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Analysis and interpretation of first passage time distributions featuring rare events.

Published version
Peer-reviewed

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Abstract

In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.

Description

Acknowledgements: We are very grateful to Prof. Jerelle Joseph for her assistance with the CD4 database. As mentioned in the text, we are very grateful to the referees for their suggestions, especially the potential for exploiting Krylov approaches in future work. EJW gratefully acknowledges support from the Engineering and Physical Sciences Research Council [grant numbers EP/R513180/1, EP/N509620/1]. DJW gratefully acknowledges financial support from the Engineering and Physical Sciences Research Council [grant number EP/N035003/1].

Keywords

34 Chemical Sciences, 3406 Physical Chemistry, Networking and Information Technology R&D (NITRD)

Journal Title

Phys Chem Chem Phys

Conference Name

Journal ISSN

1463-9076
1463-9084

Volume Title

Publisher

Royal Society of Chemistry (RSC)
Sponsorship
Engineering and Physical Sciences Research Council (EP/N509620/1)
Engineering and Physical Sciences Research Council (EP/N035003/1)