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53
doc/Eqs/pair_dipole_sf.tex Normal file
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@ -0,0 +1,53 @@
\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
E_{LJ} & = & 4\epsilon \left\{\left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^6 \right]
+ \left[ 6\left( \frac{\sigma}{r_c} \right)^{12} - 3\left( \frac{\sigma}{r_c} \right)^6 \right] \left(\frac{r}{r_c}\right)^2
-7\left( \frac{\sigma}{r_c} \right)^{12} +4\left( \frac{\sigma}{r_c} \right)^6\right\}\\
E_{qq} & = & \frac{q_i q_j}{r}\left(1-\frac{r}{r_c}\right)^2 \\
E_{pq} & = & E_{ji} = -\frac{q}{r^3} \left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right](\vec{p} \bullet \vec{r})
\\
E_{qp} & = & E_{ij} = \frac{q}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] (\vec{p} \bullet \vec{r})
\\
E_{pp} & = & \left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right]\left[\frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right]
\end{eqnarray*}
\begin{eqnarray*}
F_{LJ} & = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{12} -
24\epsilon \left(\frac{\sigma}{r}\right)^6 \right]\frac{1}{r^2} -
\left[48\epsilon \left(\frac{\sigma}{r_c}\right)^{12} -
24\epsilon \left(\frac{\sigma}{r_c}\right)^6 \right]\frac{1}{r_c^2}
\right\}\vec{r}\\
F_{qq} & = & \frac{q_i q_j}{r}\left(\frac{1}{r^2}-\frac{1}{r_c^2}\right)
\vec{r} \\
F_{pq} &=& F_{ij } = -\frac{3q}{r^5}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^2\right] (\vec{p} \bullet \vec{r}) \vec{r}+\frac{q}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] \vec{p} \\
F_{qp} &=& F_{ij} = \frac{3q}{r^5}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^2\right] (\vec{p} \bullet \vec{r}) \vec{r}-\frac{q}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] \vec{p} \\
F_{pp} & = & \frac{3}{r^5} \left\{\left[1-\left(\frac{r}{r_c}\right)^4\right]
\left[(\vec{p_i} \bullet \vec{p_j}) -
\frac{3}{r^2} (\vec{p_i} \bullet \vec{r})
(\vec{p_j} \bullet \vec{r})\right]
\vec{r} \right\\&&
+ \left\left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right]
\left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} +
(\vec{p_i} \bullet \vec{r}) \vec{p_j} -\frac{2}{r^2}
(\vec{p_i} \bullet \vec{r})
(\vec{p_j} \bullet \vec{r})\vec{r}\right]
\right\}\\
\end{eqnarray*}
\begin{eqnarray*}
T_{pq} = T_{ij} & = & \frac{q_j}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] (\vec{p_i} \times \vec{r}) \\
T_{qp} = T_{ji} & = & - \frac{q_i}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] (\vec{p_j} \times \vec{r}) \\
T_{pp} = T_{ij} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right] (\vec{p_i} \times \vec{p_j}) +
\frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right] (\vec{p_j} \bullet \vec{r})
(\vec{p_i} \times \vec{r}) \\
T_{pp} = T_{ji} & = & -\frac{1}{r^3} \left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right](\vec{p_j} \times \vec{p_i}) +
\frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right] (\vec{p_i} \bullet \vec{r})
(\vec{p_j} \times \vec{r}) \\
\end{eqnarray*}
\end{document}

4
doc/Section_commands.html
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@ -432,8 +432,8 @@ potentials. Click on the style itself for a full description:
</P>
<DIV ALIGN=center><TABLE BORDER=1 >
<TR ALIGN="center"><TD ><A HREF = "pair_awpmd.html">awpmd/cut</A></TD><TD ><A HREF = "pair_buck_coul.html">buck/coul</A></TD><TD ><A HREF = "pair_cmm.html">cg/cmm</A></TD><TD ><A HREF = "pair_cmm.html">cg/cmm/coul/cut</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_cmm.html">cg/cmm/coul/long</A></TD><TD ><A HREF = "pair_eam.html">eam/cd</A></TD><TD ><A HREF = "pair_eff.html">eff/cut</A></TD><TD ><A HREF = "pair_lj_coul.html">lj/coul</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_reax_c.html">reax/c</A>
<TR ALIGN="center"><TD ><A HREF = "pair_cmm.html">cg/cmm/coul/long</A></TD><TD ><A HREF = "pair_dipole.html">dipole/sf</A></TD><TD ><A HREF = "pair_eam.html">eam/cd</A></TD><TD ><A HREF = "pair_eff.html">eff/cut</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_lj_coul.html">lj/coul</A></TD><TD ><A HREF = "pair_reax_c.html">reax/c</A>
</TD></TR></TABLE></DIV>
<P>These are accelerated pair styles, which can be used if LAMMPS is

1
doc/Section_commands.txt
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@ -666,6 +666,7 @@ These are pair styles contributed by users, which can be used if
"cg/cmm"_pair_cmm.html,
"cg/cmm/coul/cut"_pair_cmm.html,
"cg/cmm/coul/long"_pair_cmm.html,
"dipole/sf"_pair_dipole.html,
"eam/cd"_pair_eam.html,
"eff/cut"_pair_eff.html,
"lj/coul"_pair_lj_coul.html,

58
doc/pair_dipole.html
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@ -11,10 +11,14 @@
<H3>pair_style dipole/cut command
</H3>
<H3>pair_style dipole/sf command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style dipole/cut cutoff (cutoff2)
</PRE>
<PRE>pair_style dipole/sf cutoff (cutoff2)
</PRE>
<UL><LI>cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)
<LI>cutoff2 = global cutoff for Coulombic (optional) (distance units)
</UL>
@ -24,6 +28,10 @@
pair_coeff * * 1.0 1.0
pair_coeff 2 3 1.0 1.0 2.5 4.0
</PRE>
<PRE>pair_style dipole/sf 9.0
pair_coeff * * 1.0 1.0
pair_coeff 2 3 1.0 1.0 2.5 4.0
</PRE>
<P><B>Description:</B>
</P>
<P>Style <I>dipole/cut</I> computes interactions between pairs of particles
@ -43,6 +51,34 @@ and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
torques do not act symmetrically. These formulas are discussed in
<A HREF = "#Allen">(Allen)</A> and in <A HREF = "#Toukmaji">(Toukmaji)</A>.
</P>
<P>Style <I>dipole/sf</I> computes "shifted-force" interactions between pairs
of particles that each have a charge and/or a point dipole moment. In
general, a shifted-force potential is a (sligthly) modified potential
containing extra terms that make both the energy and its derivative go
to zero at the cutoff distance; this removes (cutoff-related) problems
in energy conservation and any numerical instability in the equations
of motion <A HREF = "#Allen">(Allen)</A>. Shifted-force interactions for the
Lennard-Jones (E_LJ), charge-charge (Eqq), charge-dipole (Eqp),
dipole-charge (Epq) and dipole-dipole (Epp) potentials are computed by
these formulas for the energy (E), force (F), and torque (T) between
particles I and J:
</P>
<CENTER><IMG SRC = "Eqs/pair_dipole_sf.jpg">
</CENTER>
<P>where qi and qj are the charges on the two particles, pi and pj are
the dipole moment vectors of the two particles, r is their separation
distance, and the vector r = Ri - Rj is the separation vector between
the two particles. Note that Eqq and Fqq are simply Coulombic energy
and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
torques do not act symmetrically. The shifted-force formula for the
Lennard-Jones potential is reported in <A HREF = "#Stoddard">(Stoddard)</A>. The
original (unshifted) formulas for the electrostatic potentials, forces
and torques can be found in <A HREF = "#Price">(Price)</A>. The shifted-force
electrostatic potentials have been obtained by applying equation 5.13
of <A HREF = "#Allen">(Allen)</A>. The formulas for the corresponding forces and
torques have been obtained by applying the 'chain rule' as in appendix
C.3 of <A HREF = "#Allen">(Allen)</A>.
</P>
<P>If one cutoff is specified in the pair_style command, it is used for
both the LJ and Coulombic (q,p) terms. If two cutoffs are specified,
they are used as cutoffs for the LJ and Coulombic (q,p) terms
@ -93,9 +129,9 @@ is an energy value mixed like a LJ epsilon. D1 and d2 are distance
values and are mixed like sigma. The default mix value is
<I>geometric</I>. See the "pair_modify" command for details.
</P>
<P>This pair style supports the <A HREF = "pair_modify.html">pair_modify</A> shift
option for the energy of the Lennard-Jones portion of the pair
interaction.
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
shift option for the energy of the Lennard-Jones portion of the pair
interaction; such energy goes to zero at the cutoff by construction.
</P>
<P>The <A HREF = "pair_modify.html">pair_modify</A> table option is not relevant
for this pair style.
@ -114,8 +150,12 @@ to be specified in an input script that reads a restart file.
</P>
<P><B>Restrictions:</B>
</P>
<P>This style is part of the "dipole" package. It is only enabled if
LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
<P>The <I>dipole/cut</I> style is part of the "dipole" package. It is only
enabled if LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
LAMMPS</A> section for more info.
</P>
<P>The <I>dipole/sf</I> style is part of the "user-misc" package. It is only
enabled if LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
LAMMPS</A> section for more info.
</P>
<P><B>Related commands:</B>
@ -136,4 +176,12 @@ Clarendon Press, Oxford, 1987.
<P><B>(Toukmaji)</B> Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
10913 (2000).
</P>
<A NAME = "Stoddard"></A>
<P><B>(Stoddard)</B> Stoddard and Ford, Phys Rev A, 8, 1504 (1973).
</P>
<A NAME = "Price"></A>
<P><B>(Price)</B> Price, Stone and Alderton, Mol Phys, 52, 987 (1984).
</P>
</HTML>

54
doc/pair_dipole.txt
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@ -7,10 +7,12 @@
:line
pair_style dipole/cut command :h3
pair_style dipole/sf command :h3
[Syntax:]
pair_style dipole/cut cutoff (cutoff2) :pre
pair_style dipole/sf cutoff (cutoff2) :pre
cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)
cutoff2 = global cutoff for Coulombic (optional) (distance units) :ul
@ -21,6 +23,10 @@ pair_style dipole/cut 10.0
pair_coeff * * 1.0 1.0
pair_coeff 2 3 1.0 1.0 2.5 4.0 :pre
pair_style dipole/sf 9.0
pair_coeff * * 1.0 1.0
pair_coeff 2 3 1.0 1.0 2.5 4.0 :pre
[Description:]
Style {dipole/cut} computes interactions between pairs of particles
@ -40,6 +46,34 @@ and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
torques do not act symmetrically. These formulas are discussed in
"(Allen)"_#Allen and in "(Toukmaji)"_#Toukmaji.
Style {dipole/sf} computes "shifted-force" interactions between pairs
of particles that each have a charge and/or a point dipole moment. In
general, a shifted-force potential is a (sligthly) modified potential
containing extra terms that make both the energy and its derivative go
to zero at the cutoff distance; this removes (cutoff-related) problems
in energy conservation and any numerical instability in the equations
of motion "(Allen)"_#Allen. Shifted-force interactions for the
Lennard-Jones (E_LJ), charge-charge (Eqq), charge-dipole (Eqp),
dipole-charge (Epq) and dipole-dipole (Epp) potentials are computed by
these formulas for the energy (E), force (F), and torque (T) between
particles I and J:
:c,image(Eqs/pair_dipole_sf.jpg)
where qi and qj are the charges on the two particles, pi and pj are
the dipole moment vectors of the two particles, r is their separation
distance, and the vector r = Ri - Rj is the separation vector between
the two particles. Note that Eqq and Fqq are simply Coulombic energy
and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
torques do not act symmetrically. The shifted-force formula for the
Lennard-Jones potential is reported in "(Stoddard)"_#Stoddard. The
original (unshifted) formulas for the electrostatic potentials, forces
and torques can be found in "(Price)"_#Price. The shifted-force
electrostatic potentials have been obtained by applying equation 5.13
of "(Allen)"_#Allen. The formulas for the corresponding forces and
torques have been obtained by applying the 'chain rule' as in appendix
C.3 of "(Allen)"_#Allen.
If one cutoff is specified in the pair_style command, it is used for
both the LJ and Coulombic (q,p) terms. If two cutoffs are specified,
they are used as cutoffs for the LJ and Coulombic (q,p) terms
@ -90,9 +124,9 @@ is an energy value mixed like a LJ epsilon. D1 and d2 are distance
values and are mixed like sigma. The default mix value is
{geometric}. See the "pair_modify" command for details.
This pair style supports the "pair_modify"_pair_modify.html shift
option for the energy of the Lennard-Jones portion of the pair
interaction.
This pair style does not support the "pair_modify"_pair_modify.html
shift option for the energy of the Lennard-Jones portion of the pair
interaction; such energy goes to zero at the cutoff by construction.
The "pair_modify"_pair_modify.html table option is not relevant
for this pair style.
@ -111,8 +145,12 @@ This pair style can only be used via the {pair} keyword of the
[Restrictions:]
This style is part of the "dipole" package. It is only enabled if
LAMMPS was built with that package. See the "Making
The {dipole/cut} style is part of the "dipole" package. It is only
enabled if LAMMPS was built with that package. See the "Making
LAMMPS"_Section_start.html#2_3 section for more info.
The {dipole/sf} style is part of the "user-misc" package. It is only
enabled if LAMMPS was built with that package. See the "Making
LAMMPS"_Section_start.html#2_3 section for more info.
[Related commands:]
@ -130,3 +168,9 @@ Clarendon Press, Oxford, 1987.
:link(Toukmaji)
[(Toukmaji)] Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
10913 (2000).
:link(Stoddard)
[(Stoddard)] Stoddard and Ford, Phys Rev A, 8, 1504 (1973).
:link(Price)
[(Price)] Price, Stone and Alderton, Mol Phys, 52, 987 (1984).