<p>We study the electronic structure and dynamical correlations in antiferromagnetic BiFeO<sub>3</sub>, a prototypical room-temperature multiferroic, using a variety of static and dynamical first-principles methods. Conventional static Hubbard corrections (DFT+U, DFT+U+V) incorrectly predict a deep-valence Fe 3d peak (around -7 eV) in antiferromagnetic BiFeO<sub>3</sub>, in contradiction with hard-X-ray photoemission. We resolve this failure by using a recent generalization of DFT+U to include a frequency-dependent screening – DFT+U(ω) – or using a dynamical Hubbard functional (dynH). The screened Coulomb interaction U(ω), computed with spin-polarized RPA and projected onto maximally localized Fe 3d Wannier orbitals, is expressed as a sum-over-poles, yielding a self-energy that augments the Kohn–Sham Hamiltonian. This DFT+U(ω) approach predicts a fundamental band gap of 1.53 eV, consistent with experiments, and completely eliminates the unphysical deep-valence peak. The resulting simulated HAXPES spectrum reproduces the experimental lineshape with an accuracy comparable to state-of-the-art approaches. Our work highlights the critical nature of dynamical screening in complex oxides and of DFT+U(ω) as a predictive and computationally efficient approach to address the electronic structure of correlated materials.</p>
