Recent breakthroughs in laser excitation of a unique low-energy nuclear transition in thorium-229 embedded in solid-state hosts have enabled a new generation of highly accurate, portable timekeeping devices. Compact nuclear clocks based on this transition hold an important promise to revolutionize global navigation, telecommunications, precision timing, and fundamental physics applications by offering unparalleled stability and robustness under varying environmental conditions. While advancing emerging quantum technologies, this research supports the development of a skilled quantum workforce. Materials science, quantum chemistry, condensed-matter physics, nuclear physics, and atomic, molecular, and optical physics are combined in an interdisciplinary approach. A theoretical formalism for evaluating isomer shifts, internal conversion rates, and electron-bridge decay rates is developed to inform nuclear-clock design and performance. Relativistic atomic theory is bridged with state-of-the-art quantum-chemistry and materials-science computational techniques by this framework. Couplings between electronic degrees of freedom in condensed-matter environments and thorium-229 nuclear states are of particular interest and are subjected to ab initio relativistic treatments. Quantum electrodynamics is applied in thin-film geometries to calculate Purcell enhancement factors and to establish foundational elements of nuclear quantum optics. This award reflects NSF's statutory missio