Author ORCID Identifier

https://orcid.org/0000-0003-0208-5303

Date of Award

Winter 2026

Document Type

Thesis (Ph.D.)

Department or Program

Physics and Astronomy

First Advisor

James Daniel Whitfield

Abstract

At the intersection of quantum physics, quantum chemistry, and materials science, electronic structure is the study of electrons in solid-state and molecular systems. Electronic-structure computation relies on discretizing the many-electron Hamiltonian with a finite single-particle basis set. However, basis-set construction is conventionally treated as an ad hoc preprocessing step. This thesis develops an expressive and flexible framework for active, system-oriented basis-set design and numerical modeling strategies that treat basis functions as tunable representations to encode electronic ground-state information.

We first introduce a multi-layered, differentiable basis-construction framework that embeds a set of primitive parameters into mixed-contracted Gaussian-type orbitals. We then develop an open-source software library, Quiqbox, as one of the first numerical modeling libraries focusing on custom basis-set design. In addition to basis-set construction, Quiqbox provides self-consistent mean-field methods and supports gradient-based parameter optimization. Utilizing these features, we study variational even-tempered basis sets as a system-oriented discretization strategy for atomic and molecular systems. We further extend the “basis design” philosophy to interatomic modeling by treating machine learning interatomic potentials as composable expansions of physics-inspired many-body cluster basis functions. We propose an adaptive model reconfiguration procedure that yields compact models with systematically improvable stability at training costs lower than those of generic deep neural network architectures.

In summary, this thesis demonstrates that composable numerical modeling is a viable approach to the design of both orbital basis functions for electronic-structure computations and data-driven interatomic potentials for atomistic simulations.

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