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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Williams, Kiel Troy

Contributors dc:contributor

• Wagner, Lucas K
• Dahmen, Karin
• DeMarco, Brian
• Eckstein, James

• Quantum electronic structure
• computational condensed matter

Statement dc:rights

• Copyright 2020 Kiel Williams

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/108484