129 lines
3.8 KiB
ReStructuredText
129 lines
3.8 KiB
ReStructuredText
.. index:: angle_style dipole
|
|
|
|
angle_style dipole command
|
|
==========================
|
|
|
|
angle_style dipole/omp command
|
|
==============================
|
|
|
|
Syntax
|
|
""""""
|
|
|
|
.. code-block:: LAMMPS
|
|
|
|
angle_style dipole
|
|
|
|
Examples
|
|
""""""""
|
|
|
|
.. code-block:: LAMMPS
|
|
|
|
angle_style dipole
|
|
angle_coeff 6 2.1 180.0
|
|
|
|
Description
|
|
"""""""""""
|
|
|
|
The *dipole* angle style is used to control the orientation of a dipolar
|
|
atom within a molecule :ref:`(Orsi) <Orsi>`. Specifically, the *dipole* angle
|
|
style restrains the orientation of a point dipole :math:`\mu_j` (embedded in atom
|
|
:math:`j`) with respect to a reference (bond) vector
|
|
:math:`\vec{r_{ij}} = \vec{r_i} - \vec{r_j}`, where :math:`i` is another atom of
|
|
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 :math:`\vec{\mu_j}`
|
|
and the reference (bond) vector :math:`\vec{r_{ij}}`:
|
|
|
|
.. math::
|
|
|
|
\cos\gamma = \frac{\vec{\mu_j}\cdot\vec{r_{ij}}}{\mu_j\,r_{ij}}
|
|
|
|
The *dipole* angle style uses the potential:
|
|
|
|
.. math::
|
|
|
|
E = K (\cos\gamma - \cos\gamma_0)^2
|
|
|
|
where :math:`K` is a rigidity constant and gamma0 is an equilibrium (reference)
|
|
angle.
|
|
|
|
The torque on the dipole can be obtained by differentiating the
|
|
potential using the 'chain rule' as in appendix C.3 of
|
|
:ref:`(Allen) <Allen1>`:
|
|
|
|
.. math::
|
|
|
|
\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
|
|
direction defined by the (bond) vector :math:`\vec{r_{ij}}` (in other words, :math:`\vec{\mu_j}` is
|
|
restrained to point towards atom :math:`i`).
|
|
|
|
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
|
|
couple generating a torque equivalent to the opposite of :math:`\vec{T_j}`:
|
|
|
|
.. math::
|
|
|
|
-\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
|
|
: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>`
|
|
or :doc:`read_restart <read_restart>` commands:
|
|
|
|
* :math:`K` (energy)
|
|
* :math:`\gamma_0` (degrees)
|
|
|
|
----------
|
|
|
|
.. include:: accel_styles.rst
|
|
|
|
Restrictions
|
|
""""""""""""
|
|
|
|
This angle style can only be used if LAMMPS was built with the
|
|
USER-MISC package. See the :doc:`Build package <Build_package>` doc
|
|
page for more info.
|
|
|
|
.. note::
|
|
|
|
In the "Angles" section of the data file, the atom ID :math:`j`
|
|
defining the direction of the dipole vector to restrain must come
|
|
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
|
|
definition. This atom ID :math:`k` should be chosen to be that of an atom
|
|
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,
|
|
cannot use the same atom ID of either :math:`i` or :math:`j` (this was allowed
|
|
and recommended with older LAMMPS versions).
|
|
|
|
The :doc:`newton <newton>` command for intramolecular interactions must be "on"
|
|
(which is the default except when using some accelerator packages).
|
|
|
|
This angle style should not be used with SHAKE.
|
|
|
|
Related commands
|
|
""""""""""""""""
|
|
|
|
:doc:`angle_coeff <angle_coeff>`, :doc:`angle_hybrid <angle_hybrid>`
|
|
|
|
**Default:** none
|
|
|
|
----------
|
|
|
|
.. _Orsi:
|
|
|
|
**(Orsi)** Orsi & Essex, The ELBA force field for coarse-grain modeling of
|
|
lipid membranes, PloS ONE 6(12): e28637, 2011.
|
|
|
|
.. _Allen1:
|
|
|
|
**(Allen)** Allen & Tildesley, Computer Simulation of Liquids,
|
|
Clarendon Press, Oxford, 1987.
|