The Library
Analysis of an ab initio potential energy landscape
Tools
Thomas, Jack (2021) Analysis of an ab initio potential energy landscape. PhD thesis, University of Warwick.
|
PDF
WRAP_Theses_Thomas_2021.pdf - Submitted Version - Requires a PDF viewer. Download (2896Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3781813~S15
Abstract
A wide range of electronic, optical and magnetic properties of solids are determined by electronic structure. Computational methods, such as density functional theory, have been used successfully to model electronic structure and thus allowed the investigation and prediction of properties of materials. However, even now, the high computational cost of these ab initio methods severely limits their applicability in material modelling to thousands of atoms for static and hundreds of atoms for long-time dynamic simulations. In modelling tasks involving only the mechanics of the atoms, one may bypass the electronic structure model entirely and replace it with a surrogate interatomic potential (IP), a functional form that may be fitted to theoretical data from a high fidelity ab initio model. The aim of this thesis is to provide a rigorous basis for IP models by justifying some of the underlying assumptions, in particular with an eye towards physics-informed machine learning approaches. More specifically, we consider the tight binding model, a quantum mechanical model sharing many similarities with the more complex Kohn-Sham density functional theories, and prove that the potential energy landscape (PEL) can be decomposed into atom-centred site energy contributions depending only on atoms within a small cut-off radius of the central atom. Moreover, we obtain error estimates for body-ordered approximations, which allows one to reduce the dimensionality of the site energy contributions. In particular, we are able to decompose the PEL into low dimensional components which are easier to analyse, manipulate, and fit.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
||||
Library of Congress Subject Headings (LCSH): | Atomic structure -- Computer simulation, Electronic structure, Quantum theory -- Mathematical models | ||||
Official Date: | September 2021 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Ortner, Christoph | ||||
Extent: | viii, 193 leaves | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year