Merge branch 'master' into zeeman-rework

This commit is contained in:
Axel Kohlmeyer
2019-11-19 15:29:21 -05:00
171 changed files with 881 additions and 5667 deletions

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@ -9,9 +9,7 @@ if(BUILD_DOC)
set(VIRTUALENV ${PYTHON_EXECUTABLE} -m virtualenv) set(VIRTUALENV ${PYTHON_EXECUTABLE} -m virtualenv)
file(GLOB DOC_SOURCES ${LAMMPS_DOC_DIR}/src/[^.]*.txt) file(GLOB DOC_SOURCES ${LAMMPS_DOC_DIR}/src/[^.]*.rst)
file(GLOB PDF_EXTRA_SOURCES ${LAMMPS_DOC_DIR}/src/lammps_commands*.txt ${LAMMPS_DOC_DIR}/src/lammps_support.txt ${LAMMPS_DOC_DIR}/src/lammps_tutorials.txt)
list(REMOVE_ITEM DOC_SOURCES ${PDF_EXTRA_SOURCES})
add_custom_command( add_custom_command(
OUTPUT docenv OUTPUT docenv
@ -28,25 +26,10 @@ if(BUILD_DOC)
COMMAND ${DOCENV_BINARY_DIR}/pip install --upgrade ${LAMMPS_DOC_DIR}/utils/converters COMMAND ${DOCENV_BINARY_DIR}/pip install --upgrade ${LAMMPS_DOC_DIR}/utils/converters
) )
set(RST_FILES "")
set(RST_DIR ${CMAKE_BINARY_DIR}/rst)
file(MAKE_DIRECTORY ${RST_DIR})
foreach(TXT_FILE ${DOC_SOURCES})
get_filename_component(FILENAME ${TXT_FILE} NAME_WE)
set(RST_FILE ${RST_DIR}/${FILENAME}.rst)
list(APPEND RST_FILES ${RST_FILE})
add_custom_command(
OUTPUT ${RST_FILE}
DEPENDS requirements.txt docenv ${TXT_FILE}
COMMAND ${DOCENV_BINARY_DIR}/txt2rst -o ${RST_DIR} ${TXT_FILE}
)
endforeach()
add_custom_command( add_custom_command(
OUTPUT html OUTPUT html
DEPENDS ${RST_FILES} DEPENDS ${DOC_SOURCES} docenv requirements.txt
COMMAND ${CMAKE_COMMAND} -E copy_directory ${LAMMPS_DOC_DIR}/src ${RST_DIR} COMMAND ${DOCENV_BINARY_DIR}/sphinx-build -j ${NPROCS} -b html -c ${LAMMPS_DOC_DIR}/utils/sphinx-config -d ${CMAKE_BINARY_DIR}/doctrees ${LAMMPS_DOC_DIR}/src html
COMMAND ${DOCENV_BINARY_DIR}/sphinx-build -j ${NPROCS} -b html -c ${LAMMPS_DOC_DIR}/utils/sphinx-config -d ${CMAKE_BINARY_DIR}/doctrees ${RST_DIR} html
) )
add_custom_target( add_custom_target(

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@ -5,7 +5,7 @@ sub-directories and optionally 2 PDF files and an ePUB file:
src content files for LAMMPS documentation src content files for LAMMPS documentation
html HTML version of the LAMMPS manual (see html/Manual.html) html HTML version of the LAMMPS manual (see html/Manual.html)
tools tools and settings for building the documentation utils utilities and settings for building the documentation
Manual.pdf large PDF version of entire manual Manual.pdf large PDF version of entire manual
Developer.pdf small PDF with info about how LAMMPS is structured Developer.pdf small PDF with info about how LAMMPS is structured
LAMMPS.epub Manual in ePUB format LAMMPS.epub Manual in ePUB format
@ -25,17 +25,12 @@ the fetched documentation will include those changes (but your source
code will not, unless you update your local repository). code will not, unless you update your local repository).
(b) You can build the HTML and PDF files yourself, by typing "make (b) You can build the HTML and PDF files yourself, by typing "make
html" followed by "make pdf". Note that the PDF make requires the html" or by "make pdf", respectively. This requires various tools
HTML files already exist. This requires various tools including including the Python documentation processing tool Sphinx, which the
Sphinx, which the build process will attempt to download and install build process will attempt to download and install on your system into
on your system, if not already available. See more details below. a python virtual environment, if not already available. The PDF file
will require a working LaTeX installation with several add-on packages
(c) You can genererate an older, simpler, less-fancy style of HTML in addition to the Python/Sphinx setup. See more details below.
documentation by typing "make old". This will create an "old"
directory. This can be useful if (b) does not work on your box for
some reason, or you want to quickly view the HTML version of a doc
page you have created or edited yourself within the src directory.
E.g. if you are planning to submit a new feature to LAMMPS.
---------------- ----------------
@ -46,8 +41,7 @@ Options:
make html # generate HTML in html dir using Sphinx make html # generate HTML in html dir using Sphinx
make pdf # generate 2 PDF files (Manual.pdf,Developer.pdf) make pdf # generate 2 PDF files (Manual.pdf,Developer.pdf)
# in this dir via htmldoc and pdflatex # in this dir via Sphinx and PDFLaTeX
make old # generate old-style HTML pages in old dir via txt2html
make fetch # fetch HTML doc pages and 2 PDF files from web site make fetch # fetch HTML doc pages and 2 PDF files from web site
# as a tarball and unpack into html dir and 2 PDFs # as a tarball and unpack into html dir and 2 PDFs
make epub # generate LAMMPS.epub in ePUB format using Sphinx make epub # generate LAMMPS.epub in ePUB format using Sphinx
@ -94,8 +88,17 @@ This will install virtualenv from the Python Package Index.
Installing prerequisites for PDF build Installing prerequisites for PDF build
[TBA] Same as for HTML plus a compatible LaTeX installation with
support for PDFLaTeX. Also the following LaTeX packages need
to be installed (e.g. from texlive):
- amsmath
- babel
- cmap
- fncychap
- geometry
- hyperref
- hypcap
- times
---------------- ----------------
Installing prerequisites for epub build Installing prerequisites for epub build
@ -103,7 +106,11 @@ Installing prerequisites for epub build
## ePUB ## ePUB
Same as for HTML. This uses the same tools and configuration Same as for HTML. This uses the same tools and configuration
files as the HTML tree. files as the HTML tree. The ePUB format conversion currently
does not support processing mathematical expressions via MathJAX,
so there will be limitations on some pages. For the time being
until this is resolved, building and using the PDF format file
is recommended instead.
For converting the generated ePUB file to a mobi format file For converting the generated ePUB file to a mobi format file
(for e-book readers like Kindle, that cannot read ePUB), you (for e-book readers like Kindle, that cannot read ePUB), you

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K (\theta - \theta_0)^2 + K_{UB} (r - r_{UB})^2
$$
\end{document}

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@ -1,12 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
E & = & E_a + E_{bb} + E_{ba} \\
E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\
E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\
E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)
\end{eqnarray*}
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K [1 + \cos(\theta)]
$$
\end{document}

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@ -1,15 +0,0 @@
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
$$
E = K \left[ 1 + \cos(n\theta - \theta_0)\right]
$$
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K [1 - \cos(\theta - \theta_0)]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
$$
E=C\left[ 1-B(-1)^ncos\left( n\theta\right) \right]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
$$
E=-\frac{Umin}{2} \left[ 1+Cos(\theta-\theta_0) \right]
$$
\end{document}

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@ -1,13 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
$$
E=-U_{min}
\frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1}
\quad\mbox{with}\quad
U(\theta,\theta_0)
=-0.5 \left(1+\cos(\theta-\theta_0) \right)
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K [\cos(\theta) - \cos(\theta_0)]^2
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
\thispagestyle{empty}
$$
E = K_{SS} \left(r_{12}-r_{12,0}\right)\left(r_{32}-r_{32,0}\right) + K_{BS0}\left(r_{12}-r_{12,0}\right)\left(\theta-\theta_0\right) + K_{BS1}\left(r_{32}-r_{32,0}\right)\left(\theta-\theta_0\right)
$$
\end{document}

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@ -1,10 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
-\vec{T_j} & = & \vec{r_{ij}} \times \vec{F_i}\\
\vec{F_j} & = & -\vec{F_i} \\
\end{eqnarray*}
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
\cos\gamma = \frac{\vec{\mu_j}\bullet\vec{r_{ij}}}{\mu_j\,r_{ij}}
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K (\cos\gamma - \cos\gamma_0)^2
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
\vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\,
\vec{r_{ij}} \times \vec{\mu_j}
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K [C_0 + C_1 \cos ( \theta) + C_2 \cos( 2 \theta) ]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K [ 1.0 + c \cos ( n \theta) ]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K (\theta - \theta_0)^2
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
\thispagestyle{empty}
$$
E = K (\theta - \theta_0)^2 \left[ 1 - 0.014(\theta - \theta_0) + 5.6(10)^{-5} (\theta - \theta_0)^2 - 7.0(10)^{-7} (\theta - \theta_0)^3 + 9(10)^{-10} (\theta - \theta_0)^4 \right]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K_2 (r - r_0)^2 + K_3 (r - r_0)^3 + K_4 (r - r_0)^4
$$
\end{document}

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@ -1,11 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = -0.5 K R_0^2 \ln \left[ 1 - \left(\frac{r}{R_0}\right)^2\right] +
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
$$
\end{document}

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@ -1,13 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = -0.5 K R_0^2
\ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] +
4 \epsilon \left[ \left(\frac{\sigma}{\left(r -
\Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r -
\Delta\right)}\right)^6 \right] + \epsilon
$$
\end{document}

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@ -1,10 +0,0 @@
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
$$
E = K (r^2 - r_0^2)^2
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K (r - r_0)^2
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right]
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
\thispagestyle{empty}
$$
E = K (r - r_0)^2 \left[ 1 - 2.55(r-r_0) + (7/12) 2.55^2(r-r_0)^2 \right]
$$
\end{document}

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@ -1,10 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
% E = D \left[ 1 - \exp \left( -\alpha (r - r_0) \right) \right]^2
E = D \left[ 1 - e^{-\alpha (r - r_0)} \right]^2
$$
\end{document}

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@ -1,9 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = \frac{\epsilon (r - r_0)^2}{ [ \lambda^2 - (r - r_0)^2 ]}
$$
\end{document}

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@ -1,10 +0,0 @@
\documentclass[12pt]{article}
\pagestyle{empty}
\begin{document}
$$
E = - \frac{\epsilon}{2} \ln \left[ 1 - \left(\frac{r-r0}{\Delta}\right)^2\right]
$$
\end{document}

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@ -1,11 +0,0 @@
\documentclass[12pt]{article}
\begin{document}
$$
E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 +
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
$$
\end{document}

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@ -32,12 +32,10 @@ install the `openkim-models` package
If you have problems with the installation you can post issues to If you have problems with the installation you can post issues to
`this link <conda_forge_lammps_>`_. `this link <conda_forge_lammps_>`_.
Thanks to Jan Janssen (Max-Planck-Institut fuer Eisenforschung) for setting
.. _conda_forge_lammps: https://github.com/conda-forge/lammps-feedstock/issues
Thanks to Jan Janssen (Max-Planck-Institut für Eisenforschung) for setting
up the Conda capability. up the Conda capability.
.. _conda_forge_lammps: https://github.com/conda-forge/lammps-feedstock/issues
.. _openkim: https://openkim.org .. _openkim: https://openkim.org
@ -45,9 +43,6 @@ up the Conda capability.
.. _mini_conda_install: https://docs.conda.io/en/latest/miniconda.html .. _mini_conda_install: https://docs.conda.io/en/latest/miniconda.html
.. _lws: http://lammps.sandia.gov .. _lws: http://lammps.sandia.gov
.. _ld: Manual.html .. _ld: Manual.html
.. _lc: Commands_all.html .. _lc: Commands_all.html

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@ -1,22 +1,22 @@
.. index:: angle\_style charmm .. index:: angle_style charmm
angle\_style charmm command angle_style charmm command
=========================== ==========================
angle\_style charmm/intel command angle_style charmm/intel command
================================= ================================
angle\_style charmm/kk command angle_style charmm/kk command
=============================
angle_style charmm/omp command
============================== ==============================
angle\_style charmm/omp command
===============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style charmm angle_style charmm
@ -24,7 +24,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style charmm angle_style charmm
angle_coeff 1 300.0 107.0 50.0 3.0 angle_coeff 1 300.0 107.0 50.0 3.0
@ -34,12 +34,15 @@ Description
The *charmm* angle style uses the potential The *charmm* angle style uses the potential
.. image:: Eqs/angle_charmm.jpg .. math::
:align: center
with an additional Urey\_Bradley term based on the distance *r* between E = K (\theta - \theta_0)^2 + K_{ub} (r - r_{ub})^2
the 1st and 3rd atoms in the angle. K, theta0, Kub, and Rub are
coefficients defined for each angle type.
with an additional Urey\_Bradley term based on the distance :math:`r` between
the 1st and 3rd atoms in the angle. :math:`K`, :math:`\theta_0`,
:math:`K_{ub}`, and :math:`R_{ub}` are coefficients defined for each angle
type.
See :ref:`(MacKerell) <angle-MacKerell>` for a description of the CHARMM force See :ref:`(MacKerell) <angle-MacKerell>` for a description of the CHARMM force
field. field.
@ -49,13 +52,13 @@ The following coefficients must be defined for each angle type via the
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/radian\^2) * :math:`K` (energy/radian\^2)
* theta0 (degrees) * :math:`\theta_0` (degrees)
* K\_ub (energy/distance\^2) * :math:`K_{ub}` (energy/distance\^2)
* r\_ub (distance) * :math:`r_{ub}` (distance)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2. internally; hence the units of :math:`K` are in energy/radian\^2.
---------- ----------
@ -108,8 +111,3 @@ Related commands
**(MacKerell)** MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field, **(MacKerell)** MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field,
Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998). Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,22 +1,22 @@
.. index:: angle\_style class2 .. index:: angle_style class2
angle\_style class2 command angle_style class2 command
=========================== ==========================
angle\_style class2/kk command angle_style class2/kk command
=============================
angle_style class2/omp command
============================== ==============================
angle\_style class2/omp command angle_style class2/p6 command
=============================== =============================
angle\_style class2/p6 command
==============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style class2 angle_style class2
@ -24,44 +24,49 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style class2 angle_style class2
angle_coeff \* 75.0 angle_coeff * 75.0
angle_coeff 1 bb 10.5872 1.0119 1.5228 angle_coeff 1 bb 10.5872 1.0119 1.5228
angle_coeff \* ba 3.6551 24.895 1.0119 1.5228 angle_coeff * ba 3.6551 24.895 1.0119 1.5228
Description Description
""""""""""" """""""""""
The *class2* angle style uses the potential The *class2* angle style uses the potential
.. image:: Eqs/angle_class2.jpg .. math::
:align: center
where Ea is the angle term, Ebb is a bond-bond term, and Eba is a E & = E_a + E_{bb} + E_{ba} \\
bond-angle term. Theta0 is the equilibrium angle and r1 and r2 are E_a & = K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4(\theta - \theta_0)^4 \\
E_{bb} & = M (r_{ij} - r_1) (r_{jk} - r_2) \\
E_{ba} & = N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2(r_{jk} - r_2)(\theta - \theta_0)
where :math:`E_a` is the angle term, :math:`E_{bb}` is a bond-bond term, and :math:`E_{ba}` is a
bond-angle term. :math:`\theta_0` is the equilibrium angle and :math:`r_1` and :math:`r_2` are
the equilibrium bond lengths. the equilibrium bond lengths.
See :ref:`(Sun) <angle-Sun>` for a description of the COMPASS class2 force field. See :ref:`(Sun) <angle-Sun>` for a description of the COMPASS class2 force field.
Coefficients for the Ea, Ebb, and Eba formulas must be defined for Coefficients for the :math:`E_a`, :math:`E_{bb}`, and :math:`E_{ba}` formulas must be defined for
each angle type via the :doc:`angle\_coeff <angle_coeff>` command as in each angle type via the :doc:`angle\_coeff <angle_coeff>` command as in
the example above, or in the data file or restart files read by the the example above, or in the data file or restart files read by the
:doc:`read\_data <read_data>` or :doc:`read\_restart <read_restart>` :doc:`read\_data <read_data>` or :doc:`read\_restart <read_restart>`
commands. commands.
These are the 4 coefficients for the Ea formula: These are the 4 coefficients for the :math:`E_a` formula:
* theta0 (degrees) * :math:`\theta_0` (degrees)
* K2 (energy/radian\^2) * :math:`K_2` (energy/radian\^2)
* K3 (energy/radian\^3) * :math:`K_3` (energy/radian\^3)
* K4 (energy/radian\^4) * :math:`K_4` (energy/radian\^4)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of the various K are in per-radian. internally; hence the units of the various :math:`K` are in per-radian.
For the Ebb formula, each line in a :doc:`angle\_coeff <angle_coeff>` For the :math:`E_{bb}` formula, each line in a :doc:`angle\_coeff <angle_coeff>`
command in the input script lists 4 coefficients, the first of which command in the input script lists 4 coefficients, the first of which
is "bb" to indicate they are BondBond coefficients. In a data file, is "bb" to indicate they are BondBond coefficients. In a data file,
these coefficients should be listed under a "BondBond Coeffs" heading these coefficients should be listed under a "BondBond Coeffs" heading
@ -69,11 +74,11 @@ and you must leave out the "bb", i.e. only list 3 coefficients after
the angle type. the angle type.
* bb * bb
* M (energy/distance\^2) * :math:`M` (energy/distance\^2)
* r1 (distance) * :math:`r_1` (distance)
* r2 (distance) * :math:`r_2` (distance)
For the Eba formula, each line in a :doc:`angle\_coeff <angle_coeff>` For the :math:`E_{ba}` formula, each line in a :doc:`angle\_coeff <angle_coeff>`
command in the input script lists 5 coefficients, the first of which command in the input script lists 5 coefficients, the first of which
is "ba" to indicate they are BondAngle coefficients. In a data file, is "ba" to indicate they are BondAngle coefficients. In a data file,
these coefficients should be listed under a "BondAngle Coeffs" heading these coefficients should be listed under a "BondAngle Coeffs" heading
@ -81,13 +86,13 @@ and you must leave out the "ba", i.e. only list 4 coefficients after
the angle type. the angle type.
* ba * ba
* N1 (energy/distance\^2) * :math:`N_1` (energy/distance\^2)
* N2 (energy/distance\^2) * :math:`N_2` (energy/distance\^2)
* r1 (distance) * :math:`r_1` (distance)
* r2 (distance) * :math:`r_2` (distance)
The theta0 value in the Eba formula is not specified, since it is the The :math:`\theta_0` value in the :math:`E_{ba}` formula is not specified,
same value from the Ea formula. since it is the same value from the :math:`E_a` formula.
---------- ----------
@ -117,17 +122,19 @@ instructions on how to use the accelerated styles effectively.
The *class2/p6* angle style uses the *class2* potential expanded to sixth order: The *class2/p6* angle style uses the *class2* potential expanded to sixth order:
.. image:: Eqs/angle_class2_p6.jpg .. math::
:align: center
In this expanded term 6 coefficients for the Ea formula need to be set: E_{a} = K_2\left(\theta - \theta_0\right)^2 + K_3\left(\theta - \theta_0\right)^3 + K_4\left(\theta - \theta_0\right)^4 + K_5\left(\theta - \theta_0\right)^5 + K_6\left(\theta - \theta_0\right)^6
* theta0 (degrees)
* K2 (energy/radian\^2) In this expanded term 6 coefficients for the :math:`E_a` formula need to be set:
* K3 (energy/radian\^3)
* K4 (energy/radian\^4) * :math:`\theta_0` (degrees)
* K5 (energy/radian\^5) * :math:`K_2` (energy/radian\^2)
* K6 (energy/radian\^6) * :math:`K_3` (energy/radian\^3)
* :math:`K_4` (energy/radian\^4)
* :math:`K_5` (energy/radian\^5)
* :math:`K_6` (energy/radian\^6)
The bond-bond and bond-angle terms remain unchanged. The bond-bond and bond-angle terms remain unchanged.
@ -160,8 +167,3 @@ Related commands
**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998). **(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_coeff .. index:: angle_coeff
angle\_coeff command angle_coeff command
==================== ===================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_coeff N args angle_coeff N args
@ -18,11 +18,11 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_coeff 1 300.0 107.0 angle_coeff 1 300.0 107.0
angle_coeff \* 5.0 angle_coeff * 5.0
angle_coeff 2\*10 5.0 angle_coeff 2*10 5.0
Description Description
""""""""""" """""""""""
@ -30,7 +30,7 @@ Description
Specify the angle force field coefficients for one or more angle types. Specify the angle force field coefficients for one or more angle types.
The number and meaning of the coefficients depends on the angle style. The number and meaning of the coefficients depends on the angle style.
Angle coefficients can also be set in the data file read by the Angle coefficients can also be set in the data file read by the
:doc:`read\_data <read_data>` command or in a restart file. :doc:`read_data <read_data>` command or in a restart file.
N can be specified in one of two ways. An explicit numeric value can N can be specified in one of two ways. An explicit numeric value can
be used, as in the 1st example above. Or a wild-card asterisk can be be used, as in the 1st example above. Or a wild-card asterisk can be
@ -41,18 +41,18 @@ leading asterisk means all types from 1 to n (inclusive). A trailing
asterisk means all types from n to N (inclusive). A middle asterisk asterisk means all types from n to N (inclusive). A middle asterisk
means all types from m to n (inclusive). means all types from m to n (inclusive).
Note that using an angle\_coeff command can override a previous setting Note that using an :doc:`angle_coeff <angle_coeff>` command can override a previous setting
for the same angle type. For example, these commands set the coeffs for the same angle type. For example, these commands set the coeffs
for all angle types, then overwrite the coeffs for just angle type 2: for all angle types, then overwrite the coeffs for just angle type 2:
.. parsed-literal:: .. code-block:: LAMMPS
angle_coeff \* 200.0 107.0 1.2 angle_coeff * 200.0 107.0 1.2
angle_coeff 2 50.0 107.0 angle_coeff 2 50.0 107.0
A line in a data file that specifies angle coefficients uses the exact A line in a data file that specifies angle coefficients uses the exact
same format as the arguments of the angle\_coeff command in an input same format as the arguments of the :doc:`angle_coeff <angle_coeff>` command in an input
script, except that wild-card asterisks should not be used since script, except that wild-card asterisks should not be used since
coefficients for all N types must be listed in the file. For example, coefficients for all N types must be listed in the file. For example,
under the "Angle Coeffs" section of a data file, the line that under the "Angle Coeffs" section of a data file, the line that
@ -63,7 +63,7 @@ corresponds to the 1st example above would be listed as
1 300.0 107.0 1 300.0 107.0
The :doc:`angle\_style class2 <angle_class2>` is an exception to this The :doc:`angle_style class2 <angle_class2>` is an exception to this
rule, in that an additional argument is used in the input script to rule, in that an additional argument is used in the input script to
allow specification of the cross-term coefficients. See its allow specification of the cross-term coefficients. See its
doc page for details. doc page for details.
@ -73,13 +73,13 @@ doc page for details.
The list of all angle styles defined in LAMMPS is given on the The list of all angle styles defined in LAMMPS is given on the
:doc:`angle\_style <angle_style>` doc page. They are also listed in more :doc:`angle_style <angle_style>` doc page. They are also listed in more
compact form on the :ref:`Commands angle <angle>` doc compact form on the :ref:`Commands angle <angle>` doc
page. page.
On either of those pages, click on the style to display the formula it On either of those pages, click on the style to display the formula it
computes and its coefficients as specified by the associated computes and its coefficients as specified by the associated
angle\_coeff command. :doc:`angle_coeff <angle_coeff>` command.
---------- ----------
@ -90,8 +90,8 @@ Restrictions
This command must come after the simulation box is defined by a This command must come after the simulation box is defined by a
:doc:`read\_data <read_data>`, :doc:`read\_restart <read_restart>`, or :doc:`read_data <read_data>`, :doc:`read_restart <read_restart>`, or
:doc:`create\_box <create_box>` command. :doc:`create_box <create_box>` command.
An angle style must be defined before any angle coefficients are An angle style must be defined before any angle coefficients are
set, either in the input script or in a data file. set, either in the input script or in a data file.
@ -99,11 +99,6 @@ set, either in the input script or in a data file.
Related commands Related commands
"""""""""""""""" """"""""""""""""
:doc:`angle\_style <angle_style>` :doc:`angle_style <angle_style>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,19 +1,19 @@
.. index:: angle\_style cosine .. index:: angle_style cosine
angle\_style cosine command angle_style cosine command
=========================== ==========================
angle\_style cosine/omp command angle_style cosine/omp command
===============================
angle\_style cosine/kk command
============================== ==============================
angle_style cosine/kk command
=============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine angle_style cosine
@ -21,27 +21,29 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine angle_style cosine
angle_coeff \* 75.0 angle_coeff * 75.0
Description Description
""""""""""" """""""""""
The *cosine* angle style uses the potential The *cosine* angle style uses the potential
.. image:: Eqs/angle_cosine.jpg .. math::
:align: center
where K is defined for each angle type. E = K [1 + \cos(\theta)]
where :math:`K` is defined for each angle type.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy) * :math:`K` (energy)
---------- ----------
@ -83,8 +85,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style cosine/buck6d .. index:: angle_style cosine/buck6d
angle\_style cosine/buck6d command angle_style cosine/buck6d command
================================== =================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/buck6d angle_style cosine/buck6d
@ -15,7 +15,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/buck6d angle_style cosine/buck6d
angle_coeff 1 cosine/buck6d 1.978350 4 180.000000 angle_coeff 1 cosine/buck6d 1.978350 4 180.000000
@ -25,22 +25,23 @@ Description
The *cosine/buck6d* angle style uses the potential The *cosine/buck6d* angle style uses the potential
.. image:: Eqs/angle_cosine_buck6d.jpg .. math::
:align: center
where K is the energy constant, n is the periodic multiplicity and E = K \left[ 1 + \cos(n\theta - \theta_0)\right]
Theta0 is the equilibrium angle.
where :math:`K` is the energy constant, :math:`n` is the periodic multiplicity and
:math:`\theta_0` is the equilibrium angle.
The coefficients must be defined for each angle type via the The coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands in the following order: or :doc:`read\_restart <read_restart>` commands in the following order:
* K (energy) * :math:`K` (energy)
* n * :math:`n`
* Theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally. internally.
Additional to the cosine term the *cosine/buck6d* angle style computes Additional to the cosine term the *cosine/buck6d* angle style computes
@ -73,8 +74,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style cosine/delta .. index:: angle_style cosine/delta
angle\_style cosine/delta command angle_style cosine/delta command
================================= ================================
angle\_style cosine/delta/omp command angle_style cosine/delta/omp command
===================================== ====================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/delta angle_style cosine/delta
@ -18,31 +18,33 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/delta angle_style cosine/delta
angle_coeff 2\*4 75.0 100.0 angle_coeff 2*4 75.0 100.0
Description Description
""""""""""" """""""""""
The *cosine/delta* angle style uses the potential The *cosine/delta* angle style uses the potential
.. image:: Eqs/angle_cosine_delta.jpg .. math::
:align: center
where theta0 is the equilibrium value of the angle, and K is a E = K [1 - \cos(\theta - \theta_0)]
prefactor. Note that the usual 1/2 factor is included in K.
where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a
prefactor. Note that the usual 1/2 factor is included in :math:`K`.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy) * :math:`K` (energy)
* theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally. internally.
@ -85,8 +87,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>`, :doc:`angle\_style cosine/squared <angle_cosine_squared>` :doc:`angle\_coeff <angle_coeff>`, :doc:`angle\_style cosine/squared <angle_cosine_squared>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style cosine/periodic .. index:: angle_style cosine/periodic
angle\_style cosine/periodic command angle_style cosine/periodic command
==================================== ===================================
angle\_style cosine/periodic/omp command angle_style cosine/periodic/omp command
======================================== =======================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/periodic angle_style cosine/periodic
@ -18,24 +18,26 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/periodic angle_style cosine/periodic
angle_coeff \* 75.0 1 6 angle_coeff * 75.0 1 6
Description Description
""""""""""" """""""""""
The *cosine/periodic* angle style uses the following potential, which The *cosine/periodic* angle style uses the following potential, which
is commonly used in the :doc:`DREIDING <Howto_bioFF>` force field, is commonly used in the :doc:`DREIDING <Howto_bioFF>` force field,
particularly for organometallic systems where *n* = 4 might be used particularly for organometallic systems where :math:`n` = 4 might be used
for an octahedral complex and *n* = 3 might be used for a trigonal for an octahedral complex and :math:`n` = 3 might be used for a trigonal
center: center:
.. image:: Eqs/angle_cosine_periodic.jpg .. math::
:align: center
where C, B and n are coefficients defined for each angle type. E = C \left[ 1 - B(-1)^n\cos\left( n\theta\right) \right]
where :math:`C`, :math:`B` and :math:`n` are coefficients defined for each angle type.
See :ref:`(Mayo) <cosine-Mayo>` for a description of the DREIDING force field See :ref:`(Mayo) <cosine-Mayo>` for a description of the DREIDING force field
@ -44,13 +46,13 @@ The following coefficients must be defined for each angle type via the
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* C (energy) * :math:`C` (energy)
* B = 1 or -1 * :math:`B` = 1 or -1
* n = 1, 2, 3, 4, 5 or 6 for periodicity * :math:`n` = 1, 2, 3, 4, 5 or 6 for periodicity
Note that the prefactor C is specified and not the overall force Note that the prefactor :math:`C` is specified and not the overall force
constant K = C / n\^2. When B = 1, it leads to a minimum for the constant :math:`K = \frac{C}{n^2}`. When :math:`B = 1`, it leads to a minimum for the
linear geometry. When B = -1, it leads to a maximum for the linear linear geometry. When :math:`B = -1`, it leads to a maximum for the linear
geometry. geometry.
@ -104,8 +106,3 @@ Related commands
**(Mayo)** Mayo, Olfason, Goddard III, J Phys Chem, 94, 8897-8909 **(Mayo)** Mayo, Olfason, Goddard III, J Phys Chem, 94, 8897-8909
(1990). (1990).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style cosine/shift .. index:: angle_style cosine/shift
angle\_style cosine/shift command angle_style cosine/shift command
================================= =================================
angle\_style cosine/shift/omp command angle_style cosine/shift/omp command
===================================== ====================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/shift angle_style cosine/shift
@ -18,30 +18,33 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/shift angle_style cosine/shift
angle_coeff \* 10.0 45.0 angle_coeff * 10.0 45.0
Description Description
""""""""""" """""""""""
The *cosine/shift* angle style uses the potential The *cosine/shift* angle style uses the potential
.. image:: Eqs/angle_cosine_shift.jpg .. math::
:align: center
where theta0 is the equilibrium angle. The potential is bounded E = -\frac{U_{\text{min}}}{2} \left[ 1 + \cos(\theta-\theta_0) \right]
between -Umin and zero. In the neighborhood of the minimum E=- Umin +
Umin/4(theta-theta0)\^2 hence the spring constant is umin/2.
where :math:`\theta_0` is the equilibrium angle. The potential is bounded
between :math:`-U_{\text{min}}` and zero. In the neighborhood of the minimum
:math:`E = - U_{\text{min}} + U_{\text{min}}/4(\theta - \theta_0)^2` hence
the spring constant is :math:`\frac{U_{\text{min}}}{2}`.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* umin (energy) * :math:`U_{\text{min}}` (energy)
* theta (angle) * :math:`\theta` (angle)
---------- ----------
@ -83,8 +86,3 @@ Related commands
:doc:`angle\_cosine\_shift\_exp <angle_cosine_shift_exp>` :doc:`angle\_cosine\_shift\_exp <angle_cosine_shift_exp>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style cosine/shift/exp .. index:: angle_style cosine/shift/exp
angle\_style cosine/shift/exp command angle_style cosine/shift/exp command
===================================== ====================================
angle\_style cosine/shift/exp/omp command angle_style cosine/shift/exp/omp command
========================================= ========================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/shift/exp angle_style cosine/shift/exp
@ -18,32 +18,33 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/shift/exp angle_style cosine/shift/exp
angle_coeff \* 10.0 45.0 2.0 angle_coeff * 10.0 45.0 2.0
Description Description
""""""""""" """""""""""
The *cosine/shift/exp* angle style uses the potential The *cosine/shift/exp* angle style uses the potential
.. image:: Eqs/angle_cosine_shift_exp.jpg .. math::
:align: center
where Umin, theta, and a are defined for each angle type. E = -U_{\text{min}} \frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1} \quad \text{with} \quad U(\theta,\theta_0) = -0.5 \left(1+\cos(\theta-\theta_0) \right)
The potential is bounded between [-Umin:0] and the minimum is where :math:`U_{\text{min}}`, :math:`\theta`, and :math:`a` are defined for each angle type.
located at the angle theta0. The a parameter can be both positive or
The potential is bounded between :math:`[-U_{\text{min}}, 0]` and the minimum is
located at the angle :math:`\theta_0`. The a parameter can be both positive or
negative and is used to control the spring constant at the negative and is used to control the spring constant at the
equilibrium. equilibrium.
The spring constant is given by k = A exp(A) Umin / [2 (Exp(a)-1)]. The spring constant is given by :math:`k = A \exp(A) U_{\text{min}} / [2 (\exp(a)-1)]`.
For a > 3, k/Umin = a/2 to better than 5% relative error. For negative For :math:`a > 3`, :math:`\frac{k}{U_{\text{min}}} = \frac{a}{2}` to better than 5% relative error. For negative
values of the a parameter, the spring constant is essentially zero, values of the :math:`a` parameter, the spring constant is essentially zero,
and anharmonic terms takes over. The potential is furthermore well and anharmonic terms takes over. The potential is furthermore well
behaved in the limit a -> 0, where it has been implemented to linear behaved in the limit :math:`a \rightarrow 0`, where it has been implemented to linear
order in a for a < 0.001. In this limit the potential reduces to the order in :math:`a` for :math:`a < 0.001`. In this limit the potential reduces to the
cosineshifted potential. cosineshifted potential.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
@ -51,9 +52,9 @@ The following coefficients must be defined for each angle type via the
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* umin (energy) * :math:`U_min` (energy)
* theta (angle) * :math:`\theta` (angle)
* A (real number) * :math:`A` (real number)
---------- ----------
@ -97,8 +98,3 @@ Related commands
:doc:`dihedral\_cosine\_shift\_exp <dihedral_cosine_shift_exp>` :doc:`dihedral\_cosine\_shift\_exp <dihedral_cosine_shift_exp>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style cosine/squared .. index:: angle_style cosine/squared
angle\_style cosine/squared command angle_style cosine/squared command
=================================== ==================================
angle\_style cosine/squared/omp command angle_style cosine/squared/omp command
======================================= ======================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/squared angle_style cosine/squared
@ -18,31 +18,33 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cosine/squared angle_style cosine/squared
angle_coeff 2\*4 75.0 100.0 angle_coeff 2*4 75.0 100.0
Description Description
""""""""""" """""""""""
The *cosine/squared* angle style uses the potential The *cosine/squared* angle style uses the potential
.. image:: Eqs/angle_cosine_squared.jpg .. math::
:align: center
where theta0 is the equilibrium value of the angle, and K is a E = K [\cos(\theta) - \cos(\theta_0)]^2
prefactor. Note that the usual 1/2 factor is included in K.
where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a
prefactor. Note that the usual 1/2 factor is included in :math:`K`.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy) * :math:`K` (energy)
* theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally. internally.
@ -85,8 +87,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style cross .. index:: angle_style cross
angle\_style cross command angle_style cross command
========================== ==========================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cross angle_style cross
@ -15,7 +15,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style cross angle_style cross
angle_coeff 1 200.0 100.0 100.0 1.25 1.25 107.0 angle_coeff 1 200.0 100.0 100.0 1.25 1.25 107.0
@ -26,13 +26,14 @@ Description
The *cross* angle style uses a potential that couples the bond stretches of The *cross* angle style uses a potential that couples the bond stretches of
a bend with the angle stretch of that bend: a bend with the angle stretch of that bend:
.. image:: Eqs/angle_cross.jpg .. math::
:align: center
where r12,0 is the rest value of the bond length between atom 1 and 2, E = K_{SS} \left(r_{12}-r_{12,0}\right)\left(r_{32}-r_{32,0}\right) + K_{BS0}\left(r_{12}-r_{12,0}\right)\left(\theta-\theta_0\right) + K_{BS1}\left(r_{32}-r_{32,0}\right)\left(\theta-\theta_0\right)
r32,0 is the rest value of the bond length between atom 2 and 2,
and theta0 is the rest value of the angle. KSS is the force constant of where :math:`r_{12,0}` is the rest value of the bond length between atom 1 and 2,
the bond stretch-bond stretch term and KBS0 and KBS1 are the force constants :math:`r_{32,0}` is the rest value of the bond length between atom 3 and 2,
and :math:`\theta_0` is the rest value of the angle. :math:`K_{SS}` is the force constant of
the bond stretch-bond stretch term and :math:`K_{BS0}` and :math:`K_{BS1}` are the force constants
of the bond stretch-angle stretch terms. of the bond stretch-angle stretch terms.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
@ -40,15 +41,15 @@ The following coefficients must be defined for each angle type via the
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* KSS (energy/distance\^2) * :math:`K_{SS}` (energy/distance\^2)
* KBS0 (energy/distance/rad) * :math:`K_{BS0}` (energy/distance/rad)
* KBS1 (energy/distance/rad) * :math:`K_{BS1}` (energy/distance/rad)
* r12,0 (distance) * :math:`r_{12,0}` (distance)
* r32,0 (distance) * :math:`r_{32,0}` (distance)
* theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of KBS0 and KBS1 are in energy/distance/radian. internally; hence the units of :math:`K_{BS0}` and :math:`K_{BS1}` are in energy/distance/radian.
Restrictions Restrictions
"""""""""""" """"""""""""
@ -64,12 +65,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
----------
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style dipole .. index:: angle_style dipole
angle\_style dipole command angle_style dipole command
=========================== ==========================
angle\_style dipole/omp command angle_style dipole/omp command
=============================== ==============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style dipole angle_style dipole
@ -18,7 +18,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style dipole angle_style dipole
angle_coeff 6 2.1 180.0 angle_coeff 6 2.1 180.0
@ -28,53 +28,63 @@ Description
The *dipole* angle style is used to control the orientation of a dipolar The *dipole* angle style is used to control the orientation of a dipolar
atom within a molecule :ref:`(Orsi) <Orsi>`. Specifically, the *dipole* angle atom within a molecule :ref:`(Orsi) <Orsi>`. Specifically, the *dipole* angle
style restrains the orientation of a point dipole mu\_j (embedded in atom style restrains the orientation of a point dipole :math:`\mu_j` (embedded in atom
'j') with respect to a reference (bond) vector r\_ij = r\_i - r\_j, where 'i' :math:`j`) with respect to a reference (bond) vector
is another atom of the same molecule (typically, 'i' and 'j' are also :math:`\vec{r_{ij}} = \vec{r_i} - \vec{r_j}`, where :math:`i` is another atom of
covalently bonded). the same molecule (typically, :math:`i` and :math:`j` are also covalently bonded).
It is convenient to define an angle gamma between the 'free' vector mu\_j It is convenient to define an angle gamma between the 'free' vector :math:`\vec{\mu_j}`
and the reference (bond) vector r\_ij: and the reference (bond) vector :math:`\vec{r_{ij}}`:
.. math::
\cos\gamma = \frac{\vec{\mu_j}\cdot\vec{r_{ij}}}{\mu_j\,r_{ij}}
.. image:: Eqs/angle_dipole_gamma.jpg
:align: center
The *dipole* angle style uses the potential: The *dipole* angle style uses the potential:
.. image:: Eqs/angle_dipole_potential.jpg .. math::
:align: center
where K is a rigidity constant and gamma0 is an equilibrium (reference) E = K (\cos\gamma - \cos\gamma_0)^2
where :math:`K` is a rigidity constant and gamma0 is an equilibrium (reference)
angle. angle.
The torque on the dipole can be obtained by differentiating the The torque on the dipole can be obtained by differentiating the
potential using the 'chain rule' as in appendix C.3 of potential using the 'chain rule' as in appendix C.3 of
:ref:`(Allen) <Allen1>`: :ref:`(Allen) <Allen1>`:
.. image:: Eqs/angle_dipole_torque.jpg .. math::
:align: center
Example: if gamma0 is set to 0 degrees, the torque generated by \vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\, \vec{r_{ij}} \times \vec{\mu_j}
Example: if :math:`\gamma_0` is set to 0 degrees, the torque generated by
the potential will tend to align the dipole along the reference the potential will tend to align the dipole along the reference
direction defined by the (bond) vector r\_ij (in other words, mu\_j is direction defined by the (bond) vector :math:`\vec{r_{ij}}` (in other words, :math:`\vec{\mu_j}` is
restrained to point towards atom 'i'). restrained to point towards atom :math:`i`).
The dipolar torque T\_j must be counterbalanced in order to conserve The dipolar torque :math:`\vec{T_j}` must be counterbalanced in order to conserve
the local angular momentum. This is achieved via an additional force the local angular momentum. This is achieved via an additional force
couple generating a torque equivalent to the opposite of T\_j: couple generating a torque equivalent to the opposite of :math:`\vec{T_j}`:
.. image:: Eqs/angle_dipole_couple.jpg .. math::
:align: center
where F\_i and F\_j are applied on atoms i and j, respectively. -\vec{T_j} & = \vec{r_{ij}} \times \vec{F_i} \\
\vec{F_j} & = -\vec{F_i}
where :math:`\vec{F_i}` and :math:`\vec{F_j}` are applied on atoms :math:`i`
and :math:`j`, respectively.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy) * :math:`K` (energy)
* gamma0 (degrees) * :math:`\gamma_0` (degrees)
---------- ----------
@ -108,17 +118,17 @@ page for more info.
.. note:: .. note::
In the "Angles" section of the data file, the atom ID 'j' In the "Angles" section of the data file, the atom ID :math:`j`
defining the direction of the dipole vector to restrain must come defining the direction of the dipole vector to restrain must come
before the atom ID of the reference atom 'i'. A third atom ID 'k' must before the atom ID of the reference atom :math:`i`. A third atom ID :math:`k` must
also be provided to comply with the requirement of a valid angle also be provided to comply with the requirement of a valid angle
definition. This atom ID k should be chosen to be that of an atom definition. This atom ID :math:`k` should be chosen to be that of an atom
bonded to atom 'i' to avoid errors with "lost angle atoms" when running bonded to atom :math:`i` to avoid errors with "lost angle atoms" when running
in parallel. Since the LAMMPS code checks for valid angle definitions, in parallel. Since the LAMMPS code checks for valid angle definitions,
cannot use the same atom ID of either 'i' or 'j' (this was allowed cannot use the same atom ID of either :math:`i` or :math:`j` (this was allowed
and recommended with older LAMMPS versions). and recommended with older LAMMPS versions).
The "newton" command for intramolecular interactions must be "on" The :doc:`newton <newton>` command for intramolecular interactions must be "on"
(which is the default except when using some accelerator packages). (which is the default except when using some accelerator packages).
This angle style should not be used with SHAKE. This angle style should not be used with SHAKE.
@ -147,8 +157,3 @@ lipid membranes, PloS ONE 6(12): e28637, 2011.
**(Allen)** Allen & Tildesley, Computer Simulation of Liquids, **(Allen)** Allen & Tildesley, Computer Simulation of Liquids,
Clarendon Press, Oxford, 1987. Clarendon Press, Oxford, 1987.
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,42 +1,46 @@
.. index:: angle\_style fourier .. index:: angle_style fourier
angle\_style fourier command angle_style fourier command
============================ ===========================
angle\_style fourier/omp command angle_style fourier/omp command
================================ ===============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style fourier angle_style fourier
Examples Examples
"""""""" """"""""
angle\_style fourier .. code-block:: LAMMPS
angle\_coeff 75.0 1.0 1.0 1.0
angle_style fourier
angle_coeff 75.0 1.0 1.0 1.0
Description Description
""""""""""" """""""""""
The *fourier* angle style uses the potential The *fourier* angle style uses the potential
.. image:: Eqs/angle_fourier.jpg .. math::
:align: center
E = K [C_0 + C_1 \cos ( \theta) + C_2 \cos( 2 \theta) ]
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy) * :math:`K` (energy)
* C0 (real) * :math:`C_0` (real)
* C1 (real) * :math:`C_1` (real)
* C2 (real) * :math:`C_2` (real)
---------- ----------
@ -78,8 +82,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,41 +1,45 @@
.. index:: angle\_style fourier/simple .. index:: angle_style fourier/simple
angle\_style fourier/simple command angle_style fourier/simple command
=================================== ==================================
angle\_style fourier/simple/omp command angle_style fourier/simple/omp command
======================================= ======================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style fourier/simple angle_style fourier/simple
Examples Examples
"""""""" """"""""
angle\_style fourier/simple .. code-block:: LAMMPS
angle\_coeff 100.0 -1.0 1.0
angle_style fourier/simple
angle_coeff 100.0 -1.0 1.0
Description Description
""""""""""" """""""""""
The *fourier/simple* angle style uses the potential The *fourier/simple* angle style uses the potential
.. image:: Eqs/angle_fourier_simple.jpg .. math::
:align: center
E = K [ 1.0 + c \cos ( n \theta) ]
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy) * :math:`K` (energy)
* c (real) * :math:`c` (real)
* n (real) * :math:`n` (real)
---------- ----------
@ -77,8 +81,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,22 +1,22 @@
.. index:: angle\_style harmonic .. index:: angle_style harmonic
angle\_style harmonic command angle_style harmonic command
============================= ============================
angle\_style harmonic/intel command angle_style harmonic/intel command
=================================== ==================================
angle\_style harmonic/kk command angle_style harmonic/kk command
===============================
angle_style harmonic/omp command
================================ ================================
angle\_style harmonic/omp command
=================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style harmonic angle_style harmonic
@ -24,7 +24,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style harmonic angle_style harmonic
angle_coeff 1 300.0 107.0 angle_coeff 1 300.0 107.0
@ -34,22 +34,24 @@ Description
The *harmonic* angle style uses the potential The *harmonic* angle style uses the potential
.. image:: Eqs/angle_harmonic.jpg .. math::
:align: center
where theta0 is the equilibrium value of the angle, and K is a E = K (\theta - \theta_0)^2
prefactor. Note that the usual 1/2 factor is included in K.
where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a
prefactor. Note that the usual 1/2 factor is included in :math:`K`.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/radian\^2) * :math:`K` (energy/radian\^2)
* theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2. internally; hence the units of :math:`K` are in energy/radian\^2.
---------- ----------
@ -91,8 +93,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style hybrid .. index:: angle_style hybrid
angle\_style hybrid command angle_style hybrid command
=========================== ==========================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style hybrid style1 style2 ... angle_style hybrid style1 style2 ...
@ -17,11 +17,11 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style hybrid harmonic cosine angle_style hybrid harmonic cosine
angle_coeff 1 harmonic 80.0 30.0 angle_coeff 1 harmonic 80.0 30.0
angle_coeff 2\* cosine 50.0 angle_coeff 2* cosine 50.0
Description Description
""""""""""" """""""""""
@ -31,19 +31,19 @@ simulation. An angle style is assigned to each angle type. For
example, angles in a polymer flow (of angle type 1) could be computed example, angles in a polymer flow (of angle type 1) could be computed
with a *harmonic* potential and angles in the wall boundary (of angle with a *harmonic* potential and angles in the wall boundary (of angle
type 2) could be computed with a *cosine* potential. The assignment type 2) could be computed with a *cosine* potential. The assignment
of angle type to style is made via the :doc:`angle\_coeff <angle_coeff>` of angle type to style is made via the :doc:`angle_coeff <angle_coeff>`
command or in the data file. command or in the data file.
In the angle\_coeff commands, the name of an angle style must be added In the :doc:`angle_coeff <angle_coeff>` commands, the name of an angle style must be added
after the angle type, with the remaining coefficients being those after the angle type, with the remaining coefficients being those
appropriate to that style. In the example above, the 2 angle\_coeff appropriate to that style. In the example above, the 2 angle\_coeff
commands set angles of angle type 1 to be computed with a *harmonic* commands set angles of angle type 1 to be computed with a *harmonic*
potential with coefficients 80.0, 30.0 for K, theta0. All other angle potential with coefficients 80.0, 30.0 for :math:`K`, :math:`\theta_0`. All other angle
types (2-N) are computed with a *cosine* potential with coefficient types :math:`(2 - N)` are computed with a *cosine* potential with coefficient
50.0 for K. 50.0 for :math:`K`.
If angle coefficients are specified in the data file read via the If angle coefficients are specified in the data file read via the
:doc:`read\_data <read_data>` command, then the same rule applies. :doc:`read_data <read_data>` command, then the same rule applies.
E.g. "harmonic" or "cosine", must be added after the angle type, for each E.g. "harmonic" or "cosine", must be added after the angle type, for each
line in the "Angle Coeffs" section, e.g. line in the "Angle Coeffs" section, e.g.
@ -77,7 +77,7 @@ input script, since BondBond (or BondAngle) coefficients need not be
specified at all for angle types that are not *class2*\ . specified at all for angle types that are not *class2*\ .
An angle style of *none* with no additional coefficients can be used An angle style of *none* with no additional coefficients can be used
in place of an angle style, either in a input script angle\_coeff in place of an angle style, either in a input script :doc:`angle_coeff <angle_coeff>`
command or in the data file, if you desire to turn off interactions command or in the data file, if you desire to turn off interactions
for specific angle types. for specific angle types.
@ -95,16 +95,11 @@ for more info.
Unlike other angle styles, the hybrid angle style does not store angle Unlike other angle styles, the hybrid angle style does not store angle
coefficient info for individual sub-styles in a :doc:`binary restart files <restart>`. Thus when restarting a simulation from a restart coefficient info for individual sub-styles in a :doc:`binary restart files <restart>`. Thus when restarting a simulation from a restart
file, you need to re-specify angle\_coeff commands. file, you need to re-specify :doc:`angle_coeff <angle_coeff>` commands.
Related commands Related commands
"""""""""""""""" """"""""""""""""
:doc:`angle\_coeff <angle_coeff>` :doc:`angle_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style mm3 .. index:: angle_style mm3
angle\_style mm3 command angle_style mm3 command
======================== =======================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style mm3 angle_style mm3
@ -15,7 +15,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style mm3 angle_style mm3
angle_coeff 1 100.0 107.0 angle_coeff 1 100.0 107.0
@ -26,23 +26,25 @@ Description
The *mm3* angle style uses the potential that is anharmonic in the angle The *mm3* angle style uses the potential that is anharmonic in the angle
as defined in :ref:`(Allinger) <mm3-allinger1989>` as defined in :ref:`(Allinger) <mm3-allinger1989>`
.. image:: Eqs/angle_mm3.jpg .. math::
:align: center
where theta0 is the equilibrium value of the angle, and K is a E = K (\theta - \theta_0)^2 \left[ 1 - 0.014(\theta - \theta_0) + 5.6(10)^{-5} (\theta - \theta_0)^2 - 7.0(10)^{-7} (\theta - \theta_0)^3 + 9(10)^{-10} (\theta - \theta_0)^4 \right]
prefactor. The anharmonic prefactors have units deg\^(-n), for example
-0.014 deg\^(-1), 5.6(10)\^(-5) deg\^(-2), ...
where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a
prefactor. The anharmonic prefactors have units :math:`\deg^{-n}`, for example
:math:`-0.014 \deg^{-1}`, :math:`5.6 \cdot 10^{-5} \deg^{-2}`, ...
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/radian\^2) * :math:`K` (energy/radian\^2)
* theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2. internally; hence the units of :math:`K` are in energy/radian\^2.
Restrictions Restrictions
"""""""""""" """"""""""""
@ -58,12 +60,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
----------
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style none .. index:: angle_style none
angle\_style none command angle_style none command
========================= ========================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style none angle_style none
@ -15,7 +15,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style none angle_style none
@ -24,23 +24,19 @@ Description
Using an angle style of none means angle forces and energies are not Using an angle style of none means angle forces and energies are not
computed, even if triplets of angle atoms were listed in the data file computed, even if triplets of angle atoms were listed in the data file
read by the :doc:`read\_data <read_data>` command. read by the :doc:`read_data <read_data>` command.
See the :doc:`angle\_style zero <angle_zero>` command for a way to See the :doc:`angle_style zero <angle_zero>` command for a way to
calculate angle statistics, but compute no angle interactions. calculate angle statistics, but compute no angle interactions.
Restrictions Restrictions
"""""""""""" """"""""""""
none none
Related commands Related commands
"""""""""""""""" """"""""""""""""
:doc:`angle\_style zero <angle_zero>` :doc:`angle_style zero <angle_zero>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style quartic .. index:: angle_style quartic
angle\_style quartic command angle_style quartic command
============================ ===========================
angle\_style quartic/omp command angle_style quartic/omp command
================================ ===============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style quartic angle_style quartic
@ -18,7 +18,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style quartic angle_style quartic
angle_coeff 1 129.1948 56.8726 -25.9442 -14.2221 angle_coeff 1 129.1948 56.8726 -25.9442 -14.2221
@ -28,24 +28,26 @@ Description
The *quartic* angle style uses the potential The *quartic* angle style uses the potential
.. image:: Eqs/angle_quartic.jpg .. math::
:align: center
where theta0 is the equilibrium value of the angle, and K is a E = K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4
prefactor. Note that the usual 1/2 factor is included in K.
where :math:`\theta_0` is the equilibrium value of the angle, and :math:`K` is a
prefactor. Note that the usual 1/2 factor is included in :math:`K`.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in :doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* theta0 (degrees) * :math:`\theta_0` (degrees)
* K2 (energy/radian\^2) * :math:`K_2` (energy/radian\^2)
* K3 (energy/radian\^3) * :math:`K_3` (energy/radian\^3)
* K4 (energy/radian\^4) * :math:`K_4` (energy/radian\^4)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2. internally; hence the units of :math:`K` are in energy/radian\^2.
---------- ----------
@ -87,8 +89,3 @@ Related commands
:doc:`angle\_coeff <angle_coeff>` :doc:`angle\_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style sdk .. index:: angle_style sdk
angle\_style sdk command angle_style sdk command
======================== =======================
angle\_style sdk/omp command angle_style sdk/omp command
============================ ===========================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style sdk angle_style sdk
@ -20,7 +20,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style sdk angle_style sdk
angle_coeff 1 300.0 107.0 angle_coeff 1 300.0 107.0
@ -30,25 +30,27 @@ Description
The *sdk* angle style is a combination of the harmonic angle potential, The *sdk* angle style is a combination of the harmonic angle potential,
.. image:: Eqs/angle_harmonic.jpg .. math::
:align: center
where theta0 is the equilibrium value of the angle and K a prefactor, E = K (\theta - \theta_0)^2
where :math:`\theta_0` is the equilibrium value of the angle and :math:`K` a prefactor,
with the *repulsive* part of the non-bonded *lj/sdk* pair style with the *repulsive* part of the non-bonded *lj/sdk* pair style
between the atoms 1 and 3. This angle potential is intended for between the atoms 1 and 3. This angle potential is intended for
coarse grained MD simulations with the CMM parameterization using the coarse grained MD simulations with the CMM parameterization using the
:doc:`pair\_style lj/sdk <pair_sdk>`. Relative to the pair\_style :doc:`pair\_style lj/sdk <pair_sdk>`. Relative to the pair\_style
*lj/sdk*\ , however, the energy is shifted by *epsilon*\ , to avoid sudden *lj/sdk*\ , however, the energy is shifted by *epsilon*\ , to avoid sudden
jumps. Note that the usual 1/2 factor is included in K. jumps. Note that the usual 1/2 factor is included in :math:`K`.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above: :doc:`angle\_coeff <angle_coeff>` command as in the example above:
* K (energy/radian\^2) * :math:`K` (energy/radian\^2)
* theta0 (degrees) * :math:`\theta_0` (degrees)
Theta0 is specified in degrees, but LAMMPS converts it to radians :math:`\theta_0` is specified in degrees, but LAMMPS converts it to radians
internally; hence the units of K are in energy/radian\^2. internally; hence the units of :math:`K` are in energy/radian\^2.
The also required *lj/sdk* parameters will be extracted automatically The also required *lj/sdk* parameters will be extracted automatically
from the pair\_style. from the pair\_style.
@ -93,8 +95,3 @@ Related commands
:doc:`pair\_style lj/sdk/coul/long <pair_sdk>` :doc:`pair\_style lj/sdk/coul/long <pair_sdk>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style .. index:: angle_style
angle\_style command angle_style command
==================== ===================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style style angle_style style
@ -17,7 +17,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style harmonic angle_style harmonic
angle_style charmm angle_style charmm
@ -29,19 +29,19 @@ Description
Set the formula(s) LAMMPS uses to compute angle interactions between Set the formula(s) LAMMPS uses to compute angle interactions between
triplets of atoms, which remain in force for the duration of the triplets of atoms, which remain in force for the duration of the
simulation. The list of angle triplets is read in by a simulation. The list of angle triplets is read in by a
:doc:`read\_data <read_data>` or :doc:`read\_restart <read_restart>` command :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>` command
from a data or restart file. from a data or restart file.
Hybrid models where angles are computed using different angle Hybrid models where angles are computed using different angle
potentials can be setup using the *hybrid* angle style. potentials can be setup using the *hybrid* angle style.
The coefficients associated with a angle style can be specified in a The coefficients associated with a angle style can be specified in a
data or restart file or via the :doc:`angle\_coeff <angle_coeff>` command. data or restart file or via the :doc:`angle_coeff <angle_coeff>` command.
All angle potentials store their coefficient data in binary restart All angle potentials store their coefficient data in binary restart
files which means angle\_style and :doc:`angle\_coeff <angle_coeff>` files which means angle_style and :doc:`angle_coeff <angle_coeff>`
commands do not need to be re-specified in an input script that commands do not need to be re-specified in an input script that
restarts a simulation. See the :doc:`read\_restart <read_restart>` restarts a simulation. See the :doc:`read_restart <read_restart>`
command for details on how to do this. The one exception is that command for details on how to do this. The one exception is that
angle\_style *hybrid* only stores the list of sub-styles in the restart angle\_style *hybrid* only stores the list of sub-styles in the restart
file; angle coefficients need to be re-specified. file; angle coefficients need to be re-specified.
@ -49,7 +49,7 @@ file; angle coefficients need to be re-specified.
.. note:: .. note::
When both an angle and pair style is defined, the When both an angle and pair style is defined, the
:doc:`special\_bonds <special_bonds>` command often needs to be used to :doc:`special_bonds <special_bonds>` command often needs to be used to
turn off (or weight) the pairwise interaction that would otherwise turn off (or weight) the pairwise interaction that would otherwise
exist between 3 bonded atoms. exist between 3 bonded atoms.
@ -62,11 +62,11 @@ between the 3 atoms in the angle.
Here is an alphabetic list of angle styles defined in LAMMPS. Click on Here is an alphabetic list of angle styles defined in LAMMPS. Click on
the style to display the formula it computes and coefficients the style to display the formula it computes and coefficients
specified by the associated :doc:`angle\_coeff <angle_coeff>` command. specified by the associated :doc:`angle_coeff <angle_coeff>` command.
Click on the style to display the formula it computes, any additional Click on the style to display the formula it computes, any additional
arguments specified in the angle\_style command, and coefficients arguments specified in the angle\_style command, and coefficients
specified by the associated :doc:`angle\_coeff <angle_coeff>` command. specified by the associated :doc:`angle_coeff <angle_coeff>` command.
There are also additional accelerated pair styles included in the There are also additional accelerated pair styles included in the
LAMMPS distribution for faster performance on CPUs, GPUs, and KNLs. LAMMPS distribution for faster performance on CPUs, GPUs, and KNLs.
@ -115,17 +115,12 @@ individual bond potentials tell if it is part of a package.
Related commands Related commands
"""""""""""""""" """"""""""""""""
:doc:`angle\_coeff <angle_coeff>` :doc:`angle_coeff <angle_coeff>`
Default Default
""""""" """""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style none angle_style none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: angle\_style table .. index:: angle_style table
angle\_style table command angle_style table command
========================== =========================
angle\_style table/omp command angle_style table/omp command
============================== =============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style table style N angle_style table style N
@ -21,7 +21,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style table linear 1000 angle_style table linear 1000
angle_coeff 3 file.table ENTRY1 angle_coeff 3 file.table ENTRY1
@ -31,7 +31,7 @@ Description
Style *table* creates interpolation tables of length *N* from angle Style *table* creates interpolation tables of length *N* from angle
potential and derivative values listed in a file(s) as a function of potential and derivative values listed in a file(s) as a function of
angle The files are read by the :doc:`angle\_coeff <angle_coeff>` angle The files are read by the :doc:`angle_coeff <angle_coeff>`
command. command.
The interpolation tables are created by fitting cubic splines to the The interpolation tables are created by fitting cubic splines to the
@ -50,7 +50,7 @@ find the appropriate set of coefficients which are used to evaluate a
cubic polynomial which computes the energy or derivative. cubic polynomial which computes the energy or derivative.
The following coefficients must be defined for each angle type via the The following coefficients must be defined for each angle type via the
:doc:`angle\_coeff <angle_coeff>` command as in the example above. :doc:`angle_coeff <angle_coeff>` command as in the example above.
* filename * filename
* keyword * keyword
@ -85,13 +85,13 @@ A section begins with a non-blank line whose 1st character is not a
between sections. The first line begins with a keyword which between sections. The first line begins with a keyword which
identifies the section. The line can contain additional text, but the identifies the section. The line can contain additional text, but the
initial text must match the argument specified in the initial text must match the argument specified in the
:doc:`angle\_coeff <angle_coeff>` command. The next line lists (in any :doc:`angle_coeff <angle_coeff>` command. The next line lists (in any
order) one or more parameters for the table. Each parameter is a order) one or more parameters for the table. Each parameter is a
keyword followed by one or more numeric values. keyword followed by one or more numeric values.
The parameter "N" is required and its value is the number of table The parameter "N" is required and its value is the number of table
entries that follow. Note that this may be different than the *N* entries that follow. Note that this may be different than the *N*
specified in the :doc:`angle\_style table <angle_style>` command. Let specified in the :doc:`angle_style table <angle_style>` command. Let
Ntable = *N* in the angle\_style command, and Nfile = "N" in the Ntable = *N* in the angle\_style command, and Nfile = "N" in the
tabulated file. What LAMMPS does is a preliminary interpolation by tabulated file. What LAMMPS does is a preliminary interpolation by
creating splines using the Nfile tabulated values as nodal points. It creating splines using the Nfile tabulated values as nodal points. It
@ -176,11 +176,6 @@ for more info.
Related commands Related commands
"""""""""""""""" """"""""""""""""
:doc:`angle\_coeff <angle_coeff>` :doc:`angle_coeff <angle_coeff>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: angle\_style zero .. index:: angle_style zero
angle\_style zero command angle_style zero command
========================= ========================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style zero *nocoeff* angle_style zero *nocoeff*
@ -15,12 +15,12 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
angle_style zero angle_style zero
angle_style zero nocoeff angle_style zero nocoeff
angle_coeff \* angle_coeff *
angle_coeff \* 120.0 angle_coeff * 120.0
Description Description
""""""""""" """""""""""
@ -32,14 +32,14 @@ other commands.
As an example, the :doc:`compute angle/local <compute_angle_local>` As an example, the :doc:`compute angle/local <compute_angle_local>`
command can be used to compute the theta values for the list of command can be used to compute the theta values for the list of
triplets of angle atoms listed in the data file read by the triplets of angle atoms listed in the data file read by the
:doc:`read\_data <read_data>` command. If no angle style is defined, :doc:`read_data <read_data>` command. If no angle style is defined,
this command cannot be used. this command cannot be used.
The optional *nocoeff* flag allows to read data files with AngleCoeff The optional *nocoeff* flag allows to read data files with AngleCoeff
section for any angle style. Similarly, any angle\_coeff commands section for any angle style. Similarly, any :doc:`angle_coeff <angle_coeff>` commands
will only be checked for the angle type number and the rest ignored. will only be checked for the angle type number and the rest ignored.
Note that the :doc:`angle\_coeff <angle_coeff>` command must be used for Note that the :doc:`angle_coeff <angle_coeff>` command must be used for
all angle types. If specified, there can be only one value, which is all angle types. If specified, there can be only one value, which is
going to be used to assign an equilibrium angle, e.g. for use with going to be used to assign an equilibrium angle, e.g. for use with
:doc:`fix shake <fix_shake>`. :doc:`fix shake <fix_shake>`.
@ -51,11 +51,6 @@ Restrictions
Related commands Related commands
"""""""""""""""" """"""""""""""""
:doc:`angle\_style none <angle_none>` :doc:`angle_style none <angle_none>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: atom\_modify .. index:: atom_modify
atom\_modify command atom_modify command
==================== ===================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
atom_modify keyword values ... atom_modify keyword values ...
@ -29,7 +29,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
atom_modify map yes atom_modify map yes
atom_modify map hash sort 10000 2.0 atom_modify map hash sort 10000 2.0
@ -188,8 +188,3 @@ defined, sorting will be turned off.
**(Meloni)** Meloni, Rosati and Colombo, J Chem Phys, 126, 121102 (2007). **(Meloni)** Meloni, Rosati and Colombo, J Chem Phys, 126, 121102 (2007).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: atom\_style .. index:: atom_style
atom\_style command atom_style command
=================== ==================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
atom_style style args atom_style style args
@ -33,7 +33,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
atom_style atomic atom_style atomic
atom_style bond atom_style bond
@ -371,8 +371,3 @@ atom\_style atomic
**(Grime)** Grime and Voth, to appear in J Chem Theory & Computation **(Grime)** Grime and Voth, to appear in J Chem Theory & Computation
(2014). (2014).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,19 +1,19 @@
.. index:: bond\_style class2 .. index:: bond_style class2
bond\_style class2 command bond_style class2 command
========================== =========================
bond\_style class2/omp command bond_style class2/omp command
==============================
bond\_style class2/kk command
============================= =============================
bond_style class2/kk command
============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style class2 bond_style class2
@ -21,7 +21,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style class2 bond_style class2
bond_coeff 1 1.0 100.0 80.0 80.0 bond_coeff 1 1.0 100.0 80.0 80.0
@ -31,10 +31,12 @@ Description
The *class2* bond style uses the potential The *class2* bond style uses the potential
.. image:: Eqs/bond_class2.jpg .. math::
:align: center
where r0 is the equilibrium bond distance. E = K_2 (r - r_0)^2 + K_3 (r - r_0)^3 + K_4 (r - r_0)^4
where :math:`r_0` is the equilibrium bond distance.
See :ref:`(Sun) <bond-Sun>` for a description of the COMPASS class2 force field. See :ref:`(Sun) <bond-Sun>` for a description of the COMPASS class2 force field.
@ -43,10 +45,10 @@ The following coefficients must be defined for each bond type via the
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* R0 (distance) * :math:`r_0` (distance)
* K2 (energy/distance\^2) * :math:`K_2` (energy/distance\^2)
* K3 (energy/distance\^3) * :math:`K_3` (energy/distance\^3)
* K4 (energy/distance\^4) * :math:`K_4` (energy/distance\^4)
---------- ----------
@ -98,8 +100,3 @@ Related commands
**(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998). **(Sun)** Sun, J Phys Chem B 102, 7338-7364 (1998).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,13 +1,13 @@
.. index:: bond\_coeff .. index:: bond_coeff
bond\_coeff command bond_coeff command
=================== ==================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
bond_coeff N args bond_coeff N args
@ -18,11 +18,11 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
bond_coeff 5 80.0 1.2 bond_coeff 5 80.0 1.2
bond_coeff \* 30.0 1.5 1.0 1.0 bond_coeff * 30.0 1.5 1.0 1.0
bond_coeff 1\*4 30.0 1.5 1.0 1.0 bond_coeff 1*4 30.0 1.5 1.0 1.0
bond_coeff 1 harmonic 200.0 1.0 bond_coeff 1 harmonic 200.0 1.0
Description Description
@ -47,9 +47,9 @@ for the same bond type. For example, these commands set the coeffs
for all bond types, then overwrite the coeffs for just bond type 2: for all bond types, then overwrite the coeffs for just bond type 2:
.. parsed-literal:: .. code-block:: LAMMPS
bond_coeff \* 100.0 1.2 bond_coeff * 100.0 1.2
bond_coeff 2 200.0 1.2 bond_coeff 2 200.0 1.2
A line in a data file that specifies bond coefficients uses the exact A line in a data file that specifies bond coefficients uses the exact
@ -97,8 +97,3 @@ Related commands
:doc:`bond\_style <bond_style>` :doc:`bond\_style <bond_style>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,22 +1,22 @@
.. index:: bond\_style fene .. index:: bond_style fene
bond\_style fene command bond_style fene command
======================== =======================
bond\_style fene/intel command bond_style fene/intel command
============================== =============================
bond\_style fene/kk command bond_style fene/kk command
==========================
bond_style fene/omp command
=========================== ===========================
bond\_style fene/omp command
============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style fene bond_style fene
@ -24,7 +24,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style fene bond_style fene
bond_coeff 1 30.0 1.5 1.0 1.0 bond_coeff 1 30.0 1.5 1.0 1.0
@ -34,24 +34,26 @@ Description
The *fene* bond style uses the potential The *fene* bond style uses the potential
.. image:: Eqs/bond_fene.jpg .. math::
:align: center
E = -0.5 K R_0^2 \ln \left[ 1 - \left(\frac{r}{R_0}\right)^2\right] + 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
to define a finite extensible nonlinear elastic (FENE) potential to define a finite extensible nonlinear elastic (FENE) potential
:ref:`(Kremer) <fene-Kremer>`, used for bead-spring polymer models. The first :ref:`(Kremer) <fene-Kremer>`, used for bead-spring polymer models. The first
term is attractive, the 2nd Lennard-Jones term is repulsive. The term is attractive, the 2nd Lennard-Jones term is repulsive. The
first term extends to R0, the maximum extent of the bond. The 2nd first term extends to :math:`R_0`, the maximum extent of the bond. The 2nd
term is cutoff at 2\^(1/6) sigma, the minimum of the LJ potential. term is cutoff at :math:`2^\frac{1}{6} \sigma`, the minimum of the LJ potential.
The following coefficients must be defined for each bond type via the The following coefficients must be defined for each bond type via the
:doc:`bond\_coeff <bond_coeff>` command as in the example above, or in :doc:`bond\_coeff <bond_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/distance\^2) * :math:`K` (energy/distance\^2)
* R0 (distance) * :math:`R_0` (distance)
* epsilon (energy) * :math:`\epsilon` (energy)
* sigma (distance) * :math:`\sigma` (distance)
---------- ----------
@ -107,8 +109,3 @@ Related commands
**(Kremer)** Kremer, Grest, J Chem Phys, 92, 5057 (1990). **(Kremer)** Kremer, Grest, J Chem Phys, 92, 5057 (1990).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: bond\_style fene/expand .. index:: bond_style fene/expand
bond\_style fene/expand command bond_style fene/expand command
=============================== ==============================
bond\_style fene/expand/omp command bond_style fene/expand/omp command
=================================== ==================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style fene/expand bond_style fene/expand
@ -18,7 +18,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style fene/expand bond_style fene/expand
bond_coeff 1 30.0 1.5 1.0 1.0 0.5 bond_coeff 1 30.0 1.5 1.0 1.0 0.5
@ -28,29 +28,30 @@ Description
The *fene/expand* bond style uses the potential The *fene/expand* bond style uses the potential
.. image:: Eqs/bond_fene_expand.jpg .. math::
:align: center
E = -0.5 K R_0^2 \ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] + 4 \epsilon \left[ \left(\frac{\sigma}{\left(r - \Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r - \Delta\right)}\right)^6 \right] + \epsilon
to define a finite extensible nonlinear elastic (FENE) potential to define a finite extensible nonlinear elastic (FENE) potential
:ref:`(Kremer) <feneexpand-Kremer>`, used for bead-spring polymer models. The first :ref:`(Kremer) <feneexpand-Kremer>`, used for bead-spring polymer models. The first
term is attractive, the 2nd Lennard-Jones term is repulsive. term is attractive, the 2nd Lennard-Jones term is repulsive.
The *fene/expand* bond style is similar to *fene* except that an extra The *fene/expand* bond style is similar to *fene* except that an extra
shift factor of delta (positive or negative) is added to *r* to shift factor of :math:`\Delta` (positive or negative) is added to :math:`r` to
effectively change the bead size of the bonded atoms. The first term effectively change the bead size of the bonded atoms. The first term
now extends to R0 + delta and the 2nd term is cutoff at 2\^(1/6) sigma now extends to :math:`R_0 + \Delta` and the 2nd term is cutoff at :math:`2^\frac{1}{6} \sigma + \Delta`.
+ delta.
The following coefficients must be defined for each bond type via the The following coefficients must be defined for each bond type via the
:doc:`bond\_coeff <bond_coeff>` command as in the example above, or in :doc:`bond\_coeff <bond_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/distance\^2) * :math:`K` (energy/distance\^2)
* R0 (distance) * :math:`R_0` (distance)
* epsilon (energy) * :math:`\epsilon` (energy)
* sigma (distance) * :math:`\sigma` (distance)
* delta (distance) * :math:`\Delta` (distance)
---------- ----------
@ -106,8 +107,3 @@ Related commands
**(Kremer)** Kremer, Grest, J Chem Phys, 92, 5057 (1990). **(Kremer)** Kremer, Grest, J Chem Phys, 92, 5057 (1990).
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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@ -1,16 +1,16 @@
.. index:: bond\_style gromos .. index:: bond_style gromos
bond\_style gromos command bond_style gromos command
========================== =========================
bond\_style gromos/omp command bond_style gromos/omp command
============================== =============================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style gromos bond_style gromos
@ -18,7 +18,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style gromos bond_style gromos
bond_coeff 5 80.0 1.2 bond_coeff 5 80.0 1.2
@ -28,19 +28,21 @@ Description
The *gromos* bond style uses the potential The *gromos* bond style uses the potential
.. image:: Eqs/bond_gromos.jpg .. math::
:align: center
where r0 is the equilibrium bond distance. Note that the usual 1/4 E = K (r^2 - r_0^2)^2
factor is included in K.
where :math:`r_0` is the equilibrium bond distance. Note that the usual 1/4
factor is included in :math:`K`.
The following coefficients must be defined for each bond type via the The following coefficients must be defined for each bond type via the
:doc:`bond\_coeff <bond_coeff>` command as in the example above, or in :doc:`bond\_coeff <bond_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/distance\^4) * :math:`K` (energy/distance\^4)
* r0 (distance) * :math:`r_0` (distance)
---------- ----------
@ -82,8 +84,3 @@ Related commands
:doc:`bond\_coeff <bond_coeff>`, :doc:`delete\_bonds <delete_bonds>` :doc:`bond\_coeff <bond_coeff>`, :doc:`delete\_bonds <delete_bonds>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

View File

@ -1,22 +1,22 @@
.. index:: bond\_style harmonic .. index:: bond_style harmonic
bond\_style harmonic command bond_style harmonic command
============================ ===========================
bond\_style harmonic/intel command bond_style harmonic/intel command
================================== =================================
bond\_style harmonic/kk command bond_style harmonic/kk command
==============================
bond_style harmonic/omp command
=============================== ===============================
bond\_style harmonic/omp command
================================
Syntax Syntax
"""""" """"""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style harmonic bond_style harmonic
@ -24,7 +24,7 @@ Examples
"""""""" """"""""
.. parsed-literal:: .. code-block:: LAMMPS
bond_style harmonic bond_style harmonic
bond_coeff 5 80.0 1.2 bond_coeff 5 80.0 1.2
@ -34,19 +34,21 @@ Description
The *harmonic* bond style uses the potential The *harmonic* bond style uses the potential
.. image:: Eqs/bond_harmonic.jpg .. math::
:align: center
where r0 is the equilibrium bond distance. Note that the usual 1/2 E = K (r - r_0)^2
factor is included in K.
where :math:`r_0` is the equilibrium bond distance. Note that the usual 1/2
factor is included in :math:`K`.
The following coefficients must be defined for each bond type via the The following coefficients must be defined for each bond type via the
:doc:`bond\_coeff <bond_coeff>` command as in the example above, or in :doc:`bond\_coeff <bond_coeff>` command as in the example above, or in
the data file or restart files read by the :doc:`read\_data <read_data>` the data file or restart files read by the :doc:`read\_data <read_data>`
or :doc:`read\_restart <read_restart>` commands: or :doc:`read\_restart <read_restart>` commands:
* K (energy/distance\^2) * :math:`K` (energy/distance\^2)
* r0 (distance) * :math:`r_0` (distance)
---------- ----------
@ -88,8 +90,3 @@ Related commands
:doc:`bond\_coeff <bond_coeff>`, :doc:`delete\_bonds <delete_bonds>` :doc:`bond\_coeff <bond_coeff>`, :doc:`delete\_bonds <delete_bonds>`
**Default:** none **Default:** none
.. _lws: http://lammps.sandia.gov
.. _ld: Manual.html
.. _lc: Commands_all.html

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