LAUSR

Kinetic transition networks of local minima and transition states are able to capture the dynamics of numerous systems in chemistry, biology and materials science. However, extracting observables is numerically challenging for large networks and will in general be sensitive to additional computational discovery. To have any measure of convergence for observables, these sensitivities must be regularly calculated. We present a matrix formulation of the discrete path sampling framework for kinetic transition networks, deriving expressions for branching probabilities, transition rates, and waiting times. Using the concept of the quasistationary distribution a clear hierarchy of expressions for network observables is established, from exact results to steady state approximations. We use these results in combination with the graph transformation method to derive the sensitivity with respect to perturbations of the known kinetic transition network, giving explicit terms for the pairwise sensitivity, and discussing the pathwise sensitivity. These results provide guidelines for converging the network with respect to additional sampling, focusing on the estimates obtained for the overall rate coefficients between product and reactant states. We demonstrate this procedure for transitions in the double-funnel landscape of the 38 atom Lennard-Jones cluster.