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\section{The DUFF Energy Function} |
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\label{sec:energyFunctionals} |
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\section{The DUFF Energy Functionals} |
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\label{sec:energyFunctionals} |
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The main energy functional set in OOPSE is DUFF (the Dipolar |
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The main energy function in OOPSE is DUFF (the Dipolar |
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Unified-atom Force Field). DUFF is a collection of parameters taken |
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from Seipman \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
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from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
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al.}\cite{liu96:new_model} The total energy of interaction is given by |
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Eq.~\ref{eq:totalPotential}: |
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\begin{equation} |
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V_{\text{Total}} = |
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\overbrace{V_{\theta} + V_{\phi}}^{\text{bonded}} + |
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\underbrace{V_{\text{LJ}} + V_{\text{Dp}} + % |
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V_{\text{SSD}}}_{\text{non-bonded}} \label{eq:totalPotential} |
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\end{equation} |
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\begin{multline}\label{eq:totalPotential} |
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V_{\text{lipid}} = |
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\sum_{i}V_{i}^{\text{internal}} |
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+ \sum_i \sum_{j>i} \sum_{\alpha_i} |
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\sum_{\beta_j}V_{\text{LJ}}(r_{\alpha_{i}\beta_{j}}) \\ |
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+\sum_i\sum_{j>i}V_{\text{dp}}(r_{1_i,1_j},\Omega_{1_i},\Omega_{1_j}) |
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\end{multline} |
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\subsection{Bonded Interactions} |
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\label{subSec:bondedInteractions} |
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The bonded interactions in the DUFF functional set are limited to the |
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bend potential and the torsional potential. Bond potentials are not |
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calculated, instead all bond lengths are fixed to allow for large time |
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steps to be taken between force evaluations. |
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The bend functional is of the form: |
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\begin{equation} |
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V_{\theta} = \sum k_{\theta}( \theta - \theta_0 )^2 \label{eq:bendPot} |
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\end{equation} |
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$k_{\theta}$, the force constant, and $\theta_0$, the equilibrium bend |
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angle, were taken from the TraPPE forcefield of Siepmann. |
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The torsion functional has the form: |
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\begin{equation} |
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V_{\phi} = \sum ( k_3 \cos^3 \phi + k_2 \cos^2 \phi + k_1 \cos \phi + k_0) |
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\label{eq:torsionPot} |
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\end{equation} |
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Here, the authors decided to use a potential in terms of a power |
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expansion in $\cos \phi$ rather than the typical expansion in |
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$\phi$. This prevents the need for repeated trigonemtric |
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evaluations. Again, all $k_n$ constants were based on those in TraPPE. |
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\subsection{Non-Bonded Interactions} |
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\label{subSec:nonBondedInteractions} |
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\begin{equation} |
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V_{\text{LJ}} = \text{internal + external} |
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\end{equation} |
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