Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session T38: Focus Session: The Transition State in Physics, Chemistry, and Astrophysics I |
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Sponsoring Units: DCP Chair: Greg Ezra, Cornell University Room: 410 |
Wednesday, March 18, 2009 2:30PM - 3:06PM |
T38.00001: Transition State Theory for Higher-Rank Saddles Invited Speaker: Recent developments in transition state theory have lead to a geometric characterization of molecular reactions in phase space. Central to this new characterization is the existence of codimension-one surfaces in the energy shell; these invariant surfaces guide reacting trajectories through sections of no return, the transition states. The existence of codimension-one invariant surfaces has only been shown in the vicinity of rank-one saddles, i.e., near fixed points with one stable and one unstable direction in addition to neutrally stable directions. For higher-rank saddles, the current framework of geometric transition state theory has remained inapplicable. Here we describe a generalization of the theory to saddles of arbitrary rank. As an application, we describe the nonsequential ionization of helium atoms, a problem with a rank-two saddle. [Preview Abstract] |
Wednesday, March 18, 2009 3:06PM - 3:42PM |
T38.00002: Exploring Topographies and Dynamics on Many-Dimensional Landscapes Invited Speaker: A major challenge to understanding and using kinetics is finding the relationships between the topography of the many-dimensional potential energy landscape (or landscapes, for systems with multiple accessible electronic states) and the way that topography, local and large-scale, determines how systems change their structures, relax and anneal. One major difficulty is simply the complexity of the landscape; one is forced to work with small statistical samples of the surface; how should these samples best be chosen? What characteristics of the topography provide the most important information? Another: how does the nature of the interparticle forces determine the topography and hence the character of motion on the surface? And what are the most useful diagnostic tools to tell us about that behavior? We shall address these questions, more in terms of progress toward, rather than providing definitive answers. [Preview Abstract] |
Wednesday, March 18, 2009 3:42PM - 4:18PM |
T38.00003: Transition State Theory: The Phase Space Perspective Invited Speaker: Transition State Theory (TST), which is at the basis of chemical reactivity calculations, assumes that once reactants pass through the Transition State, they cannot return. This ``no-recrossing'' rule serves to define the TS and is a necessary assumption in TST. Conventional transition states always lead to overestimates of the reaction rate because each intersection of the trajectory with the TS counts as a reactive event. Enforcing this no-recrossing condition beyond two degrees of freedom has been the major obstacle to applying TST in multidimensional systems. We will explain the solution of this problem based on dynamical systems theory. [Preview Abstract] |
Wednesday, March 18, 2009 4:18PM - 4:30PM |
T38.00004: Phase Space Transition States for Deterministic Thermostats Gregory Ezra, Stephen Wiggins We describe the relation between the phase space structure of Hamiltonian and non-Hamiltonian deterministic thermostats. We show that phase space structures governing reaction dynamics in Hamiltonian systems, such as the transition state, map to the same type of phase space structures for the non-Hamiltonian isokinetic equations of motion for the thermostatted Hamiltonian. Our results establish a general theoretical framework for analyzing thermostat dynamics using concepts and methods developed in reaction rate theory. Numerical results are presented for the isokinetic thermostat. [Preview Abstract] |
Wednesday, March 18, 2009 4:30PM - 4:42PM |
T38.00005: Using invariant manifolds to classify chaotic transport pathways in mixed phase space Kevin Mitchell We describe how the topological structure of stable and unstable manifolds embedded within a chaotic phase space can be used to extract a symbolic classification of chaotic transport and escape pathways. We pay particular attention to phase spaces that contain a mixture of both chaos and regularity. For such systems, the dynamics in the vicinity of ``stable islands'' is known to be particularly troublesome to analyze. We describe a technique that utilizes the structure of invariant manifolds in the vicinity of such stable islands to extract a symbolic model for the islands' influence on the transport process. Though our analysis focuses on Hamiltonian systems of two degrees-of-freedom, we also discuss the extension of our technique to higher dimensional phase spaces. [Preview Abstract] |
Wednesday, March 18, 2009 4:42PM - 4:54PM |
T38.00006: Transition State Theory: Variational Formulation, Dynamical Corrections, and Error Estimates Eric Vanden-Eijnden Transition state theory (TST) is discussed from an original viewpoint: it is shown how to compute exactly the mean frequency of transition between two predefined sets which either partition phase space (as in TST) or are taken to be well separate metastable sets corresponding to long-lived conformation states (as necessary to obtain the actual transition rate constants between these states). Exact and approximate criterions for the optimal TST dividing surface with minimum recrossing rate are derived. Some issues about the definition and meaning of the free energy in the context of TST are also discussed. Finally precise error estimates for the numerical procedure to evaluate the transmission coefficient~$\kappa_S$ of the TST dividing surface are given, and it shown that the relative error on $\kappa_S$ scales as $1/\sqrt{\kappa_S}$ when $\kappa_S$ is small. This implies that dynamical corrections to the TST rate constant can be computed efficiently if and only if the TST dividing surface has a transmission coefficient~$\kappa_S$ which is not too small. In particular the TST dividing surface must be optimized upon (for otherwise $\kappa_S$ is generally very small), but this may not be sufficient to make the procedure numerically efficient (because the optimal dividing surface has maximum $\kappa_S$, but this coefficient may still be very small). [Preview Abstract] |
Wednesday, March 18, 2009 4:54PM - 5:06PM |
T38.00007: The dynamics of a floppy molecule: a case study Xiaojian Mao Urea is a simple but interesting molecule. In the solid state it is known to be planar while in gas phase it is non-planar. This difference is attributed to the hydrogen bonding that is present in the solid state. Ab initio quantum calculations suggest that in the gas phase there exist two different non- planar minima: anti- and syn- respectively. In addition to these minima there also exist both rank-one and rank-two saddles separating these minima. In this talk I will discuss topology of the potential energy surface and its implication for the dynamics of the molecule. [Preview Abstract] |
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