Unverified Commit 08d01e64 authored by Axel Kohlmeyer's avatar Axel Kohlmeyer
Browse files

import polymorphic pair style update from Xiaowang Zhou

parent 80311891

doc/src/pair_polymorphic.rst

+197 −131
Original line number Diff line number Diff line 
.. index:: pair_style polymorphic

<HTML><META HTTP-EQUIV="content-type" CONTENT="text/html;charset=utf-8">

<PRE>.. index:: pair_style polymorphic



pair_style polymorphic command

==============================
@@ -18,22 +19,27 @@ Examples 
.. code-block:: LAMMPS



   pair_style polymorphic

   pair_coeff * * TlBr_msw.polymorphic Tl Br

   pair_coeff * * AlCu_eam.polymorphic Al Cu

   pair_coeff * * GaN_tersoff.polymorphic Ga N

   pair_coeff * * GaN_sw.polymorphic GaN

   pair_coeff * * FeCH_BOPI.poly Fe C H

   pair_coeff * * TlBr_msw.poly Tl Br

   pair_coeff * * CuTa_eam.poly Cu Ta

   pair_coeff * * GaN_tersoff.poly Ga N

   pair_coeff * * GaN_sw.poly GaN



Description

"""""""""""



The *polymorphic* pair style computes a 3-body free-form potential

(:ref:`Zhou <Zhou3>`) for the energy E of a system of atoms as

(:ref:`Zhou &lt;Zhou3&gt;`) for the energy E of a system of atoms as



.. math::



   E & = \frac{1}{2}\sum_{i=1}^{i=N}\sum_{j=1}^{j=N}\left[\left(1-\delta_{ij}\right)\cdot U_{IJ}\left(r_{ij}\right)-\left(1-\eta_{ij}\right)\cdot F_{IJ}\left(r_{ij}\right)\cdot V_{IJ}\left(r_{ij}\right)\right] \\

   X_{ij} & = \sum_{k=i_1,k\neq i,j}^{i_N}W_{IK}\left(r_{ik}\right)\cdot G_{JIK}\left(\theta_{jik}\right)\cdot P_{IK}\left(\Delta r_{jik}\right) \\

   \Delta r_{jik} & = r_{ij}-\xi_{IJ}\cdot r_{ik}

\begin{eqnarray}\nonumber

   \left\{\begin{array}{l}

   E = \frac{1}{2}\sum_{i=1}^{i=N}\sum_{j=1}^{j=N}\left[\left(1-\delta_{ij}\right)\cdot U_{IJ}\left(r_{ij}\right)-\left(1-\eta_{ij}\right)\cdot F_{IJ}\left(X_{ij}\right)\cdot V_{IJ}\left(r_{ij}\right)\right] \\

   X_{ij} = \sum_{k=i_1,k\neq j}^{i_N}W_{IK}\left(r_{ik}\right)\cdot G_{JIK}\left(\theta_{jik}\right)\cdot P_{JIK}\left(\Delta r_{jik}\right) \\

   \Delta r_{jik} = r_{ij}-\xi_{IJ}\cdot r_{ik}

   \end{array}\right.

\end{eqnarray}



where I, J, K represent species of atoms i, j, and k, :math:`i_1, ...,

i_N` represents a list of *i*\ 's neighbors, :math:`\delta_{ij}` is a
@@ -42,111 +48,157 @@ Dirac constant (i.e., :math:`\delta_{ij} = 1` when :math:`i = j`, and 
constant that can be set either to :math:`\eta_{ij} = \delta_{ij}` or

:math:`\eta_{ij} = 1 - \delta_{ij}` depending on the potential type,

:math:`U_{IJ}(r_{ij})`, :math:`V_{IJ}(r_{ij})`, :math:`W_{IK}(r_{ik})`

are pair functions, :math:`G_{JIK}(\cos(\theta))` is an angular

function, :math:`P_{IK}(\Delta r_{jik})` is a function of atomic spacing

are pair functions, :math:`G_{JIK}(\cos\theta_{jik})` is an angular

function, :math:`P_{JIK}(\Delta r_{jik})` is a function of atomic spacing

differential :math:`\Delta r_{jik} = r_{ij} - \xi_{IJ} \cdot r_{ik}`

with :math:`\xi_{IJ}` being a pair-dependent parameter, and

:math:`F_{IJ}(X_{ij})` is a function of the local environment variable

:math:`X_{ij}`. This generic potential is fully defined once the

constants :math:`\eta_{ij}` and :math:`\xi_{IJ}`, and the six functions

:math:`U_{IJ}(r_{ij})`, :math:`V_{IJ}(r_{ij})`, :math:`W_{IK}(r_{ik})`,

:math:`G_{JIK}(\cos(\theta))`, :math:`P_{IK}(\Delta r_{jik})`, and

:math:`F_{IJ}(X_{ij})` are given. Note that these six functions are all

one dimensional, and hence can be provided in an analytic or tabular

:math:`G_{JIK}(\cos\theta_{jik})`, :math:`P_{JIK}(\Delta r_{jik})`, and

:math:`F_{IJ}(X_{ij})` are given. Here LAMMPS uses a global

parameter :math:`\eta` to represent :math:`\eta_{ij}`. When

:math:`\eta = 1`, :math:`\eta_{ij} = 1 - \delta_{ij}`, otherwise

:math:`\eta_{ij} = \delta_{ij}`. Additionally, :math:`\eta = 3`

indicates that the function :math:`P_{JIK}(\Delta r)` depends on

species I, J and K, otherwise :math:`P_{JIK}(\Delta r) = P_{IK}(\Delta r)` 

only depends on species I and K. Note that these six functions are all

one dimensional, and hence can be provided in a tabular

form. This allows users to design different potentials solely based on a

manipulation of these functions. For instance, the potential reduces to

Stillinger-Weber potential (:ref:`SW <SW>`) if we set

manipulation of these functions. For instance, the potential reduces a

Stillinger-Weber potential (:ref:`SW &lt;SW&gt;`) if we set



.. math::



\begin{eqnarray}\nonumber

   \left\{\begin{array}{l}

   \eta_{ij} = \delta_{ij},\xi_{IJ}=0 \\

   \eta_{ij} = \delta_{ij} (\eta = 2~or~\eta = 0),\xi_{IJ}=0 \\

   U_{IJ}\left(r\right) = A_{IJ}\cdot\epsilon_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^q\cdot \left[B_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^{p-q}-1\right]\cdot exp\left(\frac{\sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\

   V_{IJ}\left(r\right) = \sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\

   F_{IJ}\left(X\right) = -X \\

   P_{IJ}\left(\Delta r\right)=1 \\

   P_{JIK}\left(\Delta r\right) = P_{IK}\left(\Delta r\right) = 1 \\

   W_{IJ}\left(r\right) = \sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\

   G_{JIK}\left(\theta\right) = \left(cos\theta+\frac{1}{3}\right)^2

   \end{array}\right.

\end{eqnarray}



The potential reduces to Tersoff types of potential

(:ref:`Tersoff <Tersoff>` or :ref:`Albe <poly-Albe>`) if we set

The potential reduces to a Tersoff potential (:ref:`Tersoff &lt;Tersoff&gt;

` or :ref:`Albe &lt;poly-Albe&gt;`) if we set



.. math::



\begin{eqnarray}\nonumber

   \left\{\begin{array}{l}

   \eta_{ij}=\delta_{ij},\xi_{IJ}=1 \\

   U_{IJ}\left(r\right)=\frac{D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{2S_{IJ}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\

   V_{IJ}\left(r\right)=\frac{S_{IJ}\cdot D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{\frac{2}{S_{IJ}}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\

   \eta_{ij} = \delta_{ij} (\eta = 2~or~\eta = 0),\xi_{IJ}=1 \\

   U_{IJ}\left(r\right) = \frac{D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{2S_{IJ}}\left(r-r_{e,IJ}\right)\right]\cdot f_{c,IJ}\left(r\right) \\

   V_{IJ}\left(r\right) = \frac{S_{IJ}\cdot D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{\frac{2}{S_{IJ}}}\left(r-r_{e,IJ}\right)\right]\cdot f_{c,IJ}\left(r\right) \\

   F_{IJ}\left(X\right) = \left(1+X\right)^{-\frac{1}{2}} \\

   P_{IJ}\left(\Delta r\right)=exp\left(2\mu_{IK}\cdot \Delta r\right) \\

   W_{IJ}\left(r\right)=f_{c,IK}\left(r\right) \\

   P_{JIK}\left(\Delta r\right) = P_{IK}\left(\Delta r\right) = exp\left(2\mu_{IK}\cdot \Delta r\right) \\

   W_{IJ}\left(r\right) = f_{c,IJ}\left(r\right) \\

   G_{JIK}\left(\theta\right) = \gamma_{IK}\left[1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}\right]

   \end{array}\right.

\end{eqnarray}



where



.. math::



   f_{c,IJ}=\left\{\begin{array}{lr}

   1, & r\leq r_{s,IJ} \\

   \frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,IJ}\right)}{r_{c,IJ}-r_{s,IJ}}\right], & r_{s,IJ}<r<r_{c,IJ} \\

   0, & r \geq r_{c,IJ} \\

\begin{eqnarray}\nonumber

   f_{c,IJ}\left(r\right)=\left\{\begin{array}{l}

   1, r\leq R_{IJ}-D_{IJ} \\

   \frac{1}{2}+\frac{1}{2}cos\left[\frac{\pi\left(r+D_{IJ}-R_{IJ}\right)}{2D_{IJ}}\right], R_{IJ}-D_{IJ} < r < R_{IJ}+D_{IJ} \\

   0, r \geq R_{IJ}+D_{IJ}

   \end{array}\right.

\end{eqnarray}



The potential reduces to Rockett-Tersoff (:ref:`Wang <Wang3>`) type if we set

The potential reduces to a modified Stillinger-Weber potential (:ref:`Zhou &lt;Zhou3&gt;`) if we set



.. math::



\begin{eqnarray}\nonumber

   \left\{\begin{array}{l}

   \eta_{ij}=\delta_{ij},\xi_{IJ}=1 \\

   U_{IJ}\left(r\right)=\left\{\begin{array}{lr}

   A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right), & r\leq r_{s,1,IJ} \\

   A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right)\cdot f_{c,1,IJ}\left(r\right), & r_{s,1,IJ}<r<r_{c,1,IJ} \\

   0, & r\ge r_{c,1,IJ}

   \end{array}\right. \\

   V_{IJ}\left(r\right)=\left\{\begin{array}{lr}

   B_{IJ} \cdot exp\left(-\lambda_{2,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right), & r\le r_{s,1,IJ} \\

   B_{IJ} \cdot exp\left(-\lambda_{2,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right)+A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot & \\ ~~~~~~ f_{c,IJ}\left(r\right)\cdot \left[1-f_{c,1,IJ}\left(r\right)\right], & r_{s,1,IJ}<r<r_{c,1,IJ} \\

   B_{IJ} \cdot exp\left(-\lambda_{2,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right)+A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot & \\ ~~~~~~ f_{c,IJ}\left(r\right) & r \ge r_{c,1,IJ}

   \end{array}\right. \\

   F_{IJ}\left(X\right)=\left[1+\left(\beta_{IJ}\cdot X\right)^{n_{IJ}}\right]^{-\frac{1}{2n_{IJ}}} \\

   P_{IJ}\left(\Delta r\right)=exp\left(\lambda_{3,IK}\cdot \Delta r^3\right) \\

   W_{IJ}\left(r\right)=f_{c,IK}\left(r\right) \\

   G_{JIK}\left(\theta\right)=1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}

   \eta_{ij} = \delta_{ij} (\eta = 2~or~\eta = 0),\xi_{IJ}=0 \\

   U_{IJ}\left(r\right) = \varphi_{R,IJ}\left(r\right)-\varphi_{A,IJ}\left(r\right) \\

   V_{IJ}\left(r\right) = u_{IJ}\left(r\right) \\

   F_{IJ}\left(X\right) = -X \\

   P_{JIK}\left(\Delta r\right) = P_{IK}\left(\Delta r\right) = 1 \\

   W_{IJ}\left(r\right) = u_{IJ}\left(r\right) \\

   G_{JIK}\left(\theta\right) = g_{JIK}\left(cos\theta\right)

   \end{array}\right.

\end{eqnarray}





The potential reduces to a Rockett-Tersoff potential (:ref:`Wang &lt;Wang3&gt;`) if we set



.. math::



   f_{c,IJ}=\left\{\begin{array}{lr}

   1, & r\leq r_{s,IJ} \\

   \frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,IJ}\right)}{r_{c,IJ}-r_{s,IJ}}\right], & r_{s,IJ}<r<r_{c,IJ} \\

   0, & r \geq r_{c,IJ} \\

\begin{eqnarray}\nonumber

   \left\{ \begin{array}{l}

   \eta_{ij} = \delta_{ij} (\eta = 2~or~\eta = 0),\xi_{IJ}=1 \\

   U_{IJ}\left(r\right) = A_{IJ}exp\left(-\lambda_{1,IJ}\cdot r\right)f_{c,IJ}\left(r\right)f_{ca,IJ}\left(r\right) \\

   V_{IJ}\left(r\right) = \left\{\begin{array}{l}B_{IJ}exp\left(-\lambda_{2,IJ}\cdot r\right)f_{c,IJ}\left(r\right)+ \\ A_{IJ}exp\left(-\lambda_{1,IJ}\cdot r\right)f_{c,IJ}\left(r\right) \left[1-f_{ca,IJ}\left(r\right)\right]\end{array} \right\} \\

   F_{IJ}\left(X\right) = \left[1+\left(\beta_{IJ}X\right)^{n_{IJ}}\right]^{-\frac{1}{2n_{IJ}}} \\

   P_{JIK}\left(\Delta r\right) = P_{IK}\left(\Delta r\right) = exp\left(\lambda_{3,IK}\cdot \Delta r^3\right) \\

   W_{IJ}\left(r\right) = f_{c,IJ}\left(r\right) \\

   G_{JIK}\left(\theta\right) = 1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}

   \end{array}\right.

\end{eqnarray}



where :math:`f_{ca,IJ}(r)` is similar to the :math:`f_{c,IJ}(r)` defined above:  



.. math::



   f_{c,1,IJ}=\left\{\begin{array}{lr}

   1, & r\leq r_{s,1,IJ} \\

   \frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,1,IJ}\right)}{r_{c,1,IJ}-r_{s,1,IJ}}\right], & r_{s,1,IJ}<r<r_{c,1,IJ} \\

   0, & r \geq r_{c,1,IJ} \\

\begin{eqnarray}\nonumber

   f_{ca,IJ}\left(r\right)=\left\{\begin{array}{l}

   1, r\leq R_{a,IJ}-D_{a,IJ} \\

   \frac{1}{2}+\frac{1}{2}cos\left[\frac{\pi\left(r+D_{a,IJ}-R_{a,IJ}\right)}{2D_{a,IJ}}\right], R_{a,IJ}-D_{a,IJ} < r < R_{a,IJ}+D_{a,IJ} \\

   0, r \geq R_{a,IJ}+D_{a,IJ}

   \end{array}\right.

\end{eqnarray}



The potential becomes embedded atom method (:ref:`Daw <poly-Daw>`) if we set

The potential becomes embedded atom method (:ref:`Daw &lt;poly-Daw&gt;`) if we set



.. math::



\begin{eqnarray}\nonumber

   \left\{\begin{array}{l}

   \eta_{ij}=1-\delta_{ij},\xi_{IJ}=0 \\

   \eta_{ij} = 1-\delta_{ij} (\eta = 1),\xi_{IJ}=0 \\

   U_{IJ}\left(r\right) = \phi_{IJ}\left(r\right) \\

   V_{IJ}\left(r\right) = 1 \\

   F_{II}\left(X\right) = -2F_I\left(X\right) \\

   P_{IJ}\left(\Delta r\right)=1 \\

   W_{IJ}\left(r\right)=f_{K}\left(r\right) \\

   P_{JIK}\left(\Delta r\right) = P_{IK}\left(\Delta r\right) = 1 \\

   W_{IJ}\left(r\right) = f_{J}\left(r\right) \\

   G_{JIK}\left(\theta\right) = 1

   \end{array}\right.

\end{eqnarray}



In the embedded atom method case, :math:`\phi_{IJ}(r_{ij})` is the pair

In the embedded atom method case, :math:`\phi_{IJ}(r)` is the pair

energy, :math:`F_I(X)` is the embedding energy, *X* is the local

electron density, and :math:`f_K(r)` is the atomic electron density function.

electron density, and :math:`f_J(r)` is the atomic electron density function.



The potential reduces to another type of Tersoff potential 

(:ref:`Zhou &lt;Zhou4&gt;`) if we set



.. math::



\begin{eqnarray}\nonumber

   \left\{\begin{array}{l}

   \eta_{ij} = \delta_{ij} (\eta = 3),\xi_{IJ}=1 \\

   U_{IJ}\left(r\right) = \frac{D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{2S_{IJ}}\left(r-r_{e,IJ}\right)\right]\cdot f_{c,IJ}\left(r\right) \cdot T_{IJ}\left(r\right)+V_{ZBL,IJ}\left(r\right)\left[1-T_{IJ}\left(r\right)\right] \\

   V_{IJ}\left(r\right) = \frac{S_{IJ}\cdot D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{\frac{2}{S_{IJ}}}\left(r-r_{e,IJ}\right)\right]\cdot f_{c,IJ}\left(r\right) \cdot T_{IJ}\left(r\right) \\

   F_{IJ}\left(X\right) = \left(1+X\right)^{-\frac{1}{2}} \\

   P_{JIK}\left(\Delta r\right) = \omega_{JIK} \cdot exp\left(\alpha_{JIK}\cdot \Delta r\right) \\

   W_{IJ}\left(r\right) = f_{c,IJ}\left(r\right) \\

   G_{JIK}\left(\theta\right) = \gamma_{JIK}\left[1+\frac{c_{JIK}^2}{d_{JIK}^2}-\frac{c_{JIK}^2}{d_{JIK}^2+\left(h_{JIK}+cos\theta\right)^2}\right] \\

   T_{IJ}\left(r\right) = \frac{1}{1+exp\left[-b_{f,IJ}\left(r-r_{f,IJ}\right)\right]} \\

   V_{ZBL,IJ}\left(r\right) = 14.4 \cdot \frac{Z_I \cdot Z_J}{r}\sum_{k=1}^{4}\mu_k \cdot exp\left[-\nu_k \left(Z_I^{0.23}+Z_J^{0.23}\right) r\right]

   \end{array}\right.

\end{eqnarray}



where :math:`f_{c,IJ}(r)` is the as defined above. This Tersoff potential

differs from the one above because the :math:`\P_{JIK}(\Delta r)` function

is now dependent on all three species I, J, and K. 



If the tabulated functions are created using the parameters of sw,

tersoff, and eam potentials, the polymorphic pair style will produce
@@ -157,15 +209,14 @@ corresponding tersoff and eam pair styles. However, due to a different 
partition of global properties to atom properties, the polymorphic

pair style will produce different atom properties (energies and

stresses) as the sw pair style. This does not mean that polymorphic

pair style is different from the sw pair style in this case. It just

means that the definitions of the atom energies and atom stresses are

different.

pair style is different from the sw pair style. It just means that the

definitions of the atom energies and atom stresses are different.



Only a single pair_coeff command is used with the polymorphic style

which specifies an potential file for all needed elements. These are

mapped to LAMMPS atom types by specifying N additional arguments after

the filename in the pair_coeff command, where N is the number of

LAMMPS atom types:

Only a single pair_coeff command is used with the polymorphic pair

style which specifies an potential file for all needed elements.

These are mapped to LAMMPS atom types by specifying 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 Tersoff elements to atom types
@@ -175,19 +226,19 @@ the potential file. Several files for polymorphic potentials are 
included in the potentials directory of the LAMMPS distribution. They

have a "poly" suffix.



As an example, imagine the SiC_tersoff.poly file has tabulated

functions for Si-C tersoff potential. If your LAMMPS simulation has 4

atoms types and you want the 1st 3 to be Si, and the 4th to be C, you

As an example, imagine the GaN_tersoff.poly file has tabulated

functions for Ga-N tersoff potential. If your LAMMPS simulation has 4

atoms types and you want the 1st 3 to be Ga, and the 4th to be N, you

would use the following pair_coeff command:



.. code-block:: LAMMPS



   pair_coeff * * SiC_tersoff.poly Si Si Si C

   pair_coeff * * GaN_tersoff.poly Ga Ga Ga N



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

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

Si element in the polymorphic file. The final C argument maps LAMMPS

atom type 4 to the C element in the polymorphic file. If a mapping

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

Ga element in the polymorphic file. The final N argument maps LAMMPS

atom type 4 to the N element in the polymorphic file. If a mapping

value is specified as NULL, the mapping is not performed. This can be

used when an polymorphic potential is used as part of the hybrid pair

style. The NULL values are placeholders for atom types that will be
@@ -203,20 +254,38 @@ and are ignored by LAMMPS. The next line lists two numbers: 
   ntypes :math:`\eta`



Here ntypes represent total number of species defined in the potential

file, and :math:`\eta = 0` or 1. The number ntypes must equal the total

number of different species defined in the pair_coeff command. When

:math:`\eta = 1`, :math:\eta_{ij}` defined in the potential functions

above is set to :math:`1 - \delta_{ij}`, otherwise :math:`\eta_{ij}` is

set to :math:`\delta_{ij}`. The next ntypes lines each lists two numbers

and a character string representing atomic number, atomic mass, and name

of the species of the ntypes elements:

file, :math:`\eta = 1` reduces to embedded atom method, :math:`\eta = 3`

assumes three spcies dependent :math:`P_{JIK}(\Delta r)` function, and

all other :math:`\eta` assumes two species dependent

:math:`P_{JK}(\Delta r)` function. The number ntypes must equal the total

number of different species defined in the pair_coeff command. The next

ntypes lines each lists two numbers and a character string representing

atomic number, atomic mass, and name of the species of the ntypes elements:



.. parsed-literal::



   atomic_number atomic-mass element (1)

   atomic_number atomic-mass element (2)

   atomic-number atomic-mass element-name(1)

   atomic-number atomic-mass element-name(2)

   ...

   atomic_number atomic-mass element (ntypes)

   atomic-number atomic-mass element-name(ntypes)



The next line contains four numbers:



.. parsed-literal::



   nr ntheta nx xmax



Here nr is total number of tabular points for radial functions U, V, W, P,

ntheta is total number of tabular points for the angular function G, nx is

total number of tabular points for the function F, xmax is a maximum

value of the argument of function F. Note that the pair functions

:math:`U_{IJ}(r)`, :math:`V_{IJ}(r)`, :math:`W_{IJ}(r)` are uniformly

tabulated between 0 and cutoff distance of the IJ pair,

:math:`G_{JIK}(\theta)` is uniformly tabulated between -1 and 1,

:math:`P_{JIK}(\Delta r)` is uniformly tabulated between -rcmax

and rcmax where rcmax is the maximum cutoff distance of all pairs, and

:math:`F_{IJ}(X)` is uniformly tabulated between 0 and xmax. Linear

extrapolation is assumed if actual simulations exceed these ranges. 



The next ntypes\*(ntypes+1)/2 lines contain two numbers:
@@ -230,40 +299,34 @@ The next ntypes\*(ntypes+1)/2 lines contain two numbers: 
Here cut means the cutoff distance of the pair functions, :math:`\xi` is

the same as defined in the potential functions above. The

ntypes\*(ntypes+1)/2 lines are related to the pairs according to the

sequence of first ii (self) pairs, i = 1, 2, ..., ntypes, and then then

sequence of first ii (self) pairs, i = 1, 2, ..., ntypes, and then

ij (cross) pairs, i = 1, 2, ..., ntypes-1, and j = i+1, i+2, ..., ntypes

(i.e., the sequence of the ij pairs follows 11, 22, ..., 12, 13, 14,

..., 23, 24, ...).



The final blocks of the potential file are the U, V, W, P, G, and F

In the final blocks of the potential file, U, V, W, P, G, and F

functions are listed sequentially. First, U functions are given for

each of the ntypes\*(ntypes+1)/2 pairs according to the sequence

described above. For each of the pairs, nr values are listed. Next,

similar arrays are given for V, W, and P functions. Then G functions

are given for all the ntypes\*ntypes\*ntypes ijk triplets in a natural

sequence i from 1 to ntypes, j from 1 to ntypes, and k from 1 to

ntypes (i.e., ijk = 111, 112, 113, ..., 121, 122, 123 ..., 211, 212,

...). Each of the ijk functions contains ng values. Finally, the F

functions are listed for all ntypes\*(ntypes+1)/2 pairs, each

containing nx values. Either analytic or tabulated functions can be

specified. Currently, constant, exponential, sine and cosine analytic

functions are available which are specified with: constant c1 , where

f(x) = c1 exponential c1 c2 , where f(x) = c1 exp(c2\*x) sine c1 c2 ,

where f(x) = c1 sin(c2\*x) cos c1 c2 , where f(x) = c1 cos(c2\*x)

Tabulated functions are specified by spline n x1 x2, where n=number of

point, (x1,x2)=range and then followed by n values evaluated uniformly

over these argument ranges.  The valid argument ranges of the

functions are between 0 <= r <= cut for the U(r), V(r), W(r)

functions, -cutmax <= delta_r <= cutmax for the P(delta_r) functions,

-1 <= :math:`\cos\theta` <= 1 for the G(:math:`\cos\theta`) functions,

and 0 <= X <= maxX for the F(X) functions.

similar arrays are given for V and W functions. If P functions

depend only on pair species, i.e., :math:`\eta \neq 3`, then P

functions are also listed the same way the next. If P functions

depend on three species, i.e., :math:`\eta = 3`, then P functions

are listed for all the ntypes*ntypes*ntypes IJK triplets in a

natural sequence I from 1 to ntypes, J from 1 to ntypes, and K from

1 to ntypes (i.e., IJK = 111, 112, 113, ..., 121, 122, 123 ..., 211,

212, ...). Next, G functions are listed for all the ntypes*ntypes*ntypes

IJK triplets similarly. For each of the G functions, ntheta values

are listed. Finally, F functions are listed for all the

ntypes*(ntypes+1)/2 pairs in the same sequence as described above.

For each of the F functions, nx values are listed.



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



This pair styles does not support the :doc:`pair_modify <pair_modify>`

This pair styles does not support the :doc:`pair_modify &lt;pair_modify&gt;`

shift, table, and tail options.



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

This pair style does not write their information to :doc:`binary restart files &lt;restart&gt;`, since it is stored in potential files. Thus, you

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

script that reads a restart file.
@@ -277,31 +340,34 @@ input script. If using read_data, atomic masses must be defined in the 
atomic structure data file.



This pair style is part of the MANYBODY package. It is only enabled if

LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.

LAMMPS was built with that package. See the :doc:`Build package &lt;Build_package&gt;` doc page for more info.



This pair potential requires the :doc:`newtion <newton>` setting to be

This pair potential requires the :doc:`newtion &lt;newton&gt;` setting to be

"on" for pair interactions.



The potential files provided with LAMMPS (see the potentials

directory) are parameterized for metal :doc:`units <units>`. You can use

directory) are parameterized for metal :doc:`units &lt;units&gt;`. You can use

any LAMMPS units, but you would need to create your own potential

files.



Related commands

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



:doc:`pair_coeff <pair_coeff>`

:doc:`pair_coeff &lt;pair_coeff&gt;`



----------



.. _Zhou3:



**(Zhou)** X. W. Zhou, M. E. Foster, R. E. Jones, P. Yang, H. Fan, and

F. P. Doty, J. Mater. Sci. Res., 4, 15 (2015).

**(Zhou)** X. W. Zhou, M. E. Foster, R. E. Jones, P. Yang, H. Fan, and F. P. Doty, J. Mater. Sci. Res., 4, 15 (2015).



.. _Zhou4:



**(Zhou)** X. W. Zhou, M. E. Foster, J. A. Ronevich, and C. W. San Marchi, J. Comp. Chem., 41, 1299 (2020).



.. _SW:



**(SW)** F. H. Stillinger-Weber, and T. A. Weber, Phys. Rev. B, 31, 5262 (1985).

**(SW)** F. H. Stillinger, and T. A. Weber, Phys. Rev. B, 31, 5262 (1985).



.. _Tersoff:
@@ -309,8 +375,7 @@ F. P. Doty, J. Mater. Sci. Res., 4, 15 (2015). 


.. _poly-Albe:



**(Albe)** K. Albe, K. Nordlund, J. Nord, and A. Kuronen, Phys. Rev. B,

66, 035205 (2002).

**(Albe)** K. Albe, K. Nordlund, J. Nord, and A. Kuronen, Phys. Rev. B, 66, 035205 (2002).



.. _Wang3:
@@ -319,3 +384,4 @@ F. P. Doty, J. Mater. Sci. Res., 4, 15 (2015). 
.. _poly-Daw:



**(Daw)** M. S. Daw, and M. I. Baskes, Phys. Rev. B, 29, 6443 (1984).

</PRE>

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