deletions | additions       diff --git a/Using_the_framework_of_transition__.tex b/Using_the_framework_of_transition__.tex  index 1cb6008..a14ffe7 100644  --- a/Using_the_framework_of_transition__.tex  +++ b/Using_the_framework_of_transition__.tex 
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\label{eqn:tst}  k^{TST}_{A \rightarrow B}=\frac{1}{2}(\frac{2}{\pi \beta m})^{1/2} \frac{\int d\textbf{x} \Theta_A \delta^{\dagger}_{AB} \exp(-\beta V)}{\int d\textbf{x} \Theta_A \exp(-\beta V)},  \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 $\textbf{A}$. Recrossings Neglecting the recrossings  of the dividing surface once the trajectories exits from $\textbf{A}$ is the central approximation made in transition-state theory. For our simulation, the dividing hypersurface is the energy barrier, state $\textbf{A}$ is the local minimum on the right side of the energy barrier, state $\textbf{B}$ is the global 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 $RT$ from local minimum on the right side of the energy barrier. We obtain the rate constant of atom flux towards Ag111 and Ag100 to be $30.7 ns^{-1}$ and $12.4 ns^{-1}$, respectively.