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update docs to cleanly translate

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Axel Kohlmeyer 2020-04-16 18:17:38 -04:00
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doc/src/pair_momb.rst
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@ -31,7 +31,7 @@ Style *momb* computes pairwise van der Waals (vdW) and short-range
interactions using the Morse potential and :ref:`(Grimme) <Grimme>` method
implemented in the Many-Body Metal-Organic (MOMB) force field
described comprehensively in :ref:`(Fichthorn) <Fichthorn>` and
:ref:`(Zhou) <Zhou4>`. Grimme's method is widely used to correct for
:ref:`(Zhou) <Zhou5>`. Grimme's method is widely used to correct for
dispersion in density functional theory calculations.
.. math::
@ -76,6 +76,6 @@ Related commands
**(Fichthorn)** Fichthorn, Balankura, Qi, CrystEngComm, 18(29), 5410-5417 (2016).
.. _Zhou4:
.. _Zhou5:
**(Zhou)** Zhou, Saidi, Fichthorn, J Phys Chem C, 118(6), 3366-3374 (2014).

170
doc/src/pair_polymorphic.rst
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@ -1,5 +1,4 @@
<HTML><META HTTP-EQUIV="content-type" CONTENT="text/html;charset=utf-8">
<PRE>.. index:: pair_style polymorphic
.. index:: pair_style polymorphic
pair_style polymorphic command
==============================
@ -19,7 +18,7 @@ Examples
.. code-block:: LAMMPS
pair_style polymorphic
pair_coeff * * FeCH_BOPI.poly Fe C H
pair_coeff * * FeCH_BOP_I.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
@ -29,17 +28,13 @@ Description
"""""""""""
The *polymorphic* pair style computes a 3-body free-form potential
(:ref:`Zhou &lt;Zhou3&gt;`) for the energy E of a system of atoms as
(:ref:`Zhou <Zhou3>`) for the energy E of a system of atoms as
.. math::
\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}
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}
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
@ -67,137 +62,108 @@ 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 a
Stillinger-Weber potential (:ref:`SW &lt;SW&gt;`) if we set
Stillinger-Weber potential (:ref:`SW <SW>`) if we set
.. math::
\begin{eqnarray}\nonumber
\left\{\begin{array}{l}
\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_{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}
\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_{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
The potential reduces to a Tersoff potential (:ref:`Tersoff &lt;Tersoff&gt;
` or :ref:`Albe &lt;poly-Albe&gt;`) if we set
The potential reduces to a Tersoff potential (:ref:`Tersoff <Tersoff>`
or :ref:`Albe <poly-Albe>`) if we set
.. math::
\begin{eqnarray}\nonumber
\left\{\begin{array}{l}
\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_{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}
\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_{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]
where
.. math::
\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 a modified Stillinger-Weber potential (:ref:`Zhou &lt;Zhou3&gt;`) if we set
The potential reduces to a modified Stillinger-Weber potential (:ref:`Zhou <Zhou3>`) if we set
.. math::
\begin{eqnarray}\nonumber
\left\{\begin{array}{l}
\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}
\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)
The potential reduces to a Rockett-Tersoff potential (:ref:`Wang &lt;Wang3&gt;`) if we set
The potential reduces to a Rockett-Tersoff potential (:ref:`Wang <Wang3>`) if we set
.. math::
\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}
\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}
where :math:`f_{ca,IJ}(r)` is similar to the :math:`f_{c,IJ}(r)` defined above:
.. math::
\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 &lt;poly-Daw&gt;`) if we set
The potential becomes embedded atom method (:ref:`Daw <poly-Daw>`) if we set
.. math::
\begin{eqnarray}\nonumber
\left\{\begin{array}{l}
\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_{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}
\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_{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
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_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
(:ref:`Zhou <Zhou4>`) 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}
\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]
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
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,
@ -251,7 +217,7 @@ and are ignored by LAMMPS. The next line lists two numbers:
.. parsed-literal::
ntypes :math:`\eta`
ntypes eta
Here ntypes represent total number of species defined in the potential
file, :math:`\eta = 1` reduces to embedded atom method, :math:`\eta = 3`
@ -291,10 +257,10 @@ The next ntypes\*(ntypes+1)/2 lines contain two numbers:
.. parsed-literal::
cut :math:`xi`(1)
cut :math:`xi`(2)
cut xi(1)
cut xi(2)
...
cut :math:`xi`(ntypes\*(ntypes+1)/2)
cut xi(ntypes\*(ntypes+1)/2)
Here cut means the cutoff distance of the pair functions, :math:`\xi` is
the same as defined in the potential functions above. The
@ -323,10 +289,10 @@ 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 &lt;pair_modify&gt;`
This pair styles does not support the :doc:`pair_modify <pair_modify>`
shift, table, and tail options.
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
This pair style does 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
script that reads a restart file.
@ -340,20 +306,20 @@ 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 &lt;Build_package&gt;` doc page for more info.
LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
This pair potential requires the :doc:`newtion &lt;newton&gt;` setting to be
This pair potential requires the :doc:`newtion <newton>` setting to be
"on" for pair interactions.
The potential files provided with LAMMPS (see the potentials
directory) are parameterized for metal :doc:`units &lt;units&gt;`. You can use
directory) are parameterized for metal :doc:`units <units>`. You can use
any LAMMPS units, but you would need to create your own potential
files.
Related commands
""""""""""""""""
:doc:`pair_coeff &lt;pair_coeff&gt;`
:doc:`pair_coeff <pair_coeff>`
----------