deletions | additions       diff --git a/Using_the_framework_of_transition__.tex b/Using_the_framework_of_transition__.tex  index 295a2c4..075d041 100644  --- a/Using_the_framework_of_transition__.tex  +++ b/Using_the_framework_of_transition__.tex 
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\end{equation}  where $\textbf{x}$ is the 3\textit{N}-dimensional configuration of the \textit{N}-particle system, $\beta = 1/k_B T$, $m$ is the effective mass, $V$ is the potential energies, $\Theta_A$ has a value of one if the system is in state $\textbf{A}$ and is zero otherwise, $\delta^{\dagger}_{AB}$ is the delta function defining the location of the dividing hypersurface and it is considered to reside within the domain of $\textbf{A}$, and the factor of $1/2$ limits the flux to trajectories that are exiting from $\textbf{A}$. We neglect the recrossings of the dividing surface once the trajectories exits from $\textbf{A}$.  For our model, the dividing hypersurface is at the energy barrier, state $\textbf{A}$ is the local minimum basin  on the right side of the energy barrier, state $\textbf{B}$ is the global energy  minimum on the left side of the energy barrier, $\textbf{x}$ is the reaction coordinate, $m$ is the mass of one Ag atom, and $V$ is the potential of mean force. The domain space of state $A$ is the region within one $RT$ fromlocal minimum on the right side of  the energy barrier. local basin.  We obtained calculated  the rate constant of atom flux towards Ag111 and Ag100 to be $25.5 ns^{-1}$ $25.5$ ns^{-1}  and $12.2 ns^{-1}$, respectively. The ratio of rate constant of atom flux towards \{111\} over \{100\} facets $\frac{k_{111}}{k_{100}}$ is calculated to be $2.10$. Using Fig. \ref{fig:kinetic-wulff}, our calculations indicate that cubes will be form from this relative flux of deposition. The atom flux calculated in this section is one order-of-magnitude larger than the atom flux calculated by atom deposition. This is likely to be a consequence from the assumption of unity transmission coefficient causing the over-estimation of the atom flux by the transition state theory. Studies have found that the transmission coefficient can be as low as 0.1 \cite{Pritchard_2005}, especially for our system where the energy barrier is only $2$ to $4 k_B T$. The accuracy of the relative flux $\frac{F_{111}}{F_{100}}$ is more important because it can be used to define the shape of the grown NCs.