368 lines
16 KiB
ReStructuredText
368 lines
16 KiB
ReStructuredText
.. index:: pair_style lj/cut/dipole/cut
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.. index:: pair_style lj/cut/dipole/cut/gpu
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.. index:: pair_style lj/cut/dipole/cut/omp
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.. index:: pair_style lj/sf/dipole/sf
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.. index:: pair_style lj/sf/dipole/sf/gpu
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.. index:: pair_style lj/sf/dipole/sf/omp
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.. index:: pair_style lj/cut/dipole/long
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.. index:: pair_style lj/cut/dipole/long/gpu
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.. index:: pair_style lj/long/dipole/long
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pair_style lj/cut/dipole/cut command
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====================================
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Accelerator Variants: *lj/cut/dipole/cut/gpu*, *lj/cut/dipole/cut/omp*
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pair_style lj/sf/dipole/sf command
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==================================
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Accelerator Variants: *lj/sf/dipole/sf/gpu*, *lj/sf/dipole/sf/omp*
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pair_style lj/cut/dipole/long command
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=====================================
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Accelerator Variants: *lj/cut/dipole/long/gpu*
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pair_style lj/long/dipole/long command
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======================================
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Syntax
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""""""
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.. code-block:: LAMMPS
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pair_style lj/cut/dipole/cut cutoff (cutoff2)
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pair_style lj/sf/dipole/sf cutoff (cutoff2)
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pair_style lj/cut/dipole/long cutoff (cutoff2)
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pair_style lj/long/dipole/long flag_lj flag_coul cutoff (cutoff2)
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* cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)
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* cutoff2 = global cutoff for Coulombic and dipole (optional) (distance units)
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* flag_lj = *long* or *cut* or *off*
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.. parsed-literal::
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*long* = use long-range damping on dispersion 1/r\^6 term
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*cut* = use a cutoff on dispersion 1/r\^6 term
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*off* = omit disperion 1/r\^6 term entirely
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* flag_coul = *long* or *off*
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.. parsed-literal::
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*long* = use long-range damping on Coulombic 1/r and point-dipole terms
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*off* = omit Coulombic and point-dipole terms entirely
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Examples
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""""""""
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.. code-block:: LAMMPS
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pair_style lj/cut/dipole/cut 10.0
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pair_coeff * * 1.0 1.0
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pair_coeff 2 3 1.0 1.0 2.5 4.0
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pair_style lj/sf/dipole/sf 9.0
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pair_coeff * * 1.0 1.0
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pair_coeff 2 3 1.0 1.0 2.5 4.0 scale 0.5
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pair_coeff 2 3 1.0 1.0 2.5 4.0
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pair_style lj/cut/dipole/long 10.0
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pair_coeff * * 1.0 1.0
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pair_coeff 2 3 1.0 1.0 2.5 4.0
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pair_style lj/long/dipole/long long long 3.5 10.0
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pair_coeff * * 1.0 1.0
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pair_coeff 2 3 1.0 1.0 2.5 4.0
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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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.. math::
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E_{LJ} = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
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\left(\frac{\sigma}{r}\right)^6 \right] \\
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E_{qq} = & \frac{q_i q_j}{r} \\
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E_{qp} = & \frac{q}{r^3} (p \bullet \vec{r}) \\
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E_{pp} = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) -
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\frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r}) \\
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& \\
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F_{qq} = & \frac{q_i q_j}{r^3} \vec{r} \\
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F_{qp} = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5}
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(\vec{p} \bullet \vec{r}) \vec{r} \\
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F_{pp} = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} -
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\frac{15}{r^7} (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \bullet \vec{r}) \vec{r} +
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\frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} +
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(\vec{p_i} \bullet \vec{r}) \vec{p_j} \right] \\
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& \\
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T_{pq} = T_{ij} = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\
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T_{qp} = T_{ji} = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\
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T_{pp} = T_{ij} = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) +
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\frac{3}{r^5} (\vec{p_j} \bullet \vec{r})
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(\vec{p_i} \times \vec{r}) \\
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T_{pp} = T_{ji} = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) +
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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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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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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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styles.
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Style *lj/sf/dipole/sf* computes "shifted-force" interactions between
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pairs of particles that each have a charge and/or a point dipole
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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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.. math::
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E_{LJ} = & 4\epsilon \left\{ \left[ \left( \frac{\sigma}{r} \right)^{\!12} -
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\left( \frac{\sigma}{r} \right)^{\!6} \right] +
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\left[ 6\left( \frac{\sigma}{r_c} \right)^{\!12} -
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3\left(\frac{\sigma}{r_c}\right)^{\!6}\right]\left(\frac{r}{r_c}\right)^{\!2}
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- 7\left( \frac{\sigma}{r_c} \right)^{\!12} +
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4\left( \frac{\sigma}{r_c} \right)^{\!6}\right\} \\
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E_{qq} = & \frac{q_i q_j}{r}\left(1-\frac{r}{r_c}\right)^{\!2} \\
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E_{pq} = & E_{ji} = -\frac{q}{r^3} \left[ 1 -
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3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
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E_{qp} = & E_{ij} = \frac{q}{r^3} \left[ 1 -
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3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
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E_{pp} = & \left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right]\left[\frac{1}{r^3}
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(\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5}
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(\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right] \\
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& \\
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F_{LJ} = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{\!12} -
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24\epsilon \left(\frac{\sigma}{r}\right)^{\!6} \right]\frac{1}{r^2} -
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\left[48\epsilon \left(\frac{\sigma}{r_c}\right)^{\!12} - 24\epsilon
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\left(\frac{\sigma}{r_c}\right)^{\!6} \right]\frac{1}{r_c^2}\right\}\vec{r}\\
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F_{qq} = & \frac{q_i q_j}{r}\left(\frac{1}{r^2} -
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\frac{1}{r_c^2}\right)\vec{r} \\
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F_{pq} = & F_{ij } = -\frac{3q}{r^5} \left[ 1 -
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\left(\frac{r}{r_c}\right)^{\!2}\right](\vec{p}\bullet\vec{r})\vec{r} +
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\frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
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F_{qp} = & F_{ij} = \frac{3q}{r^5} \left[ 1 -
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\left(\frac{r}{r_c}\right)^{\!2}\right] (\vec{p}\bullet\vec{r})\vec{r} -
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\frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
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F_{pp} = &\frac{3}{r^5}\Bigg\{\left[1-\left(\frac{r}{r_c}\right)^{\!4}\right]
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\left[(\vec{p_i}\bullet\vec{p_j}) - \frac{3}{r^2} (\vec{p_i}\bullet\vec{r})
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(\vec{p_j} \bullet \vec{r})\right] \vec{r} + \\
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& \left[1 -
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4\left(\frac{r}{r_c}\right)^{\!3}+3\left(\frac{r}{r_c}\right)^{\!4}\right]
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\left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + (\vec{p_i} \bullet \vec{r})
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\vec{p_j} -\frac{2}{r^2} (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \bullet \vec{r})\vec{r}\right] \Bigg\}
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.. math::
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T_{pq} = T_{ij} = & \frac{q_j}{r^3} \left[ 1 -
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3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\
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T_{qp} = T_{ji} = & - \frac{q_i}{r^3} \left[ 1 -
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3\left(\frac{r}{r_c}\right)^{\!2} +
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2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\
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T_{pp} = T_{ij} = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\
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& \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r})
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(\vec{p_i} \times \vec{r}) \\
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T_{pp} = T_{ji} = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\
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& \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
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3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \times \vec{r})
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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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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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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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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/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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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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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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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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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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above, or in the data file or restart files read by the
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:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
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commands, or by mixing as described below:
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* :math:`\epsilon` (energy units)
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* :math:`\sigma` (distance units)
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* cutoff1 (distance units)
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* cutoff2 (distance units)
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The latter 2 coefficients are optional. If not specified, the global
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LJ and Coulombic cutoffs specified in the pair_style command are used.
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If only one cutoff is specified, it is used as the cutoff for both LJ
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and Coulombic interactions for this type pair. If both coefficients
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are specified, they are used as the LJ and Coulombic cutoffs for this
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type pair.
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----------
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.. include:: accel_styles.rst
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----------
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Mixing, shift, table, tail correction, restart, rRESPA info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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For atom type pairs I,J and I != J, the epsilon and sigma coefficients
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and cutoff distances for this pair style can be mixed. The default
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mix value is *geometric*\ . See the "pair_modify" command for details.
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For atom type pairs I,J and I != J, the A, sigma, d1, and d2
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coefficients and cutoff distance for this pair style can be mixed. A
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is an energy value mixed like a LJ epsilon. D1 and d2 are distance
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values and are mixed like sigma. The default mix value is
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*geometric*\ . See the "pair_modify" command for details.
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This pair style does not support the :doc:`pair_modify <pair_modify>`
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shift option for the energy of the Lennard-Jones portion of the pair
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interaction; such energy goes to zero at the cutoff by construction.
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The :doc:`pair_modify <pair_modify>` table option is not relevant
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for this pair style.
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This pair style does not support the :doc:`pair_modify <pair_modify>`
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tail option for adding long-range tail corrections to energy and
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pressure.
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This pair style writes its information to :doc:`binary restart files <restart>`, so pair_style and pair_coeff commands do not need
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to be specified in an input script that reads a restart file.
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This pair style can only be used via the *pair* keyword of the
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:doc:`run_style respa <run_style>` command. It does not support the
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*inner*\ , *middle*\ , *outer* keywords.
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Restrictions
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""""""""""""
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The *lj/cut/dipole/cut*\ , *lj/cut/dipole/long*\ , and
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*lj/long/dipole/long* styles are part of the DIPOLE package. They are
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only enabled if LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
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The *lj/sf/dipole/sf* style is part of the USER-MISC package. It is
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only enabled if LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
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Using dipole pair styles with *electron* :doc:`units <units>` is not
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currently supported.
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Related commands
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""""""""""""""""
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:doc:`pair_coeff <pair_coeff>`, :doc:`set <set>`, :doc:`read_data <read_data>`,
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:doc:`fix nve/sphere <fix_nve_sphere>`, :doc:`fix nvt/sphere <fix_nvt_sphere>`
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Default
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"""""""
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none
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----------
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.. _Allen2:
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**(Allen)** Allen and Tildesley, Computer Simulation of Liquids,
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Clarendon Press, Oxford, 1987.
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.. _Toukmaji2:
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**(Toukmaji)** Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
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.. _Stoddard:
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**(Stoddard)** Stoddard and Ford, Phys Rev A, 8, 1504 (1973).
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.. _Price2:
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**(Price)** Price, Stone and Alderton, Mol Phys, 52, 987 (1984).
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