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

Abstract

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.