Revisiting the band gap problem in bulk Co ₃ O ₄ and its isostructural Zn and Al derivatives through the lens of theoretical spectroscopy

In this work, a systematic computational investigation of the optical band gap (BG) problem of Co₃O₄ is carried out on the basis of the embedded cluster approach in combination with a series of particle/hole and wavefunction-based approaches. A total number of three experimental band gap energies for the bulk Co₃O₄ have been reported in the literature, the nature of which have remained controversial. This work will show that accurately describing the excited states and rationalizing these experimental band gaps require explicit treatment and analysis of strong electron correlation effects. These correlation effects enable low-energy optical excitations to emerge from both 'neutral' and 'ionic' antiferromagnetic configurations, depending on how the electronic structure reorganizes across the coupled high-spin tetrahedral Co(II) (site A) and low-spin octahedral Co(III) (site B) centers. To disentangle the contributions from these two distinct sites, this work introduces reference systems, Al₂Co(II)O₄ and Co(III)₂ZnO₄, which isolate the Co(II) and Co(II) sites, respectively. Tackling such a complex excited state problem requires going beyond density functional theory (DFT) particle/hole approaches and employing a range of single and multi-reference wavefunction based methods. In particular, complete active space configuration interaction self-consistent field (CASSCF) and its approximate CI variants in conjunction with 2nd order N-electron valence perturbation theory (NEVPT2) provide access to an accurate prediction of all three experimentally observed BG energies in Co₃O₄. Our calculations are consistent with the notion that the lowest energy band gap corresponds to the ligand field (LF) type of transitions within the local tetrahedral Co(II) centers. Furthermore, the calculations predict that the middle energy band gap is a mixture of LF transitions at site A and metal-to-metal charge transfer (MMCT) transition across A-A' and A-B/B-A' pairs. These transitions give rise to Co(I) and Co(III) configurations at site A, deviating from the original Co(II) based configurations. This intermediate band is assigned to the actual experimentally observed optical band gap of Co₃O₄. Finally, the highest energy band gap is again a mixture of LF transitions at site A and ligand-to-metal charge transfer (LMCT), involving O 2p → Co(II)-3d transitions, with our calculations also indicating some contributions from other MMCT states. Hence, this later energy band corresponds to the actual semiconducting band gap that defines the semiconductor properties of Co₃O₄.