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Defining, Calculating, and Converging Observables of a Kinetic Transition Network.

Accepted version
Peer-reviewed

Type

Article

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Authors

Abstract

Kinetic transition networks (KTNs) 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 generally will 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 KTNs, deriving expressions for branching probabilities, transition rates, and waiting times. Using the concept of the quasi-stationary 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 KTN, 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.

Description

Keywords

34 Chemical Sciences, 3406 Physical Chemistry, 3407 Theoretical and Computational Chemistry

Journal Title

J Chem Theory Comput

Conference Name

Journal ISSN

1549-9618
1549-9626

Volume Title

16

Publisher

American Chemical Society (ACS)

Rights

All rights reserved
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epsrc