| 6 |
|
|
| 7 |
|
The main energy functional set in OOPSE is DUFF (the Dipolar |
| 8 |
|
Unified-atom Force Field). DUFF is a collection of parameters taken |
| 9 |
< |
from Seipman \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
| 9 |
> |
from Seipmann \emph{et al.}\cite{Siepmann1998} and Ichiye \emph{et |
| 10 |
|
al.}\cite{liu96:new_model} The total energy of interaction is given by |
| 11 |
|
Eq.~\ref{eq:totalPotential}: |
| 12 |
+ |
\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 |
|
|
| 19 |
< |
\begin{multline}\label{eq:totalPotential} |
| 20 |
< |
V_{\text{lipid}} = |
| 15 |
< |
\sum_{i}V_{i}^{\text{internal}} |
| 16 |
< |
+ \sum_i \sum_{j>i} \sum_{\alpha_i} |
| 17 |
< |
\sum_{\beta_j}V_{\text{LJ}}(r_{\alpha_{i}\beta_{j}}) \\ |
| 18 |
< |
+\sum_i\sum_{j>i}V_{\text{dp}}(r_{1_i,1_j},\Omega_{1_i},\Omega_{1_j}) |
| 19 |
< |
\end{multline} |
| 19 |
> |
\subsection{Bonded Interactions} |
| 20 |
> |
\label{subSec:bondedInteractions} |
| 21 |
|
|
| 22 |
+ |
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 |
|
|
| 27 |
+ |
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 |
+ |
V_{\phi} = \sum ( k_1 \cos^3 \phi + k_2 \cos^2 \phi + k_3 \cos \phi + k_4) |
| 37 |
+ |
\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 |
+ |
|
