Update pair_adp

\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}

E_i & = & F_\alpha \left( \sum_{j\neq i} \rho_\beta (r_{ij}) \right) + \frac{1}{2} \sum_{j\neq i}\phi_{\alpha\beta}(r_{ij})+ \frac{1}{2} \sum_s (\mu_i^s)^2 + \frac{1}{2} \sum_{s,t} (\lambda_i^{st})^2 - \frac{1}{6} \nu_i^2 \\

%

\mu_i^s & = & \sum_{j\neq i}u_{\alpha\beta}(r_{ij})r_{ij}^s\\

%

\lambda_i^{st} & = & \sum_{j\neq i}w_{\alpha\beta}(r_{ij})r_{ij}^sr_{ij}^t\\

%

\nu_i & = & \sum_s\lambda_i^{ss}

\end{eqnarray*}

\end{document}

.. index:: pair\_style adp

.. index:: pair_style adp

pair\_style adp command

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

pair_style adp command

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

pair\_style adp/omp command

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

pair_style adp/omp command

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

Syntax

""""""

.. parsed-literal::

.. code-block:: LAMMPS

   pair_style adp

""""""""

.. parsed-literal::

.. code-block:: LAMMPS

   pair_style adp

   pair_coeff \* \* Ta.adp Ta

   pair_coeff \* \* ../potentials/AlCu.adp Al Al Cu

   pair_coeff * * Ta.adp Ta

   pair_coeff * * ../potentials/AlCu.adp Al Al Cu

Description

"""""""""""

which is a generalization of the :doc:`embedded atom method (EAM) potential <pair_eam>`.  The LAMMPS implementation is discussed in

:ref:`(Singh) <Singh>`.  The total energy Ei of an atom I is given by

.. image:: Eqs/pair_adp.jpg

   :align: center

.. math::

where F is the embedding energy which is a function of the atomic

electron density rho, phi is a pair potential interaction, alpha and

beta are the element types of atoms I and J, and s and t = 1,2,3 and

refer to the cartesian coordinates.  The mu and lambda terms represent

the dipole and quadruple distortions of the local atomic environment

which extend the original EAM framework by introducing angular forces.

   E_i            & = F_\alpha \left( \sum_{j\neq i} \rho_\beta (r_{ij}) \right) + \frac{1}{2} \sum_{j\neq i}\phi_{\alpha\beta}(r_{ij})+ \frac{1}{2} \sum_s (\mu_i^s)^2 + \frac{1}{2} \sum_{s,t} (\lambda_i^{st})^2 - \frac{1}{6} \nu_i^2 \\

   \mu_i^s        & = \sum_{j\neq i}u_{\alpha\beta}(r_{ij})r_{ij}^s\\

   \lambda_i^{st} & = \sum_{j\neq i}w_{\alpha\beta}(r_{ij})r_{ij}^sr_{ij}^t\\

   \nu_i          & = \sum_s\lambda_i^{ss}

where :math:`F` is the embedding energy which is a function of the atomic

electron density :math:`\rho`, :math:`\phi` is a pair potential interaction,

:math:`\alpha` and :math:`\beta` are the element types of atoms :math:`I` and

:math:`J`, and :math:`s` and :math:`t = 1,2,3` and refer to the cartesian

coordinates.  The :math:`\mu` and :math:`\lambda` terms represent the dipole

and quadruple distortions of the local atomic environment which extend the

original EAM framework by introducing angular forces.

Note that unlike for other potentials, cutoffs for ADP potentials are

not set in the pair\_style or pair\_coeff command; they are specified in

Only a single pair\_coeff command is used with the *adp* style which

specifies an extended DYNAMO *setfl* file, which contains information

for M elements.  These are mapped to LAMMPS atom types by specifying N

for :math:`M` elements.  These are mapped to LAMMPS atom types by specifying :math:`N`

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

where N is the number of LAMMPS atom types:

where :math:`N` is the number of LAMMPS atom types:

* filename

* N element names = mapping of extended *setfl* elements to atom types

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

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

specify the path for the potential file.

the following pair\_coeff command:

.. parsed-literal::

.. code-block:: LAMMPS

   pair_coeff \* \* AlCu.adp Al Al Al Cu

   pair_coeff * * AlCu.adp Al Al Al Cu

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

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

command for further details on the *setfl* format.

* lines 1,2,3 = comments (ignored)

* line 4: Nelements Element1 Element2 ... ElementN

* line 5: Nrho, drho, Nr, dr, cutoff

* line 4: :math:`N_{\text{elements}}` Element1 Element2 ... ElementN

* line 5: :math:`N_\rho`, :math:`d_\rho`, :math:`N_r`, :math:`d_r`, cutoff

Following the 5 header lines are Nelements sections, one for each

Following the 5 header lines are :math:`N_{\text{elements}}` sections, one for each

element, each with the following format:

* line 1 = atomic number, mass, lattice constant, lattice type (e.g. FCC)

* embedding function F(rho) (Nrho values)

* density function rho(r) (Nr values)

Following the Nelements sections, Nr values for each pair potential

phi(r) array are listed for all i,j element pairs in the same format

as other arrays.  Since these interactions are symmetric (i,j = j,i)

only phi arrays with i >= j are listed, in the following order: i,j =

(1,1), (2,1), (2,2), (3,1), (3,2), (3,3), (4,1), ..., (Nelements,

Nelements).  The tabulated values for each phi function are listed as

r\*phi (in units of eV-Angstroms), since they are for atom pairs, the

* embedding function :math:`F(\rho)` (:math:`N_\rho` values)

* density function :math:`\rho(r)` (:math:`N_r` values)

Following the :math:`N_{\text{elements}}` sections, :math:`N_r` values for each pair potential

:math:`\phi(r)` array are listed for all :math:`i,j` element pairs in the same format

as other arrays.  Since these interactions are symmetric (:math:`i,j = j,i`)

only :math:`\phi` arrays with :math:`i \geq j` are listed, in the following order:

.. math::

   i,j = (1,1), (2,1), (2,2), (3,1), (3,2), (3,3), (4,1), ..., (N_{\text{elements}},N_{\text{elements}}).

The tabulated values for each :math:`\phi` function are listed as

:math:`r*\phi` (in units of eV-Angstroms), since they are for atom pairs, the

same as for :doc:`other EAM files <pair_eam>`.

After the phi(r) arrays, each of the u(r) arrays are listed in the

After the :math:`\phi(r)` arrays, each of the :math:`u(r)` arrays are listed in the

same order with the same assumptions of symmetry.  Directly following

the u(r), the w(r) arrays are listed.  Note that phi(r) is the only

array tabulated with a scaling by r.

the :math:`u(r)`, the :math:`w(r)` arrays are listed.  Note that :math:`\phi(r)` is the only

array tabulated with a scaling by :math:`r`.

----------