A nonequilibrium rate formula for collective motions of complex molecular systems

Tomohiro Yanao*, Wang Sang Koon, Jerrold E. Marsden

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)


We propose a compact reaction rate formula that accounts for a non-equilibrium distribution of residence times of complex molecules, based on a detailed study of the coarse-grained phase space of a reaction coordinate. We take the structural transition dynamics of a six-atom Morse cluster between two isomers as a prototype of multi-dimensional molecular reactions. Residence time distribution of one of the isomers shows an exponential decay, while that of the other isomer deviates largely from the exponential form and has multiple peaks. Our rate formula explains such equilibrium and non-equilibrium distributions of residence times in terms of the rates of diffusions of energy and the phase of the oscillations of the reaction coordinate. Rapid diffusions of energy and the phase generally give rise to the exponential decay of residence time distribution, while slow diffusions give rise to a non-exponential decay with multiple peaks. We finally make a conjecture about a general relationship between the rates of the diffusions and the symmetry of molecular mass distributions.

Original languageEnglish
Pages (from-to)1597-1600
Number of pages4
JournalAIP Conference Proceedings
Publication statusPublished - 2010
EventInternational Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010 - Rhodes, Greece
Duration: 2010 Sept 192010 Sept 25


  • cluster
  • diffusion
  • dimension reduction
  • hyperspherical coordinates
  • non-RRKM
  • reaction coordinate
  • reaction rate

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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