Low-Dimensional Representations of Transitions in Molecular Systems

Citation

Grubits, Katalin Anna (2008) Low-Dimensional Representations of Transitions in Molecular Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YMTC-WQ16. https://resolver.caltech.edu/CaltechETD:etd-06062008-171210

Abstract

A major difficulty in modeling molecular systems is that the number of dimensions, even for a small system, is commonly too large for computation to be feasible. To overcome this challenge, a combination of lower-dimensional representations of the system and improved computational methods are required. In this thesis, we investigate techniques to achieve both of these aims via three model problems.

By exploiting an understanding of the mechanism and dynamics of reaction in the systems considered, we attain a low-dimensional description of the transition that captures the essential dynamics. For the ionization of a Rydberg atom we utilize concepts from dynamical systems theory that reveal the geometric structures in phase space that mediate the reaction. The gyration radius formalism captures the kinematic effects of the secondary particles in a coarse variable that reduces the number of dimensions of the model, thereby providing a simple description of our methane and oxygen dissociation example. These methods are applicable more generally and provide a coarse model of chemical reactions that can be combined with efficient computational tools, such as the set-oriented method employed in our Rydberg example, to efficiently compute reaction rates of previously difficult problems.

The third model problem considered is the self-assembly of particles into an ordered lattice configuration under the influence of an isotropic inter-particle potential. With the aim of characterizing the transition from a disordered to an ordered state, we develop metrics that assess the quality of the lattice with respect to the target lattice configuration. The five metrics presented use a single number to quantify the order within this large system of particles. We explore numerous applications of these quality assessment tools, in particular, finding the optimal potential for self-assembly. The very noisy, highly variable nature of our expensive-to-evaluate objective function prompted the development of a trend optimization algorithm that efficiently minimizes the objective function, using upper and lower envelopes that are responsible for the robustness of the method and the solution. This trend optimization scheme is widely applicable to problems in other fields.

Thesis Files