Update pair_airebo docs

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$$ 

  E = \frac{1}{2} \sum_i \sum_{j \neq i} 

  \left[ E^{REBO}_{ij} + E^{LJ}_{ij} + 

    \sum_{k \neq i,j} \sum_{l \neq i,j,k} E^{TORSION}_{kijl} \right] 

$$

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.. index:: pair\_style airebo

.. index:: pair_style airebo

pair\_style airebo command

==========================

pair_style airebo command

=========================

pair\_style airebo/intel command

================================

pair_style airebo/intel command

===============================

pair\_style airebo/omp command

==============================

pair_style airebo/omp command

=============================

pair\_style airebo/morse command

================================

pair_style airebo/morse command

===============================

pair\_style airebo/morse/intel command

======================================

pair_style airebo/morse/intel command

=====================================

pair\_style airebo/morse/omp command

====================================

pair_style airebo/morse/omp command

===================================

pair\_style rebo command

========================

pair_style rebo command

=======================

pair\_style rebo/intel command

==============================

pair_style rebo/intel command

=============================

pair\_style rebo/omp command

============================

pair_style rebo/omp command

===========================

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   pair_style style cutoff LJ_flag TORSION_flag cutoff_min

* style = *airebo* or *airebo/morse* or *rebo*

* cutoff = LJ or Morse cutoff (sigma scale factor) (AIREBO and AIREBO-M only)

* cutoff = LJ or Morse cutoff (:math:`\sigma` scale factor) (AIREBO and AIREBO-M only)

* LJ\_flag = 0/1 to turn off/on the LJ or Morse term (AIREBO and AIREBO-M only, optional)

* TORSION\_flag = 0/1 to turn off/on the torsion term (AIREBO and AIREBO-M only, optional)

* cutoff\_min = Start of the transition region of cutoff (sigma scale factor) (AIREBO and AIREBO-M only, optional)

* cutoff\_min = Start of the transition region of cutoff (:math:`\sigma` scale factor) (AIREBO and AIREBO-M only, optional)

Examples

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   pair_style airebo 3.0

   pair_style airebo 2.5 1 0

   pair_coeff \* \* ../potentials/CH.airebo H C

   pair_coeff * * ../potentials/CH.airebo H C

   pair_style airebo/morse 3.0

   pair_coeff \* \* ../potentials/CH.airebo-m H C

   pair_coeff * * ../potentials/CH.airebo-m H C

   pair_style rebo

   pair_coeff \* \* ../potentials/CH.rebo H C

   pair_coeff * * ../potentials/CH.rebo H C

Description

"""""""""""

The AIREBO potential consists of three terms:

.. image:: Eqs/pair_airebo.jpg

   :align: center

.. math::

   E & = \frac{1}{2} \sum_i \sum_{j \neq i} 

   \left[ E^{\text{REBO}}_{ij} + E^{\text{LJ}}_{ij} + 

    \sum_{k \neq i,j} \sum_{l \neq i,j,k} E^{\text{TORSION}}_{kijl} \right] \\

By default, all three terms are included.  For the *airebo* style, if

the first two optional flag arguments to the pair\_style command are

both or neither of the flags must be included.  If both of the LJ an

torsional terms are turned off, it becomes the 2nd-generation REBO

potential, with a small caveat on the spline fitting procedure

mentioned below.  This can be specified directly as pair\_style *rebo*

mentioned below.  This can be specified directly as pair_style *rebo*

with no additional arguments.

The detailed formulas for this potential are given in

:ref:`(Stuart) <Stuart>`; here we provide only a brief description.

The E\_REBO term has the same functional form as the hydrocarbon REBO

The :math:`E^{\text{REBO}}` term has the same functional form as the hydrocarbon REBO

potential developed in :ref:`(Brenner) <Brenner>`.  The coefficients for

E\_REBO in AIREBO are essentially the same as Brenner's potential, but

:math:`E^{\text{REBO}}` in AIREBO are essentially the same as Brenner's potential, but

a few fitted spline values are slightly different.  For most cases the

E\_REBO term in AIREBO will produce the same energies, forces and

:math:`E^{\text{REBO}}` term in AIREBO will produce the same energies, forces and

statistical averages as the original REBO potential from which it was

derived.  The E\_REBO term in the AIREBO potential gives the model its

derived.  The :math:`E^{\text{REBO}}` term in the AIREBO potential gives the model its

reactive capabilities and only describes short-ranged C-C, C-H and H-H

interactions (r < 2 Angstroms). These interactions have strong

interactions (:math:`r < 2` Angstroms). These interactions have strong

coordination-dependence through a bond order parameter, which adjusts

the attraction between the I,J atoms based on the position of other

nearby atoms and thus has 3- and 4-body dependence.

The E\_LJ term adds longer-ranged interactions (2 < r < cutoff) using a

The :math:`E^{\text{LJ}}` term adds longer-ranged interactions (:math:`2 < r < \text{cutoff}`) using a

form similar to the standard :doc:`Lennard Jones potential <pair_lj>`.

The E\_LJ term in AIREBO contains a series of switching functions so

that the short-ranged LJ repulsion (1/r\^12) does not interfere with

the energetics captured by the E\_REBO term.  The extent of the E\_LJ

interactions is determined by the *cutoff* argument to the pair\_style

The :math:`E^{\text{LJ}}` term in AIREBO contains a series of switching functions so

that the short-ranged LJ repulsion (:math:`1/r^{12}`) does not interfere with

the energetics captured by the :math:`E^{\text{REBO}}` term.  The extent of the :math:`E^{\text{LJ}}`

interactions is determined by the *cutoff* argument to the pair_style

command which is a scale factor.  For each type pair (C-C, C-H, H-H)

the cutoff is obtained by multiplying the scale factor by the sigma

value defined in the potential file for that type pair.  In the

standard AIREBO potential, sigma\_CC = 3.4 Angstroms, so with a scale

factor of 3.0 (the argument in pair\_style), the resulting E\_LJ cutoff

standard AIREBO potential, :math:`\sigma_{CC} = 3.4` Angstroms, so with a scale

factor of 3.0 (the argument in pair_style), the resulting :math:`E^{\text{LJ}}` cutoff

would be 10.2 Angstroms.

By default, the longer-ranged interaction is smoothly switched off

between 2.16 and 3.0 sigma. By specifying *cutoff\_min* in addition

between 2.16 and 3.0 :math:`\sigma`. By specifying *cutoff\_min* in addition

to *cutoff*\ , the switching can be configured to take place between

*cutoff\_min* and *cutoff*\ . *cutoff\_min* can only be specified if all

optional arguments are given.

The E\_TORSION term is an explicit 4-body potential that describes

The :math:`E^{\text{TORSION}}` term is an explicit 4-body potential that describes

various dihedral angle preferences in hydrocarbon configurations.

----------

Only a single pair\_coeff command is used with the *airebo*\ , *airebo*

Only a single pair_coeff command is used with the *airebo*\ , *airebo*

or *rebo* style which specifies an AIREBO, REBO, or AIREBO-M potential

file with parameters for C and H.  Note that as of LAMMPS version

15 May 2019 the *rebo* style in LAMMPS uses its own potential

file (CH.rebo).  These are mapped to LAMMPS atom types by specifying

N additional arguments after the filename in the pair\_coeff command,

N additional arguments after the filename in the pair_coeff command,

where N is the number of LAMMPS atom types:

* filename

* N element names = mapping of AIREBO elements to atom types

* :math:`N` element names = mapping of AIREBO elements to atom types

See the :doc:`pair_coeff <pair_coeff>` doc page for alternate ways

to specify the path for the potential file.

As an example, if your LAMMPS simulation has 4 atom types and you want

the 1st 3 to be C, and the 4th to be H, you would use the following

pair\_coeff command:

pair_coeff command:

.. parsed-literal::

.. code-block:: LAMMPS

   pair_coeff \* \* CH.airebo C C C H

   pair_coeff * * CH.airebo C C C H

The 1st 2 arguments must be \* \* so as to span all LAMMPS atom types.

The first three C arguments map LAMMPS atom types 1,2,3 to the C

paper. Thus the parameters are specific to this potential and the way

it was fit, so modifying the file should be done cautiously. The

AIREBO-M Morse potentials were parameterized using a cutoff of

3.0 (sigma). Modifying this cutoff may impact simulation accuracy.

3.0 (:math:`\sigma`). Modifying this cutoff may impact simulation accuracy.

This pair style tallies a breakdown of the total AIREBO potential

energy into sub-categories, which can be accessed via the :doc:`compute pair <compute_pair>` command as a vector of values of length 3.

The 3 values correspond to the following sub-categories:

1. *E\_REBO* = REBO energy

2. *E\_LJ* = Lennard-Jones energy

3. *E\_TORSION* = Torsion energy

1. :math:`E_{\text{REBO}}` = REBO energy

2. :math:`E_{\text{LJ}}` = Lennard-Jones energy

3. :math:`E_{\text{TORSION}}` = Torsion energy

To print these quantities to the log file (with descriptive column

headings) the following commands could be included in an input script:

.. parsed-literal::

.. code-block:: LAMMPS

   compute 0 all pair airebo

   variable REBO     equal c_0[1]

mix, shift, table, and tail options.

These pair styles do not write their information to :doc:`binary restart files <restart>`, since it is stored in potential files.  Thus, you

need to re-specify the pair\_style and pair\_coeff commands in an input

need to re-specify the pair_style and pair_coeff commands in an input

script that reads a restart file.

These pair styles can only be used via the *pair* keyword of the

:doc:`run_style respa <run_style>` command.  They do not support the

*inner*\ , *middle*\ , *outer* keywords.

*inner* , *middle*, *outer* keywords.

Restrictions

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