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Accelerating minimum energy path finding method
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Makri, Stela (2019) Accelerating minimum energy path finding method. PhD thesis, University of Warwick.
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WRAP_Theses_Makri_2019.pdf - Submitted Version - Requires a PDF viewer. Download (6Mb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3501257~S15
Abstract
The behaviour of physical systems is often characterised by rare transitions between energy minima. Due to their rarity, these events are not observed in typical molecular simulations but can be observed in simulations on the mesoscale provided that the rate of transition is known. For the evaluation of the transition rate, knowledge of the energy barrier the system overcomes during the transition, is necessary.
In Transition State theory this is achieved by finding the saddle point, which lies between the reactant and product states. Popular techniques include the nudged elastic band method and the string method which evaluate the minimum energy path of the transition, as well as the walker-type dimer method. These are iterative schemes evolving a chain of states along projected steepest descent directions. In this thesis, saddle point finding methods are studied with respect to their performance and stability. An adaptive step selection scheme is proposed, motivated from adaptive ODE numerical solving. The scheme improves the robustness of saddle point search methods and enjoys convergence efficiency.
An important factor contributing to slow convergence, comes from not considering potential energy curvature information. This has been addressed for walker-type methods but not for methods which identify transition paths. A preconditioning scheme is proposed to address this issue, which substantially reduces the computational cost of transition path finding algorithms.
Finally, momentum descent methods are explored in conjunction with saddle point finding techniques. A momentum term is introduced in the dynamics of string, nudged elastic band and dimer methods introducing an added inertia which accelerates the dynamics and achieves faster convergence. We demonstrate the improved performance of our approaches in a range of examples including vacancy and dislocation migration modelled with both inter atomic potentials and density functional theory.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QD Chemistry |
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Library of Congress Subject Headings (LCSH): | Chemical systems, Method of steepest descent (Numerical analysis), Chemical reactions | ||||
Official Date: | September 2019 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | School of Engineering | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Kermode, James R. ; Ortner, Christoph | ||||
Sponsors: | University of Warwick. School of Engineering ; Engineering and Physical Sciences Research Council ; European Research Council ; Royal Society (Great Britain) | ||||
Format of File: | |||||
Extent: | xx, 134 leaves : illustrations (chiefly colour) | ||||
Language: | eng |
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