Compound-tunable embedding potential method to model local electronic excitations on f -element ions in solids: Pilot relativistic coupled cluster study of Ce and Th impurities in yttrium orthophosphate, YPO4

A method to simulate local properties and processes in crystals with impurities via constructing cluster models within the frame of the compound-tunable embedding potential (CTEP) and highly accurate ab initio relativistic molecular-type electronic structure calculations is developed and applied to the Ce- and Th-doped yttrium orthophosphate crystals, YPO₄, having xenotime structure. Two embedded cluster models are considered, the ``minimal'' one, YO₈@CTEPₘᵢₙ, consisting of the central Y³⁺ cation and its first coordination sphere of eight O^2- anions (i.e., with broken P--O bonds), and its extended counterpart, Y(PO₄)₆@CTEPₑₓₜ, implying the full treatment of all atoms of the PO₄^3- anions nearest to the central Y³⁺ cation. CTEPmin,ext denote here the corresponding cluster environment described within the CTEP method. The Fock space relativistic coupled cluster (FS RCC) theory is applied to the minimal cluster model to study electronic excitations localized on Ce³⁺ and Th³⁺ impurity ions. Calculated transition energies for the cerium-doped xenotime are in a good agreement with the available experimental data (mean absolute deviation of ca. 0.3 eV for 4f→5d type transitions). For the thorium-doped crystal the picture of electronic states is predicted to be quite complicated, and the ground state is expected to be of the $6d$ character. The uncertainty for the excitation energies of thorium-doped xenotime is estimated to be within 0.35 eV. Radiative lifetimes of excited states are calculated at the FS RCC level for both doped crystals. The calculated lifetime of the lowest $5d$ state of Ce³⁺ differs from the experimentally measured one by no more than twice.