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root/group/trunk/oopsePaper/DUFF.tex
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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