From 3fa655e3e336e8904c6e43cda292bd94f9215ce0 Mon Sep 17 00:00:00 2001
From: David van der Spoel <spoel@xray.bmc.uu.se>
Date: Wed, 17 Aug 2016 09:05:15 +0200
Subject: [PATCH] Added documentation for shell potentials.

Added documentation for simple and anharmonic shell potentials.
Added two references.

Change-Id: Ica2b694b9b57bcf52bfe8434cfb3f8fe4dc7b9a2
---
 docs/manual/forcefield.tex | 38 +++++++++++++++++++++++++++++++++++++-
 docs/manual/monster.bib    | 21 +++++++++++++++++++++
 2 files changed, 58 insertions(+), 1 deletion(-)

diff --git a/docs/manual/forcefield.tex b/docs/manual/forcefield.tex
index c754382c77..59d8650e80 100644
--- a/docs/manual/forcefield.tex
+++ b/docs/manual/forcefield.tex
@@ -1653,7 +1653,43 @@ virtual sites. The energy of the shell particle is then minimized at
 each time step in order to remain on the Born-Oppenheimer surface.
 
 \subsection{Simple polarization}
-This is merely a harmonic potential with equilibrium distance 0.
+This is implemented as a harmonic potential with equilibrium distance
+0.
+The input given in the topology file is the polarizability $\alpha$ (in
+{\gromacs} units) as follows:
+\begin{verbatim}
+[ polarization ]
+; Atom i  j  type  alpha
+1         2  1     0.001
+\end{verbatim}
+in this case the polarizability volume is 0.001 nm$^3$ (or 1
+{\AA$^3$}). In order to compute the harmonic force constant $k_{cs}$
+(where $cs$ stands for core-shell), the
+following is used~\cite{Maaren2001a}:
+\begin{equation}
+k_{cs} ~=~ \frac{q_s^2}{\alpha}
+\end{equation}
+where $q_s$ is the charge on the shell particle.
+
+\subsection{Anharmonic polarization}
+For the development of the Drude force field by Roux and McKerell~\cite{Lopes2013a}
+it was found
+that some particles can overpolarize and this was fixed by introducing
+a higher order term in the polarization energy:
+\begin{eqnarray}
+V_{pol} ~=& \frac{k_{cs}}{2} r_{cs}^2 & r_{cs} \le \delta \\
+            =& \frac{k_{cs}}{2} r_{cs}^2 + k_{hyp} (r_{cs}-\delta)^4 & r_{cs} > \delta
+\end{eqnarray}
+where $\delta$ is a user-defined constant that is set to 0.02 nm for
+anions in the Drude force field~\cite{HYu2010}. Since this original introduction it
+has also been used in other atom types~\cite{Lopes2013a}.
+\begin{verbatim}
+[ polarization ]
+;Atom i j    type   alpha (nm^3)    delta  khyp
+1       2       2       0.001786     0.02  16.736e8
+\end{verbatim}
+The above force constant $k_{hyp}$ corresponds to 4$\cdot$10$^8$
+kcal/mol/nm$^4$, hence the strange number.
 
 \subsection{Water polarization}
 A special potential for water that allows anisotropic polarization of
diff --git a/docs/manual/monster.bib b/docs/manual/monster.bib
index b6d97cc0b7..cc94429cf0 100644
--- a/docs/manual/monster.bib
+++ b/docs/manual/monster.bib
@@ -6487,6 +6487,18 @@ pages = {2044--2053}
   pages =        "294--305",
 }
 
+@ARTICLE{HYu2010,
+  author = {Yu, Haibo and Whitfield, Troy W and Harder, Edward and Lamoureux,
+	Guillaume and Vorobyov, Igor and Anisimov, Victor M and {MacKerell,
+	Jr.}, Alexander D and Roux, Benoit},
+  title = {{Simulating Monovalent and Divalent Ions in Aqueous Solution Using
+	a Drude Polarizable Force Field}},
+  journal = BTjctc,
+  year = {2010},
+  volume = {6},
+  pages = {774--786},
+}
+
 @Article{Zettlmeissl83,
   author =       "Gerd Zettlmeissl and Rainer Rudolph and Rainer
                  Jaenicke",
@@ -8756,3 +8768,12 @@ doi = "http://dx.doi.org/10.1016/j.softx.2015.06.001"
 	volume = {31},
 	pages = {2169--2174}
 }
+
+@Article{Lopes2013a,
+  author =       {Lopes, Pedro E. M. and Huang, Jing and Shim, Jihyun and Luo, Yun and Li, Hui and Roux, Benoit and MacKerell, Alexander D., Jr.},
+  title =        {Polarizable Force Field for Peptides and Proteins Based on the Classical Drude Oscillator},
+  journal =      {J. Chem. Theory Comput},
+  year =         2013,
+  volume =    9,
+  pages =     {5430-5449}}
+
-- 
2.11.4.GIT