trunk/oopsePaper/DUFF.tex


\section{The DUFF Energy Function}
\label{sec:energyFunctionals}


The main energy function in OOPSE is DUFF (the Dipolar
Unified-atom Force Field). DUFF is a collection of parameters taken
from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et
al.}\cite{liu96:new_model} The total energy of interaction is given by
Eq.~\ref{eq:totalPotential}:
\begin{equation}
V_{\text{Total}} =
        \overbrace{V_{\theta} + V_{\phi}}^{\text{bonded}} +
        \underbrace{V_{\text{LJ}} + V_{\text{Dp}} + %
        V_{\text{SSD}}}_{\text{non-bonded}} \label{eq:totalPotential}
\end{equation}

\subsection{Bonded Interactions}
\label{subSec:bondedInteractions}

The bonded interactions in the DUFF functional set are limited to the
bend potential and the torsional potential. Bond potentials are not
calculated, instead all bond lengths are fixed to allow for large time
steps to be taken between force evaluations.

The bend functional is of the form:
\begin{equation}
V_{\theta} = \sum k_{\theta}( \theta - \theta_0 )^2 \label{eq:bendPot}
\end{equation}
$k_{\theta}$, the force constant, and $\theta_0$, the equilibrium bend
angle, were taken from the TraPPE forcefield of Siepmann.

The torsion functional has the form:
\begin{equation}
V_{\phi} =  \sum ( k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0)
\label{eq:torsionPot}
\end{equation}
Here, the authors decided to use a potential in terms of a power
expansion in $\cos \phi$ rather than the typical expansion in
$\phi$. This prevents the need for repeated trigonemtric
evaluations. Again, all $k_n$ constants were based on those in TraPPE.

\subsection{Non-Bonded Interactions}
\label{subSec:nonBondedInteractions}

\begin{equation}
V_{\text{LJ}} = \text{internal + external}
\end{equation}


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#	User	Rev	Content
1	mmeineke	664
2	mmeineke	709	\section{The DUFF Energy Function}
3	mmeineke	666	\label{sec:energyFunctionals}
4	mmeineke	664
5	mmeineke	710
6
7	mmeineke	709	The main energy function in OOPSE is DUFF (the Dipolar
8	mmeineke	664	Unified-atom Force Field). DUFF is a collection of parameters taken
9	mmeineke	698	from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et
10	mmeineke	664	al.}\cite{liu96:new_model} The total energy of interaction is given by
11	mmeineke	666	Eq.~\ref{eq:totalPotential}:
12	mmeineke	698	\begin{equation}
13			V_{\text{Total}} =
14			\overbrace{V_{\theta} + V_{\phi}}^{\text{bonded}} +
15			\underbrace{V_{\text{LJ}} + V_{\text{Dp}} + %
16			V_{\text{SSD}}}_{\text{non-bonded}} \label{eq:totalPotential}
17			\end{equation}
18	mmeineke	666
19	mmeineke	698	\subsection{Bonded Interactions}
20			\label{subSec:bondedInteractions}
21	mmeineke	664
22	mmeineke	698	The bonded interactions in the DUFF functional set are limited to the
23			bend potential and the torsional potential. Bond potentials are not
24			calculated, instead all bond lengths are fixed to allow for large time
25			steps to be taken between force evaluations.
26	mmeineke	666
27	mmeineke	698	The bend functional is of the form:
28			\begin{equation}
29			V_{\theta} = \sum k_{\theta}( \theta - \theta_0 )^2 \label{eq:bendPot}
30			\end{equation}
31			$k_{\theta}$, the force constant, and $\theta_0$, the equilibrium bend
32			angle, were taken from the TraPPE forcefield of Siepmann.
33
34			The torsion functional has the form:
35			\begin{equation}
36	mmeineke	709	V_{\phi} = \sum ( k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0)
37	mmeineke	698	\label{eq:torsionPot}
38			\end{equation}
39			Here, the authors decided to use a potential in terms of a power
40			expansion in $\cos \phi$ rather than the typical expansion in
41			$\phi$. This prevents the need for repeated trigonemtric
42			evaluations. Again, all $k_n$ constants were based on those in TraPPE.
43
44			\subsection{Non-Bonded Interactions}
45			\label{subSec:nonBondedInteractions}
46
47			\begin{equation}
48			V_{\text{LJ}} = \text{internal + external}
49			\end{equation}
50
51