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
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",
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}}
+