Multi-reference calculation for correlated transition-metal oxides from delta-learning

Density-functional theory (DFT) often fails for strongly correlated materials due to the limitations of approximate exchange-correlation functionals. While wavefunction methods, such as configuration interaction, address multi-reference correlations explicitly, their application is largely restricted to small molecule systems and their extension to bulk materials with embedding approaches is hindered by inherent complexity. In this work, we present a delta-learning[1-3] approach that elevates DFT energetics to multi-determinant accuracy and demonstrates the improvement for first row transition metal monoxides (MnO, FeO, CoO, and NiO). Motivated by the locality of the strong correlation, we compute the difference in energy landscapes on extracted clusters between DFT and multi-reference theory (i.e., CASSCF/NEVPT2), and add the correction to bulk systems. This approach separates localized strong correlation from long-range interactions, achieving beyond-DFT accuracy. The effect in recovering strong correlations is evident in the improved prediction of lattice parameters, bulk moduli and phonon frequencies. We further show the synergy of this method with machine learning interatomic potential (MLIP) to enhance the applicability.

1.N. O’Neill et al., doi:10.48550/arXiv.2508.13391 (2025).

2. S. Schönbauer, J. P. Carbone, and A. Grüneis, doi:10.48550/arXiv.2507.06929 (2025).

3. J. Daru, H. Forbert, J. Behler, and D. Marx, Phys. Rev. Lett. 129(22), 226001 (2022).