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doc/Eqs/angle_dipole_potential.tex
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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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doc/Eqs/angle_dipole_torque.tex
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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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@ -904,7 +904,8 @@ package"_Section_start.html#start_3.
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"sdk"_angle_sdk.html,
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"cosine/shift"_angle_cosine_shift.html,
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"cosine/shift/exp"_angle_cosine_shift_exp.html :tb(c=4,ea=c)
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"cosine/shift/exp"_angle_cosine_shift_exp.html,
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"dipole"_angle_dipole.html :tb(c=4,ea=c)
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These are accelerated angle styles, which can be used if LAMMPS is
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built with the "appropriate accelerated
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105
doc/angle_dipole.html
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doc/angle_dipole.html
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<HTML>
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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</CENTER>
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<HR>
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<H3>angle_style dipole command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>angle_style dipole
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</PRE>
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<P><B>Examples:</B>
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</P>
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<PRE>angle_style dipole
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angle_coeff 6 2.1 180.0
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>The <I>dipole</I> angle style is used to control the orientation of a dipolar
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atom within a molecule <A HREF = "#Orsi">(Orsi)</A>. Specifically, the <I>dipole</I> 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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</P>
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<P>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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</P>
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<CENTER><IMG SRC = "Eqs/angle_dipole_gamma.jpg">
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</CENTER>
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<P>The <I>dipole</I> angle style uses the potential:
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</P>
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<CENTER><IMG SRC = "Eqs/angle_dipole_potential.jpg">
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</CENTER>
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<P>where K is a rigidity constant and gamma0 is an equilibrium (reference)
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angle.
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</P>
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<P>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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<A HREF = "#Allen">(Allen)</A>:
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</P>
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<CENTER><IMG SRC = "Eqs/angle_dipole_torque.jpg">
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</CENTER>
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<P>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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</P>
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<P>Note that the angle dipole potential does not give rise to any force,
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because it does not depend on the distance between i and j (it only
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depends on the angle between mu_j and r_ij).
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</P>
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<P>The following coefficients must be defined for each angle type via the
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<A HREF = "angle_coeff.html">angle_coeff</A> command as in the example above, or in
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the data file or restart files read by the <A HREF = "read_data.html">read_data</A>
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or <A HREF = "read_restart.html">read_restart</A> commands:
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</P>
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<UL><LI>K (energy)
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<LI>gamma0 (degrees)
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</UL>
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<P><B>Restrictions:</B>
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</P>
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<P>This angle style can only be used if LAMMPS was built with the
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"user-misc" package. See the <A HREF = "Section_start.html#2_3">Making LAMMPS</A>
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section for more info on packages.
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</P>
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<P>IMPORTANT: In the "Angles" section of the data file, the atom id 'j'
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corresponding to the dipole to restrain must come before the atom id
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of the reference atom 'i'. A third atom id 'k' must also be provided,
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although 'k' is just a 'dummy' atom which can be any atom; it may be
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useful to choose a convention (e.g., 'k'='i') and adhere to it. For
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example, if id=1 for the dipolar atom to restrain, and id=2 for the
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reference atom, the corresponding line in the "Angles" section of the
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data file would read: X X 1 2 2
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</P>
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<P>The "newton" command for intramolecular interactions must be "on"
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(which is the default).
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</P>
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<P>This angle style should not be used with SHAKE.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "angle_coeff.html">angle_coeff</A>, <A HREF = "angle_hybrid.html">angle_hybrid</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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<A NAME = "Orsi"></A>
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<P><B>(Orsi)</B> 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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</P>
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<A NAME = "Allen"></A>
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<P><B>(Allen)</B> Allen & Tildesley, Computer Simulation of Liquids,
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Clarendon Press, Oxford, 1987.
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</P>
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</HTML>
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doc/angle_dipole.txt
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doc/angle_dipole.txt
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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,Section_commands.html#comm)
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:line
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angle_style dipole 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)"_#Allen:
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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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|
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Note that the angle dipole potential does not give rise to any force,
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because it does not depend on the distance between i and j (it only
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depends on the angle between mu_j and r_ij).
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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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[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 "Making LAMMPS"_Section_start.html#2_3
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section for more info on packages.
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IMPORTANT: In the "Angles" section of the data file, the atom id 'j'
|
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corresponding to the dipole to restrain must come before the atom id
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of the reference atom 'i'. A third atom id 'k' must also be provided,
|
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although 'k' is just a 'dummy' atom which can be any atom; it may be
|
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useful to choose a convention (e.g., 'k'='i') and adhere to it. For
|
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example, if id=1 for the dipolar atom to restrain, and id=2 for the
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reference atom, the corresponding line in the "Angles" section of the
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data file would read: X X 1 2 2
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The "newton" command for intramolecular interactions must be "on"
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(which is the default).
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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(Allen)
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[(Allen)] Allen & Tildesley, Computer Simulation of Liquids,
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Clarendon Press, Oxford, 1987.
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