Accurately determining the effective Hubbard parameter $(U_{eff})$ in Density Functional Theory plus U (DFT+U) remains a significant challenge, often relying on empirical methods or linear response theory, which frequently fail to predict accurate material properties. This study introduces BMach, an advanced Bayesian optimization algorithm that refines $U_{eff}$ by incorporating electronic properties, such as band gaps and eigenvalues, alongside structural properties like lattice parameters. Implemented within the Quantum Espresso platform, BMach demonstrates superior accuracy and reduced computational cost compared to traditional methods. The BMach-optimized $U_{eff}$ values yield electronic properties that align closely with experimental and high-level theoretical results, providing a robust framework for high-throughput materials discovery and detailed electronic property characterization across diverse material systems.
First-principles Hubbard U and Hund's J corrected approximate density-functional theory predicts an accurate fundamental gap in rutile and anatase TiO2
DFT+U+V is equivalent to DFT+U with density-dependent hybridized projectors
Paul Scherrer Institute（保罗谢尔研究所）；National Centre for Computational Design and Discovery of Novel Materials (MARVEL), Paul Scherrer Institute（保罗谢尔研究所新型材料计算设计与发现国家中心（MARVEL））；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；University of Cambridge（剑桥大学）
Electronic structure, magnetism and exchange integrals in transition metal oxides: role of the spin polarization of the functional in DFT+$U$ calculations
