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Update docs: angle_dipole
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Richard Berger
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\documentclass[12pt]{article}
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\begin{document}
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\begin{eqnarray*}
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-\vec{T_j} & = & \vec{r_{ij}} \times \vec{F_i}\\
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\vec{F_j} & = & -\vec{F_i} \\
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\end{eqnarray*}
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\end{document}
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\documentclass[12pt]{article}
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\begin{document}
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$$
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\cos\gamma = \frac{\vec{\mu_j}\bullet\vec{r_{ij}}}{\mu_j\,r_{ij}}
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$$
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\end{document}
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\documentclass[12pt]{article}
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\begin{document}
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$$
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E = K (\cos\gamma - \cos\gamma_0)^2
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$$
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\end{document}
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\documentclass[12pt]{article}
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\begin{document}
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$$
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\vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\,
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\vec{r_{ij}} \times \vec{\mu_j}
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$$
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\end{document}
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@ -1,16 +1,16 @@
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.. index:: angle\_style dipole
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.. index:: angle_style dipole
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angle\_style dipole command
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===========================
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angle_style dipole command
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==========================
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angle\_style dipole/omp command
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===============================
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angle_style dipole/omp command
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==============================
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Syntax
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""""""
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.. parsed-literal::
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.. code-block:: LAMMPS
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angle_style dipole
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@ -18,7 +18,7 @@ Examples
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""""""""
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.. parsed-literal::
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.. code-block:: LAMMPS
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angle_style dipole
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angle_coeff 6 2.1 180.0
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@ -28,53 +28,63 @@ Description
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The *dipole* angle style is used to control the orientation of a dipolar
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atom within a molecule :ref:`(Orsi) <Orsi>`. Specifically, the *dipole* angle
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style restrains the orientation of a point dipole mu\_j (embedded in atom
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'j') with respect to a reference (bond) vector r\_ij = r\_i - r\_j, where 'i'
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is another atom of the same molecule (typically, 'i' and 'j' are also
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covalently bonded).
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style restrains the orientation of a point dipole :math:`\mu_j` (embedded in atom
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:math:`j`) with respect to a reference (bond) vector
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:math:`\vec{r_{ij}} = \vec{r_i} - \vec{r_j}`, where :math:`i` is another atom of
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the same molecule (typically, :math:`i` and :math:`j` are also covalently bonded).
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It is convenient to define an angle gamma between the 'free' vector mu\_j
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and the reference (bond) vector r\_ij:
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It is convenient to define an angle gamma between the 'free' vector :math:`\vec{\mu_j}`
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and the reference (bond) vector :math:`\vec{r_{ij}}`:
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.. math::
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\cos\gamma = \frac{\vec{\mu_j}\cdot\vec{r_{ij}}}{\mu_j\,r_{ij}}
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.. image:: Eqs/angle_dipole_gamma.jpg
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:align: center
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The *dipole* angle style uses the potential:
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.. image:: Eqs/angle_dipole_potential.jpg
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:align: center
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.. math::
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where K is a rigidity constant and gamma0 is an equilibrium (reference)
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E = K (\cos\gamma - \cos\gamma_0)^2
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where :math:`K` is a rigidity constant and gamma0 is an equilibrium (reference)
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angle.
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The torque on the dipole can be obtained by differentiating the
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potential using the 'chain rule' as in appendix C.3 of
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:ref:`(Allen) <Allen1>`:
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.. image:: Eqs/angle_dipole_torque.jpg
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:align: center
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.. math::
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Example: if gamma0 is set to 0 degrees, the torque generated by
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\vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\, \vec{r_{ij}} \times \vec{\mu_j}
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Example: if :math:`\gamma_0` is set to 0 degrees, the torque generated by
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the potential will tend to align the dipole along the reference
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direction defined by the (bond) vector r\_ij (in other words, mu\_j is
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restrained to point towards atom 'i').
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direction defined by the (bond) vector :math:`\vec{r_{ij}}` (in other words, :math:`\vec{\mu_j}` is
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restrained to point towards atom :math:`i`).
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The dipolar torque T\_j must be counterbalanced in order to conserve
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The dipolar torque :math:`\vec{T_j}` must be counterbalanced in order to conserve
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the local angular momentum. This is achieved via an additional force
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couple generating a torque equivalent to the opposite of T\_j:
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couple generating a torque equivalent to the opposite of :math:`\vec{T_j}`:
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.. image:: Eqs/angle_dipole_couple.jpg
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:align: center
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.. math::
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where F\_i and F\_j are applied on atoms i and j, respectively.
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-\vec{T_j} & = & \vec{r_{ij}} \times \vec{F_i}\\
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\vec{F_j} & = & -\vec{F_i} \\
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where :math:`\vec{F_i}` and :math:`\vec{F_j}` are applied on atoms :math:`i`
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and :math:`j`, respectively.
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The following coefficients must be defined for each angle type via the
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:doc:`angle\_coeff <angle_coeff>` command as in the example above, or in
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the data file or restart files read by the :doc:`read\_data <read_data>`
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or :doc:`read\_restart <read_restart>` commands:
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* K (energy)
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* gamma0 (degrees)
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* :math:`K` (energy)
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* :math:`\gamma_0` (degrees)
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----------
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@ -108,17 +118,17 @@ page for more info.
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.. note::
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In the "Angles" section of the data file, the atom ID 'j'
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In the "Angles" section of the data file, the atom ID :math:`j`
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defining the direction of the dipole vector to restrain must come
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before the atom ID of the reference atom 'i'. A third atom ID 'k' must
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before the atom ID of the reference atom :math:`i`. A third atom ID :math:`k` must
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also be provided to comply with the requirement of a valid angle
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definition. This atom ID k should be chosen to be that of an atom
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bonded to atom 'i' to avoid errors with "lost angle atoms" when running
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definition. This atom ID :math:`k` should be chosen to be that of an atom
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bonded to atom :math:`i` to avoid errors with "lost angle atoms" when running
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in parallel. Since the LAMMPS code checks for valid angle definitions,
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cannot use the same atom ID of either 'i' or 'j' (this was allowed
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cannot use the same atom ID of either :math:`i` or :math:`j` (this was allowed
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and recommended with older LAMMPS versions).
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The "newton" command for intramolecular interactions must be "on"
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The :doc:`newton <newton>` command for intramolecular interactions must be "on"
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(which is the default except when using some accelerator packages).
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This angle style should not be used with SHAKE.
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@ -147,8 +157,3 @@ lipid membranes, PloS ONE 6(12): e28637, 2011.
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**(Allen)** Allen & Tildesley, Computer Simulation of Liquids,
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Clarendon Press, Oxford, 1987.
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Commands_all.html
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@ -1,126 +0,0 @@
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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Commands_all.html)
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:line
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angle_style dipole command :h3
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angle_style dipole/omp command :h3
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[Syntax:]
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angle_style dipole :pre
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[Examples:]
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angle_style dipole
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angle_coeff 6 2.1 180.0 :pre
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[Description:]
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The {dipole} angle style is used to control the orientation of a dipolar
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atom within a molecule "(Orsi)"_#Orsi. Specifically, the {dipole} angle
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style restrains the orientation of a point dipole mu_j (embedded in atom
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'j') with respect to a reference (bond) vector r_ij = r_i - r_j, where 'i'
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is another atom of the same molecule (typically, 'i' and 'j' are also
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covalently bonded).
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It is convenient to define an angle gamma between the 'free' vector mu_j
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and the reference (bond) vector r_ij:
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:c,image(Eqs/angle_dipole_gamma.jpg)
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The {dipole} angle style uses the potential:
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:c,image(Eqs/angle_dipole_potential.jpg)
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where K is a rigidity constant and gamma0 is an equilibrium (reference)
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angle.
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The torque on the dipole can be obtained by differentiating the
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potential using the 'chain rule' as in appendix C.3 of
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"(Allen)"_#Allen1:
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:c,image(Eqs/angle_dipole_torque.jpg)
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Example: if gamma0 is set to 0 degrees, the torque generated by
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the potential will tend to align the dipole along the reference
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direction defined by the (bond) vector r_ij (in other words, mu_j is
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restrained to point towards atom 'i').
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The dipolar torque T_j must be counterbalanced in order to conserve
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the local angular momentum. This is achieved via an additional force
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couple generating a torque equivalent to the opposite of T_j:
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:c,image(Eqs/angle_dipole_couple.jpg)
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where F_i and F_j are applied on atoms i and j, respectively.
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The following coefficients must be defined for each angle type via the
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"angle_coeff"_angle_coeff.html command as in the example above, or in
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the data file or restart files read by the "read_data"_read_data.html
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or "read_restart"_read_restart.html commands:
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K (energy)
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gamma0 (degrees) :ul
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:line
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Styles with a {gpu}, {intel}, {kk}, {omp}, or {opt} suffix are
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functionally the same as the corresponding style without the suffix.
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They have been optimized to run faster, depending on your available
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hardware, as discussed on the "Speed packages"_Speed_packages.html doc
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page. The accelerated styles take the same arguments and should
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produce the same results, except for round-off and precision issues.
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These accelerated styles are part of the GPU, USER-INTEL, KOKKOS,
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USER-OMP and OPT packages, respectively. They are only enabled if
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LAMMPS was built with those packages. See the "Build
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package"_Build_package.html doc page for more info.
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You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the "-suffix command-line
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switch"_Run_options.html when you invoke LAMMPS, or you can use the
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"suffix"_suffix.html command in your input script.
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See the "Speed packages"_Speed_packages.html doc page for more
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instructions on how to use the accelerated styles effectively.
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[Restrictions:]
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This angle style can only be used if LAMMPS was built with the
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USER-MISC package. See the "Build package"_Build_package.html doc
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page for more info.
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NOTE: In the "Angles" section of the data file, the atom ID 'j'
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defining the direction of the dipole vector to restrain must come
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before the atom ID of the reference atom 'i'. A third atom ID 'k' must
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also be provided to comply with the requirement of a valid angle
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definition. This atom ID k should be chosen to be that of an atom
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bonded to atom 'i' to avoid errors with "lost angle atoms" when running
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in parallel. Since the LAMMPS code checks for valid angle definitions,
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cannot use the same atom ID of either 'i' or 'j' (this was allowed
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and recommended with older LAMMPS versions).
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The "newton" command for intramolecular interactions must be "on"
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(which is the default except when using some accelerator packages).
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This angle style should not be used with SHAKE.
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[Related commands:]
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"angle_coeff"_angle_coeff.html, "angle_hybrid"_angle_hybrid.html
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[Default:] none
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:line
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:link(Orsi)
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[(Orsi)] Orsi & Essex, The ELBA force field for coarse-grain modeling of
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lipid membranes, PloS ONE 6(12): e28637, 2011.
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:link(Allen1)
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[(Allen)] Allen & Tildesley, Computer Simulation of Liquids,
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Clarendon Press, Oxford, 1987.
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