Energy splitting and isomer shift of ²²⁹Th in VUV-transparent crystals

摘要: The ²²⁹Th isomeric transition around 8.4 eV offers a route to solid-state nuclear clocks, but its frequency is modified by the isomer shift and by the electric quadrupole interaction in the host crystal. We report a first-principles study of seven Th defect sites in four VUV-transparent hosts: ThF₄, Th:CaF₂, Th:SrF₂ and Th:LiF. Calculations are performed with PBE, R2SCAN and HSE06 functionals, yielding the Th 5f/6d/7s/7p valence weights, isomer shifts, EFG tensors (V_zz,η) and the complete I = 5/2 and I = 3/2 quadrupole level structures. The EFG and quadrupole splittings are insensitive to the functional (at most 3.8%), whereas the isomer shift varies by 25–46 MHz and tracks the Th N_l weight. The defect configuration controls the EFG: F-90 and F-180 centres have opposite V_zz signs and differ in magnitude by up to a factor of 2.5; ground-state splittings span 48/96 MHz in Th:LiF to 429/858 MHz in CaF₂ F-180, with isomer-state splittings of 91–816 MHz. The method is validated against the published ThF4 shift decomposition (0.6–1.4 MHz), an independent calculation of its level structure (0.7–1.1% in V_zz and ≤ 8 MHz in the splittings), and TDHF/RPA field-shift coefficients (0.2–1.8%). These results provide a functional- and configuration-resolved database for interpreting host-dependent ²²⁹Th clock frequencies, and identify quadrupole splitting as the more transferable electronic observable.