Understanding and extending the role of first-principles quantum Monte Carlo

Williams, Kiel Troy

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https://hdl.handle.net/2142/108484 Copy

Description

Title

Understanding and extending the role of first-principles quantum Monte Carlo

Author(s)

Williams, Kiel Troy

Issue Date

2020-07-14

Director of Research (if dissertation) or Advisor (if thesis)

Wagner, Lucas K

Doctoral Committee Chair(s)

Dahmen, Karin

Committee Member(s)

• DeMarco, Brian
• Eckstein, James

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Quantum electronic structure
• computational condensed matter

Abstract

By providing a middle way between experiment and theory, first-principles electronic structure calculations provide a powerful tool for accelerating discovery in condensed matter physics. Computation provides a fast, cost-effective supplement to experiment, while simultaneously offering a greater level of flexibility than analytic theory. Indeed, first-principles electronic structure is already in use across a range of diverse fields, from photovoltaic research to pharmaceuticals. However, to make full use of first-principles calculations, we must understand the level of accuracy different techniques can offer, and how that accuracy varies across different quantities of interest. Because different techniques vary so widely in both their computational expense and methodological formulation, great care must be taken to understand when-and-where a particular approach should be applied. To this end, I report on several comparative studies I conducted that deepen our understanding of electronic structure methods in use today. First, I present a new technique for improving trial wavefunctions in quantum Monte Carlo (QMC) calculations. Trial wavefunction quality is one of the key limiting factors to the accuracy of QMC, and in this study I demonstrate one way to systematically overcome this barrier. I also present a study comparing the energetic accuracy of QMC to a group of over 20 methods for a collection of transition metal atoms and monoxides. This study was one of the largest of its kind yet undertaken, and one of the few to include numerically exact reference energies. I also report on several studies examining the success of different techniques in treating the electronic density. I demonstrate in one study the accuracy of QMC electronic densities relative to those provided by DFT for the perovskite BaTiO3, while in another study I analyze the relationship between errors in the total energy and in the density across a collection of small molecules. Finally, I show how QMC calculations can be used to construct accurate low-energy models for different systems. The results I present not only demonstrate the accuracy of QMC in a variety of domains, but carefully contextualize that accuracy relative to many of the other numerical techniques in use today.

Graduation Semester

2020-08

Type of Resource

Thesis

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http://hdl.handle.net/2142/108484

Copyright and License Information

Copyright 2020 Kiel Williams

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