git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@6639 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/pair_dipole_sf.tex

@@ -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}
+
+

doc/Section_commands.html

@@ -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_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_reax_c.html">reax/c</A> 
+<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

doc/Section_commands.txt

@@ -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,

doc/pair_dipole.html

@@ -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
+<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A> 
-option for the energy of the Lennard-Jones portion of the pair
+shift option for the energy of the Lennard-Jones portion of the pair
-interaction.
+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
+<P>The <I>dipole/cut</I> style is part of the "dipole" package.  It is only
-LAMMPS was built with that package.  See the <A HREF = "Section_start.html#2_3">Making
+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>

doc/pair_dipole.txt

@@ -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
+This pair style does not support the "pair_modify"_pair_modify.html 
-option for the energy of the Lennard-Jones portion of the pair
+shift option for the energy of the Lennard-Jones portion of the pair
-interaction.
+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
+The {dipole/cut} style is part of the "dipole" package.  It is only
-LAMMPS was built with that package.  See the "Making
+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).