deletions | additions       diff --git a/section_Supporting_Information_subsection_Kinetic__.tex b/section_Supporting_Information_subsection_Kinetic__.tex  index 41b87b7..527e443 100644  --- a/section_Supporting_Information_subsection_Kinetic__.tex  +++ b/section_Supporting_Information_subsection_Kinetic__.tex 
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\begin{equation}  \label{eqn:min-spacing}  \delta \Delta  \xi^c < 3/ \sqrt{\beta K} \end{equation}  where $\delta $\Delta  \xi^c$ 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}. The initial configuration is equilibrated for 20 ns using the Nose-Hoover isothermal-isobaric ensemble and canonical ensemble. Trajectory of each window converged after 12 ns sampling, with convergence determined by statistical tests described by \cite{Schiferl_1985}. Trajectories were pre-processed by the block-average method \cite{allen2008computer} to eliminate time correlations.