Scientific background

Understanding the dynamics of molecules at energies where chemical bonds break or are formed is not only of academic importance but basically it is the foundation of chemistry with all the consequences that implies for our continuously advancing technological world. The progress obtained in quantum chemistry, non-linear mechanics and in the correspondence of classical to quantum mechanics [1] in the last forty years has unveiled the complexity of the interactions among the nuclei in a molecule and their internal motions. The simple statistical theory named RRKM [2], which is based on the ergodic hypothesis, is inadequate to explain detailed experimental results now available from single molecule spectroscopy and molecular beams [3]. Numerous studies show that the polyatomic molecules seen as a set of non-linear coupled oscillators is not an ergodic system, but instead, they form a mixed phase space with regular and chaotic regions [4,5]. The motions in two or more degrees of freedom may come into resonances, thus being adiabatically separated from the other degrees of freedom. This leads to the localization of energy. Transitions from normal modes (extended motions) to local modes were first observed spectroscopically in molecules. From the non-linear mechanics point of view the transition from normal to local modes can be described as an elementary pitchfork bifurcation of those periodic orbits which correspond to normal modes with the increase of the energy of the molecule [6]. Another elementary bifurcation frequently observed in non-linear systems is the saddle-node. Its importance for the dynamics of the molecules was early pointed out [7]. Systematic studies mainly in triatomic molecules have shown that the route to a bond breaking or formation with the increase of energy is paved by a cascade of such bifurcations [4,5]. The appearance of saddle-node bifurcations demonstrate that some degrees of freedom come into a resonance with the simultaneous appearance of two or more new periodic orbits. Via saddle-node bifurcations the energy can flow into regions of phase space that normal mode type motions can not penetrate. These studies revealed that elementary chemical reactions such as isomerization and dissociation occur via saddle-node bifurcations [4,5]. The energy in the resonance zones dictated by the saddle-node bifurcations is mainly localized in the bond or angle which is about to break. Spectroscopic signatures of this type of bifurcations have recently been recorded. HCP was the first molecule for which characteristics of the high energy vibrational spectra could be explained by periodic orbits analysis and exact quantum mechanical calculations [4]. Acetylene is another example of a small polyatomic molecule where normal to local mode transitions in vibrational spectra are explained by combining quantum and classical mechanical calculations [8,9,10]. Independently, while the studies in localization of energy and bifurcations of motions were carried out in small polyatomic molecules, another research community has done important advances in studying localization and coherent phenomena in extended physical, chemical and biological systems. The key ingredients are the existence of an underlying spatial lattice and the nonlinearity of the equations of motion which describe the evolution of atoms. Spatially localized excitations are found to be generic to these systems, with the internal dynamics in the core of the excitation being periodic or nearly periodic in time. The core is typically consisting of a very limited number of atoms of the extended system. Theoretically, large systems are represented by models of infinite regular lattices of one, two and three dimensions with non-linear interactions among neighboring sites. Using simple interaction potentials numerical calculations, models and in a few cases rigorous mathematical theorems prove the existence of ``Intrinsic Localized Modes (ILM)'' or ``Discrete Breathers (DB)'' [11]. DB have been used to understand the molding of light in non-linear photonic crystals, localized excitations in superconducting Josephson junction arrays, many-phonon bound states in solids, complex dynamics of micromechanical cantilever systems and protein spectroscopy [12,13,14,15]. Thus, using atomistic models to study DB it is possible to bridge the gap between small and large space scales. Biological macromolecules such as DNA and proteins are complex systems in which large conformational changes and electron transfer are responsible for their macroscopic behaviour and structures. DNA transcription through bubble opening, protein folding and biological machines involve bond breaking/formation and reveal a high degree of selectivity and specificity in conformational changes. Spectroscopic techniques (vibrational relaxation spectroscopy, NMR, laser spectroscopy) have been applied to study these phenomena. DNA ``breathing'' has been known by biologists for a long time, and it is a highly localized, large amplitude distortion of the molecule, which might be well described by a localized mode [16]. Evidence for the existence of localized modes in model compounds having the same peptide bonds as proteins has been obtained by non-linear spectroscopy [17]. Simple models have been proposed but modeling these systems at the atomistic level remains a challenging task, which is important to demonstrate the validity of the results obtained in highly simplified non-linear lattice models. By joining the forces of the two communities, the small and large molecules, we expect to further advance the field of energy localization. The two groups share common theoretical and numerical techniques for modeling localization phenomena. This is particularly true when classical mechanics are applied. Small molecules are amenable to rigorous quantum mechanical studies, something which is not feasible for large molecules. On the other hand, the breather community has developed statistical mechanical methods to study complex systems. Currently, intense research is carried out on quantum non-linear localization, and the role of quantum diffusion of breathers due to tunneling.

Motivation and objectives

Both research groups are looking for localized coherent motions in non-linear excited systems. To some extent they share the same theoretical tools and numerical techniques and apply spectroscopy in their experimental search for localization phenomena. The breather community can offer methods and models to study large biological macromolecules whereas the small molecule community can provide detailed knowledge for a few degrees of freedom systems both in classical and in quantum mechanics. Since we study localized phenomena these few degrees of freedom models may serve as good approximations to breathers. The main objective of the proposed workshop will be to bring together the two research groups which up to now have been working practically independently. Emphasis will be given to applications in the field of chemical reactions, dynamics of biomolecules, and to the theoretical tools and methods of analyzing the underlying models both in the classical and quantum regime. The fact that two communities have been accumulating knowledge rather independently will guarantee a success in mutual exchange of ideas, methods and results. Both groups will benefit from each other's experience but most importantly the participation of spectroscopists will enable us to examine characteristics of the localized motions which can be traced spectroscopically. Now the study of localized phenomena in association to the non-linear mechanics is a matured field of research with several applications. The three days meeting we are planning to organize does not allow us to cover all areas of potential interest. Thus, one additional objective of this meeting will be the planning of a regular conference or a longer workshop. The possibility of preparing a new European proposal to give us a chance to pursue some collaboration will also be examined.


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{17} J. Edler and P. Hamm, J. Chem. Phys. 117, 2415 (2002).