3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
  E_{pp} = & \left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right]\left[\frac{1}{r^3}
  (\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5}
  (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right] \\
           & \\

  F_{LJ}  = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{\!12} -
  24\epsilon \left(\frac{\sigma}{r}\right)^{\!6} \right]\frac{1}{r^2} -
  \left[48\epsilon \left(\frac{\sigma}{r_c}\right)^{\!12} - 24\epsilon
  \left(\frac{\sigma}{r_c}\right)^{\!6} \right]\frac{1}{r_c^2}\right\}\vec{r}\\
  F_{qq}  = & \frac{q_i q_j}{r}\left(\frac{1}{r^2} -
  \frac{1}{r_c^2}\right)\vec{r} \\
  F_{pq} = & F_{ij } =  -\frac{3q}{r^5} \left[ 1 -
  \left(\frac{r}{r_c}\right)^{\!2}\right](\vec{p}\bullet\vec{r})\vec{r} +
  \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
  F_{qp} = & F_{ij}  = \frac{3q}{r^5} \left[ 1 -
  \left(\frac{r}{r_c}\right)^{\!2}\right] (\vec{p}\bullet\vec{r})\vec{r} -
  \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
  F_{pp}  = &\frac{3}{r^5}\Bigg\{\left[1-\left(\frac{r}{r_c}\right)^{\!4}\right]
  \left[(\vec{p_i}\bullet\vec{p_j}) - \frac{3}{r^2} (\vec{p_i}\bullet\vec{r})
  (\vec{p_j} \bullet \vec{r})\right] \vec{r} + \\
    & \left[1 -
  4\left(\frac{r}{r_c}\right)^{\!3}+3\left(\frac{r}{r_c}\right)^{\!4}\right]
  \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + (\vec{p_i} \bullet \vec{r})
  \vec{p_j} -\frac{2}{r^2} (\vec{p_i} \bullet \vec{r})
  (\vec{p_j} \bullet \vec{r})\vec{r}\right] \Bigg\}

.. math::

   T_{pq} = T_{ij}  = & \frac{q_j}{r^3} \left[ 1 -
  3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\
  T_{qp} = T_{ji}  = & - \frac{q_i}{r^3} \left[ 1 -
  3\left(\frac{r}{r_c}\right)^{\!2} +
  2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\
  T_{pp} = T_{ij}  = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\
                     & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r})
  (\vec{p_i} \times \vec{r}) \\
  T_{pp} = T_{ji} = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\
                     & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r})
  (\vec{p_j} \times \vec{r})

where :math:`\epsilon` and :math:`\sigma` are the standard LJ
parameters, :math:`r_c` is the cutoff, :math:`q_i` and :math:`q_j` are
the charges on the two particles, :math:`\vec{p_i}` and
:math:`\vec{p_j}` are the dipole moment vectors of the two particles, r
is their separation distance, and the vector r = Ri - Rj is the
separation vector between the two particles.  Note that Eqq and Fqq are
simply Coulombic energy and force, Fij = -Fji as symmetric forces, and
Tij != -Tji since the torques do not act symmetrically.  The
shifted-force formula for the Lennard-Jones potential is reported in
:ref:`(Stoddard) <Stoddard>`.  The original (non-shifted) formulas for
the electrostatic potentials, forces and torques can be found in
:ref:`(Price) <Price2>`. The shifted-force electrostatic potentials have
been obtained by applying equation 5.13 of :ref:`(Allen) <Allen2>`. The
formulas for the corresponding forces and torques have been obtained by
applying the 'chain rule' as in appendix C.3 of :ref:`(Allen) <Allen2>`.

If one cutoff is specified in the pair_style command, it is used for
both the LJ and Coulombic (q,p) terms.  If two cutoffs are specified,
they are used as cutoffs for the LJ and Coulombic (q,p) terms
respectively. This pair style also supports an optional *scale* keyword
as part of a pair_coeff statement, where the interactions can be
scaled according to this factor. This scale factor is also made available
for use with fix adapt.

Style *lj/cut/dipole/long* computes long-range point-dipole
interactions as discussed in :ref:`(Toukmaji) <Toukmaji2>`. Dipole-dipole,
dipole-charge, and charge-charge interactions are all supported, along
with the standard 12/6 Lennard-Jones interactions, which are computed
with a cutoff.  A :doc:`kspace_style <kspace_style>` must be defined to
use this pair style.  Currently, only :doc:`kspace_style ewald/disp <kspace_style>` support long-range point-dipole
interactions.

Style *lj/long/dipole/long* also computes point-dipole interactions as
discussed in :ref:`(Toukmaji) <Toukmaji2>`. Long-range dipole-dipole,
dipole-charge, and charge-charge interactions are all supported, along
with the standard 12/6 Lennard-Jones interactions.  LJ interactions
can be cutoff or long-ranged.

For style *lj/long/dipole/long*, if *flag_lj* is set to *long*, no
cutoff is used on the LJ 1/r\^6 dispersion term.  The long-range
portion is calculated by using the :doc:`kspace_style ewald_disp <kspace_style>` command.  The specified LJ cutoff then
determines which portion of the LJ interactions are computed directly
by the pair potential versus which part is computed in reciprocal
space via the Kspace style.  If *flag_lj* is set to *cut*, the LJ
interactions are simply cutoff, as with :doc:`pair_style lj/cut <pair_lj>`.  If *flag_lj* is set to *off*, LJ interactions
are not computed at all.

If *flag_coul* is set to *long*, no cutoff is used on the Coulombic or
dipole interactions.  The long-range portion is calculated by using
*ewald_disp* of the :doc:`kspace_style <kspace_style>` command. If
*flag_coul* is set to *off*, Coulombic and dipole interactions are not
computed at all.

Atoms with dipole moments should be integrated using the :doc:`fix nve/sphere update dipole <fix_nve_sphere>` or the :doc:`fix nvt/sphere update dipole <fix_nvt_sphere>` command to rotate the
dipole moments.  The *omega* option on the :doc:`fix langevin <fix_langevin>` command can be used to thermostat the
rotational motion.  The :doc:`compute temp/sphere <compute_temp_sphere>`
command can be used to monitor the temperature, since it includes
rotational degrees of freedom.  The :doc:`atom_style hybrid dipole sphere <atom_style>` command should be used since
it defines the point dipoles and their rotational state.
The magnitude and orientation of the dipole moment for each particle
can be defined by the :doc:`set <set>` command or in the "Atoms" section
of the data file read in by the :doc:`read_data <read_data>` command.

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

* :math:`\epsilon` (energy units)
* :math:`\sigma` (distance units)
* cutoff1 (distance units)
* cutoff2 (distance units)

The latter 2 coefficients are optional.  If not specified, the global
LJ and Coulombic cutoffs specified in the pair_style command are used.
If only one cutoff is specified, it is used as the cutoff for both LJ
and Coulombic interactions for this type pair.  If both coefficients
are specified, they are used as the LJ and Coulombic cutoffs for this
type pair.

----------

.. include:: accel_styles.rst

----------

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

For atom type pairs I,J and I != J, the epsilon and sigma coefficients
and cutoff distances for this pair style can be mixed.  The default
mix value is *geometric*\ .  See the "pair_modify" command for details.

For atom type pairs I,J and I != J, the A, sigma, d1, and d2
coefficients and cutoff distance for this pair style can be mixed.  A
is an energy value mixed like a LJ epsilon.  D1 and d2 are distance
values and are mixed like sigma.  The default mix value is
*geometric*\ .  See the "pair_modify" command for details.

This pair style does not support the :doc:`pair_modify <pair_modify>`
shift option for the energy of the Lennard-Jones portion of the pair
interaction; such energy goes to zero at the cutoff by construction.

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 writes its information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.

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
""""""""""""

The *lj/cut/dipole/cut*, *lj/cut/dipole/long*, *lj/long/dipole/long*,
and lj/sf/dipole/sf* styles are part of the DIPOLE package.  They are only
enabled if LAMMPS was built with that package.  See the
:doc:`Build package <Build_package>` page for more info.

Using dipole pair styles with *electron* :doc:`units <units>` is not currently supported.

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

:doc:`pair_coeff <pair_coeff>`, :doc:`set <set>`, :doc:`read_data <read_data>`,
:doc:`fix nve/sphere <fix_nve_sphere>`, :doc:`fix nvt/sphere <fix_nvt_sphere>`

Default
"""""""

none

----------

.. _Allen2:

**(Allen)** Allen and Tildesley, Computer Simulation of Liquids,
Clarendon Press, Oxford, 1987.

.. _Toukmaji2:

**(Toukmaji)** Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
10913 (2000).

.. _Stoddard:

**(Stoddard)** Stoddard and Ford, Phys Rev A, 8, 1504 (1973).

.. _Price2:

**(Price)** Price, Stone and Alderton, Mol Phys, 52, 987 (1984).
