Tamiki Komatsuzaki

Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University Nada, Kobe 657-8501 Japan

How the reacting system climbs through saddles from one basin to another or, in general, How it moves about on rugged multibasin energy landscapes is one of the most intriguing subjects not only in chemistry but also physics and biology over past several decade. By using Lie canonical perturbation technique to extract normal form in the region of first-rank saddles, we have revealed in intramolecular proton transfer in malonaldehyde [1-2] and Ar6 cluster isomerization [3-9] that the action along a reaction coordinate persists as an invariant in phase space while passing through the saddle even at energies so high that the other degrees of freedom are chaotic, and that this provides not only a no-return dividing hypersurface in multidimensional phase space but also a practical scheme to visualize the multidimensional no-return dividing hypersurface and a propensity rule for transitions of reacting systems crossing the barrier from one local potential minimum to an adjacent minimum. The future of these significant developments in chemical reaction theories should hold a great promise [10-14] to reveal the whole scenario of why and how the reacting systems react from a potential basin to one another and of how they move about with bringing dynamical memory on multibasin energy landscapes during the course of reactions. In my talk, I would like to give an overview of our researches and the future perspective and problems to be overcome and also present other relevant project in our laboratory on "coarse-grained regularity" for protein dynamics in terms of chaotic time series analysis combined with principal component analysis [15-16].

References

[1] T. Komatsuzaki and M. Nagaoka 'Study on "Regularity" of the Barrier Recrossing Motion', J. Chem. Phys. (1996) 105,10838
[2] T. Komatsuzaki and M. Nagaoka 'A Dividing Surface Free From a Barrier Recrossing Motion in Many-Body Systems' Chem. Phys. Lett., (1997)265,91
[3] T. Komatsuzaki and R.S. Berry 'Regularity in Chaotic Reaction Path I: Ar6' J. Chem. Phys. (1999) 110, 9160
[4] T. Komatsuzaki and R.S. Berry 'Regularity in Chaotic Reaction Path II: Ar6 -Energy Dependence and Visualization of the Reaction Bottleneck' Phys.Chem. Chem. Phys. (1999) 1, 1387
[5] T. Komatsuzaki and R.S. Berry 'Local Regularity and Non-recrossing Path in Transition States -A New Strategy in Chemical Reaction Theories' J. Mol. Struct(THEOCHEM). (2000) 506,55
[6] T. Komatsuzaki and R.S. Berry 'Dynamical Hierarchy in Transition States: Why and How Does a System Climb over the Mountain?' Proc. Natl. Acad. Sci. USA,(2001) 98,7666
[7] T. Komatsuzaki and R.S. Berry 'Regularity in Chaotic Reaction Path III:Ar6 -Local Invariances at the Reaction Bottleneck-' J. Chem. Phys.(2001) 130, 4105
[8] T. Komatsuzaki and R.S. Berry, 'Chemical Reaction Dynamics: Many-Body Chaos and Regularity' Adv. Chem. Phys. 123,79-152, ed. by I. Prigogine and S. A. Rice (2002)
[9] T. Komatsuzaki and R.S. Berry, 'A Dynamical Propensity Rule of Transitions in Chemical Reactions' J. Phys. Chem. A (2002) 106,10945
[10] A special volume `Geometrical Structures of Phase Space in Multi-Dimensional Chaos : Applications to Chemical Reaction Dynamics in Complex Systems’ Adv. Chem. Phys. Eds. by M. Toda, T. Komatsuzaki, T. Konishi, R.S. Berry and S. A. Rice in press (references therein)
[11] S. Wiggins, L. Wiesenfeld, C. Jaffe, and T. Uzer, `Impenetrable barriers in phase-space’ Phys. Rev. Lett. (2001) 86, 5478
[12] T. Uzer, C. Jaffe, J. Palacian, P. Yanguas, S. Wiggins `The geometry of reaction dynamics’ Nonlinearity (2002) 15, 957
[13] H. Waalkens, A. Burbanks and S. Wiggins, `Phase Space Conduits for Reaction in Multi-Dimensional Systems: HCN Isomerization in Three Dimensions’ in press.
[14] M. Toda `Dynamics of Chemical Reactions and Chaos’ Adv. Chem. Phys. 123, 153-198, ed. by I. Prigogine and S. A. Rice (2002)
[15] Y. Matsunaga, K.S. Kostov and T. Komatsuzaki, 'Multi-Basin Dynamics in Off-Lattice Minimalist Protein Landscapes' J. Phys. Chem. A (2002) 106,10898
[16] T. Komatsuzaki, K. Hoshino and Y. Matsunaga, 'Regularity in Chaotic Transitions on Multi-Basin Landscapes ' Adv. Chem. Phys. Eds. by M. Toda, T. Komatsuzaki, T. Konishi, R.S. Berry and S. A. Rice in press