deletions | additions       diff --git a/section_Supporting_Information_subsection_Kinetic__.tex b/section_Supporting_Information_subsection_Kinetic__.tex  index 816f7b9..687c5cc 100644  --- a/section_Supporting_Information_subsection_Kinetic__.tex  +++ b/section_Supporting_Information_subsection_Kinetic__.tex 
...
\omega_i (\xi) = K/2 (\xi - \xi^{ref}_i)^2  \end{equation}  where $K$ is harmonic bias constant, $\xi$ is the reaction coordinate, and $\xi^{ref}_i$ is the reference point of each window $i$. For our model, the harmonic bias constant of 16.14 kcal mol^{-1} Angstrom^{-2} is sufficient to enhance the sampling. We sampled 100 windows, with window spacing of 0.38 Angstrom. For sufficient resolution and convergence, these parameters are chosen using the guideline given by \cite{Ka_stner_2006}, which is  \begin{equation}  \label{eqn:min-spacing}  \delta \xi^c < 3/ \sqrt(\beta K)  \end{equation}  where $\delta \xi^c$ is the minimum window spacing recommended, and $\beta = 1/k_B T$. Sufficient overlapping in the histograms of 100 windows are confirmed, this ensure that statistical errors are minimized from umbrella integration. Exhaustive description of the methods for umbrella sampling and umbrella integration is described in \cite{K_stner_2011,Ka_stner_2005}.  \subsection{Transition-State Theory}