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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 computations rely 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 for encoding electronic ground-state information.

We first introduce a multi-layered and differentiable basis-construction framework that maps a set of primitive parameters to mixed-contracted Gaussian-type orbitals. We then develop an open-source software library, Quiqbox, 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 tabular-data-free, 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 (MLIPs) as composable expansions of physics-inspired atomic-cluster basis functions. We propose an adaptive model reconfiguration procedure that yields compact models with systematic stability improvability at training costs lower than those of generic deep neural network architectures.

Together, these contributions demonstrate that system-oriented modeling is a viable alternative to directly adapting generic models, both for orbital basis functions in electronic structure and for data-driven interatomic potentials.

Graduate Advisor: Professor James Whitfield

Zoom Link: https://dartmouth.zoom.us/j/97607177666