Gabern, Frederic and Koon, Wang S. and Marsden, Jerrold E. and Ross, Shane D. (2005) Theory and computation of non-RRKM lifetime distributions and rates in chemical systems with three or more degrees of freedom. Physica D, 211 (3-4). pp. 391-406. ISSN 0167-2789 http://resolver.caltech.edu/CaltechAUTHORS:20100809-101747013
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The computation, starting from basic principles, of chemical reaction rates in realistic systems (with three or more degrees of freedom) has been a longstanding goal of the chemistry community. Our current work, which merges tube dynamics with Monte Carlo methods provides some key theoretical and computational tools for achieving this goal. We use basic tools of dynamical systems theory, merging the ideas of Koon et al. [W.S. Koon, M.W. Lo, J.E. Marsden, S.D. Ross, Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics, Chaos 10 (2000) 427–469.] and De Leon et al. [N. De Leon, M.A. Mehta, R.Q. Topper, Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory, J. Chem. Phys. 94 (1991) 8310–8328.], particularly the use of invariant manifold tubes that mediate the reaction, into a tool for the computation of lifetime distributions and rates of chemical reactions and scattering phenomena, even in systems that exhibit non-statistical behavior. Previously, the main problem with the application of tube dynamics has been with the computation of volumes in phase spaces of high dimension. The present work provides a starting point for overcoming this hurdle with some new ideas and implements them numerically. Specifically, an algorithm that uses tube dynamics to provide the initial bounding box for a Monte Carlo volume determination is used. The combination of a fine scale method for determining the phase space structure (invariant manifold theory) with statistical methods for volume computations (Monte Carlo) is the main contribution of this paper. The methodology is applied here to a three degree of freedom model problem and may be useful for higher degree of freedom systems as well.
|Additional Information:||© 2005 Elsevier B.V. All rights reserved. Received 7 April 2005; received in revised form 14 September 2005; accepted 16 September 2005. Communicated by C.K.R.T. Jones. The authors thank Tomohiro Yanao for interesting discussions and comments.We thank Charlie Jaff´e and Turgay Uzer for originally suggesting the Rydberg atom as an interesting example.We also thank Michael Dellnitz, Oliver Junge, Katalin Grubbits, Kathrin Padberg, and Bianca Thiere for sharing their methods, which make use of set oriented methods applied to the Rydberg atom problem; happily their results, while quite different in methodology, agree with the results obtained here. This work was partly supported by the California Institute of Technology President’s Fund, NSF-ITR grant ACI-0204932 and by ICB, the Institute for Collaborative Biology, through ARO grant DAAD19-03-D- 0004. F.G. acknowledges the support of the Fulbright– GenCat postdoctoral program, the MCyT/FEDER Grant BFM2003-07521-C02-01 and the CIRIT grant 2001SGR–70. S.D.R. acknowledges the support of National Science Foundation postdoctoral fellowship grant NSF-DMS 0402842.|
|Subject Keywords:||Dynamical systems; Transport rates; Normal forms; Invariant manifolds; Transition state theory; Ionization; Atoms in crossed fields|
|Classification Code:||PACS: 45.10.-b; 45.20.Jj; 31.15.-p; 34.10.+x; 82.20.Db|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||09 Aug 2010 20:57|
|Last Modified:||26 Dec 2012 12:18|
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