**Excited-state properties of oxygen vacancies near α-Al2O**_{3 }(0001) surfaces from first principles and quantum defect embedding

Density functional theory (DFT) has proven to be a successful mean-field approach to calculate structural and electronic properties of bulk materials as well as their surfaces. However, DFT fails to correctly describe excited-state properties, and many-body perturbation theory (MBPT) has emerged as a successful approach to predict those. But even DFT and MBPT calculations are limited due to the exponential scaling of the dimension of the many-body wave function with system size. Additionally, strongly correlated states cannot be described with static mean-field calculations.

These challenges are particularly affecting accurate modeling of defects in solids, even though they are often confined to a small space comprising of only a few correlated states. Recently, a quantum defect embedding theory (QDET) [1,2] was proposed to study such correlated defect states in solids. It treats the defect states at a high level of theory, for example, with Full Configuration Interaction (FCI), or on a Quantum computer. The host material is solved within the mean-field approach that allows to simulate systems with hundreds of atoms.

In this talk, I will present our results for surface effects on electronic and structural properties of O vacancies near the surface of α-Al2O_{3} (0001). This material is a widely studied system as it hosts a range of important technological applications such as catalysis, and natural occurring processes such as corrosion. Oxygen vacancies near the surface of α-Al2O_{3} (0001) are of significant interest as they aid in understanding the hydration of the surface which is critical to the aforementioned processes. We report large inward relaxation of the Al monolayer (~88% of the unrelaxed configuration) accompanied by the reconstruction of the surface Al ions. The vertical relaxation of the subsequent layers is concurrent with previous density-functional theory studies and experimental results from X-ray diffraction. Upon introducing the O defect, emergence of defect states is observed. These defect states are characterized to describe an active space to perform QDET calculations. An effective Hamiltonian is constructed for the active space, and we subsequently obtain excitation energies for the correlated defect states by employing FCI. Our results demonstrate that QDET is a reliable approach to study excited-state properties of large surfaces with correlated defect states, and an implementation is in progress to solve the effective Hamiltonian on a quantum computer.

[1] H. Ma, M. Govoni, and G. Galli, *npj Computational Materials ***6**, 85 (2020).

[2] N. Sheng, C. Vorwerk, M. Govoni, and G. Galli, *J. Chem. Theory Comput.* **18**, 3512 (2022).