edits to pair dipole doc page
This commit is contained in:
Steve Plimpton
@ -78,12 +78,12 @@ Examples
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Description
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"""""""""""
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Style *lj/cut/dipole/cut* computes interactions between pairs of particles
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that each have a charge and/or a point dipole moment. In addition to
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the usual Lennard-Jones interaction between the particles (Elj) the
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charge-charge (Eqq), charge-dipole (Eqp), and dipole-dipole (Epp)
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interactions are computed by these formulas for the energy (E), force
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(F), and torque (T) between particles I and J.
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Style *lj/cut/dipole/cut* computes interactions between pairs of
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particles that each have a charge and/or a point dipole moment. In
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addition to the usual Lennard-Jones interaction between the particles
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(Elj) the charge-charge (Eqq), charge-dipole (Eqp), and dipole-dipole
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(Epp) interactions are computed by these formulas for the energy (E),
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force (F), and torque (T) between particles I and J.
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.. math::
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@ -112,18 +112,18 @@ interactions are computed by these formulas for the energy (E), force
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\frac{3}{r^5} (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \times \vec{r})
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where :math:`q_i` and :math:`q_j` are the charges on the two particles,
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:math:`\vec{p_i}` and :math:`\vec{p_j}` are the dipole moment vectors of
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the two particles, r is their separation distance, and the vector r =
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Ri - Rj is the separation vector between the two particles. Note that
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Eqq and Fqq are simply Coulombic energy and force, Fij = -Fji as
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symmetric forces, and Tij != -Tji since the torques do not act
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symmetrically. These formulas are discussed in :ref:`(Allen) <Allen2>`
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and in :ref:`(Toukmaji) <Toukmaji2>`.
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where :math:`q_i` and :math:`q_j` are the charges on the two
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particles, :math:`\vec{p_i}` and :math:`\vec{p_j}` are the dipole
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moment vectors of the two particles, r is their separation distance,
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and the vector r = Ri - Rj is the separation vector between the two
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particles. Note that Eqq and Fqq are simply Coulombic energy and
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force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
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torques do not act symmetrically. These formulas are discussed in
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:ref:`(Allen) <Allen2>` and in :ref:`(Toukmaji) <Toukmaji2>`.
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Also note, that in the code, all of these terms (except Elj) have a
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:math:`C/\epsilon` prefactor, the same as the Coulombic term in the LJ +
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Coulombic pair styles discussed :doc:`here <pair_lj>`. C is an
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:math:`C/\epsilon` prefactor, the same as the Coulombic term in the
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LJ + Coulombic pair styles discussed :doc:`here <pair_lj>`. C is an
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energy-conversion constant and epsilon is the dielectric constant
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which can be set by the :doc:`dielectric <dielectric>` command. The
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same is true of the equations that follow for other dipole pair
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@ -135,11 +135,11 @@ moment. In general, a shifted-force potential is a (slightly) modified
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potential containing extra terms that make both the energy and its
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derivative go to zero at the cutoff distance; this removes
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(cutoff-related) problems in energy conservation and any numerical
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instability in the equations of motion :ref:`(Allen) <Allen2>`. Shifted-force
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interactions for the Lennard-Jones (E_LJ), charge-charge (Eqq),
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charge-dipole (Eqp), dipole-charge (Epq) and dipole-dipole (Epp)
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potentials are computed by these formulas for the energy (E), force
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(F), and torque (T) between particles I and J:
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instability in the equations of motion :ref:`(Allen)
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<Allen2>`. Shifted-force interactions for the Lennard-Jones (E_LJ),
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charge-charge (Eqq), charge-dipole (Eqp), dipole-charge (Epq) and
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dipole-dipole (Epp) potentials are computed by these formulas for the
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energy (E), force (F), and torque (T) between particles I and J:
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.. math::
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@ -207,65 +207,59 @@ potentials are computed by these formulas for the energy (E), force
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where :math:`\epsilon` and :math:`\sigma` are the standard LJ
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parameters, :math:`r_c` is the cutoff, :math:`q_i` and :math:`q_j` are
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the charges on the two particles, :math:`\vec{p_i}` and
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:math:`\vec{p_j}` are the dipole moment vectors of the two particles, r
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is their separation distance, and the vector r = Ri - Rj is the
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separation vector between the two particles. Note that Eqq and Fqq are
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simply Coulombic energy and force, Fij = -Fji as symmetric forces, and
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Tij != -Tji since the torques do not act symmetrically. The
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:math:`\vec{p_j}` are the dipole moment vectors of the two particles,
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r is their separation distance, and the vector r = Ri - Rj is the
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separation vector between the two particles. Note that Eqq and Fqq
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are simply Coulombic energy and force, Fij = -Fji as symmetric forces,
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and Tij != -Tji since the torques do not act symmetrically. The
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shifted-force formula for the Lennard-Jones potential is reported in
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:ref:`(Stoddard) <Stoddard>`. The original (non-shifted) formulas for
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the electrostatic potentials, forces and torques can be found in
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:ref:`(Price) <Price2>`. The shifted-force electrostatic potentials have
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been obtained by applying equation 5.13 of :ref:`(Allen) <Allen2>`. The
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formulas for the corresponding forces and torques have been obtained by
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applying the 'chain rule' as in appendix C.3 of :ref:`(Allen) <Allen2>`.
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:ref:`(Price) <Price2>`. The shifted-force electrostatic potentials
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have been obtained by applying equation 5.13 of :ref:`(Allen)
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<Allen2>`. The formulas for the corresponding forces and torques have
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been obtained by applying the 'chain rule' as in appendix C.3 of
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:ref:`(Allen) <Allen2>`.
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If one cutoff is specified in the pair_style command, it is used for
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both the LJ and Coulombic (q,p) terms. If two cutoffs are specified,
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they are used as cutoffs for the LJ and Coulombic (q,p) terms
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respectively. This pair style also supports an optional *scale* keyword
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as part of a pair_coeff statement, where the interactions can be
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scaled according to this factor. This scale factor is also made available
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for use with fix adapt.
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respectively. This pair style also supports an optional *scale*
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keyword as part of a pair_coeff statement, where the interactions can
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be scaled according to this factor. This scale factor is also made
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available for use with fix adapt.
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Style *lj/cut/dipole/long* computes long-range point-dipole
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interactions as discussed in :ref:`(Toukmaji) <Toukmaji2>`. Dipole-dipole,
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dipole-charge, and charge-charge interactions are all supported, along
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with the standard 12/6 Lennard-Jones interactions, which are computed
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with a cutoff. A :doc:`kspace_style <kspace_style>` must be defined to
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use this pair style. Currently, only :doc:`kspace_style ewald/disp <kspace_style>` support long-range point-dipole
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interactions.
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Style *lj/cut/dipole/long* computes the short-range portion of
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point-dipole interactions as discussed in :ref:`(Toukmaji)
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<Toukmaji2>`. Dipole-dipole, dipole-charge, and charge-charge
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interactions are all supported, along with the standard 12/6
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Lennard-Jones interactions, which are computed with a cutoff. A
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:doc:`kspace_style <kspace_style>` must be defined to use this pair
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style. It can be one of these options, all of which compute the
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long-range portion of dipole-dipole interactions:
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Style *lj/long/dipole/long* also computes point-dipole interactions as
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discussed in :ref:`(Toukmaji) <Toukmaji2>`. Long-range dipole-dipole,
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dipole-charge, and charge-charge interactions are all supported, along
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with the standard 12/6 Lennard-Jones interactions. LJ interactions
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can be cutoff or long-ranged.
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* :doc:`kspace_style ewald/dipole <kspace_style>`
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* :doc:`kspace_style ewald/disp/dipole <kspace_style>`
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* :doc:`kspace_style pppm/dipole <kspace_style>`
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For style *lj/long/dipole/long*, if *flag_lj* is set to *long*, no
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cutoff is used on the LJ 1/r\^6 dispersion term. The long-range
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portion is calculated by using the :doc:`kspace_style ewald_disp <kspace_style>` command. The specified LJ cutoff then
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determines which portion of the LJ interactions are computed directly
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by the pair potential versus which part is computed in reciprocal
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space via the Kspace style. If *flag_lj* is set to *cut*, the LJ
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interactions are simply cutoff, as with :doc:`pair_style lj/cut <pair_lj>`. If *flag_lj* is set to *off*, LJ interactions
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are not computed at all.
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Style *lj/long/dipole/long* has options to compute the short-range
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portion of both 12/6 Lennard-Jones (LJ) and point-dipole interactions
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in a long-range context. The options are selected by the *flag_lj*
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and *flag_coul* setings. For *flag_coul* is set to *long*,
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point-dipole interactions are computed as as discussed in
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:ref:`(Toukmaji) <Toukmaji2>`. Dipole-dipole, dipole-charge, and
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charge-charge interactions are all supported. If *flag_coul* is set
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to *off*, no charge and dipole interactions are computed.
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If *flag_coul* is set to *long*, no cutoff is used on the Coulombic or
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dipole interactions. The long-range portion is calculated by using
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*ewald_disp* of the :doc:`kspace_style <kspace_style>` command. If
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*flag_coul* is set to *off*, Coulombic and dipole interactions are not
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computed at all.
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For LJ interactions, the *flag_lj* setting can be *long*, *cut*, or
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*off*. If *long* is used, the doc:`kspace_style ewald/disp/dipole
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<kspace_style>` command must be used. If *cut* is used, LJ
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interactions are only short-range and any of the 3 solvers listed
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above for style *lj/cut/dipole/long* can be used. If *off* is used,
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no LJ interactions are not computed. Any of the 3 solvers listed
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above can be used for Coulombic long-range interactions.
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Atoms with dipole moments should be integrated using the :doc:`fix nve/sphere update dipole <fix_nve_sphere>` or the :doc:`fix nvt/sphere update dipole <fix_nvt_sphere>` command to rotate the
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dipole moments. The *omega* option on the :doc:`fix langevin <fix_langevin>` command can be used to thermostat the
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rotational motion. The :doc:`compute temp/sphere <compute_temp_sphere>`
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command can be used to monitor the temperature, since it includes
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rotational degrees of freedom. The :doc:`atom_style hybrid dipole sphere <atom_style>` command should be used since
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it defines the point dipoles and their rotational state.
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The magnitude and orientation of the dipole moment for each particle
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can be defined by the :doc:`set <set>` command or in the "Atoms" section
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of the data file read in by the :doc:`read_data <read_data>` command.
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----------
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The following coefficients must be defined for each pair of atoms
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types via the :doc:`pair_coeff <pair_coeff>` command as in the examples
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@ -287,6 +281,40 @@ type pair.
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----------
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Note that for systems using these pair styles, typically particles
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should be able to exert torque on each other via their dipole moments
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so that the particle and its dipole moment can rotate. This requires
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they not be point particles, but finite-size spheres. Thus you should
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use a command like :doc:`atom_style hybrid sphere dipole <atom_style>`
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to use particles with both attributes.
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The magnitude and orientation of the dipole moment for each particle
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can be defined by the :doc:`set <set>` command or in the "Atoms"
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section of the data file read in by the :doc:`read_data <read_data>`
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command.
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Rotating finite-size particles have 6 degrees of freedom (DOFs),
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translation and rotational. You can use the :doc:`compute temp/sphere
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<compute_temp_sphere>` command to monitor a temperature which includes
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all these DOFs.
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Finite-size particles with dipole moments should be integrated using
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one of these options:
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* :doc:`fix nve/sphere update dipole <fix_nve_sphere>`
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* :doc:`fix nve/sphere update dipole <fix_nve_sphere>` plus :doc:`fix langevin omega yes <fix_langevin>`
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* :doc:`fix nvt/sphere update dipole <fix_nvt_sphere>`
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* :doc:`fix npt/sphere update dipole <fix_npt_sphere>`
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In all cases the "update dipole" setting insures the dipole moments
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are also rotated when the finite-size spheres rotate. The 2nd and 3rd
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bullets perform thermostatting; in the case of a Langevin thermostat
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the "omega yes" option also thermostats the rotational degrees of
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freedom (if desired). The 4th bullet performs thermostatting and
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barostatting.
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----------
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.. include:: accel_styles.rst
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----------
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