Methodology for Electric Field Gradients in Molecules and Solids, with Application to <sup>229</sup>Th:CaF₂
POSTER
Abstract
The exceptionally low-energy nuclear transition in 229Th (ωnuc ≈ 8.35 eV) motivates the development of solid-state nuclear clocks, with 229Th:CaF₂ emerging as one of the promising hosts. Here we exploit the strong sensitivity of electric field gradients (EFGs) to local bonding, symmetry, and defect geometry, and “fingerprint” candidate Th substitutional configurations in CaF₂ by computing the EFG tensor at the 229Th nucleus. EFG is an observable that governs quadrupolar hyperfine splittings and thus quantifies local environments inferred from spectroscopy.
We evaluate EFGs for four charge-compensation sites for 229Th substituted on a Ca site: (a) two fluorine interstitials aligned at 180° (2F′i–linear), (b) two fluorine interstitials arranged at ≈90° (2F′i–bent), (c) a single neighboring Ca2+ vacancy (V′′Ca), and (d) an uncompensated Th configuration (no explicit charge compensation).
Our workflow combines periodic DFT structural relaxation with high-level embedded-cluster multireference CASSCF/CASPT2 calculations in a realistic electrostatic embedding, including a relativistic treatment appropriate for Th. To assess the theoretical accuracy, we also present a systematic methodological study of EFG predictions for representative molecules and crystalline materials using both periodic boundary-condition approaches and embedded-cluster models, benchmarking against reported experimental data. We quantify the sensitivity of the principal EFG component Vzz and the asymmetry parameter η to key computational choices, including the effective Hamiltonian and relativistic treatment, basis sets, and molecular/crystal geometries, and we clarify persistent differences in EFG tensor definitions and sign conventions employed across the literature and widely used electronic-structure codes. Together, these results provide practical guidelines for reliably computing, interpreting, and exploiting EFGs as quantitative descriptors of electronic structure and chemical environment.
We evaluate EFGs for four charge-compensation sites for 229Th substituted on a Ca site: (a) two fluorine interstitials aligned at 180° (2F′i–linear), (b) two fluorine interstitials arranged at ≈90° (2F′i–bent), (c) a single neighboring Ca2+ vacancy (V′′Ca), and (d) an uncompensated Th configuration (no explicit charge compensation).
Our workflow combines periodic DFT structural relaxation with high-level embedded-cluster multireference CASSCF/CASPT2 calculations in a realistic electrostatic embedding, including a relativistic treatment appropriate for Th. To assess the theoretical accuracy, we also present a systematic methodological study of EFG predictions for representative molecules and crystalline materials using both periodic boundary-condition approaches and embedded-cluster models, benchmarking against reported experimental data. We quantify the sensitivity of the principal EFG component Vzz and the asymmetry parameter η to key computational choices, including the effective Hamiltonian and relativistic treatment, basis sets, and molecular/crystal geometries, and we clarify persistent differences in EFG tensor definitions and sign conventions employed across the literature and widely used electronic-structure codes. Together, these results provide practical guidelines for reliably computing, interpreting, and exploiting EFGs as quantitative descriptors of electronic structure and chemical environment.
*This work was supported by NSF awards PHY-2207546, PHY-2513134, and PHY-2412869, and ARO award W911NF-25-1-0172.
Presenters
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Udeshika Chathurangani Perera
- Mississippi State University
- University of Nevada, Reno