Introducing PAIMP, the polarizable <i>ab initio</i> model potential method for embedded clusters

We introduce a polarizable ab initio model potential (PAIMP) for embedded wavefunction calculations of point defects in ionic solids. PAIMP augments the established AIMP framework with a classical, self-consistent induced-dipole operator derived from polarizable embedding formalisms, using site-resolved polarizability tensors. PAIMP is benchmarked for Cr-doped α-Al2O3 (bulk and surfaces) and a bulk oxygen-vacancy (F-center). For bulk Cr:Al2O3, PAIMP and AIMP give essentially identical d-d excitation energies and intensities in linear-response complete active space self-consistent field calculations (LR-CASSCF), consistent with the cancellation of electric-field components in a highly symmetrical crystal field. In contrast, under-coordinated surface defects show clear PAIMP effects: O(2p) → Cr(3d) charge-transfer bands are red shifted relative to the bulk and display enhanced structure and oscillator strengths with PAIMP, particularly on the thermodynamically stable (0001) facet. For the F-center, both LR-CASSCF and MS-CASPT2 predict two intense peaks (around 160-180 nm), qualitatively capturing the observed doublet, but remaining blue shifted relative to the experiment. Overall, polarization is, as expected, negligible for localized d-d transitions in bulk Cr:Al2O3 but becomes important for charge-transfer excitations and low-coordination environments, where PAIMP yields more structured spectra and higher intensities. The presented model, hence, provides a significant step toward computationally efficient and more robust descriptions of localized defects in ionic host environments.