Challenges and Advances in Elucidating the Electronic Circular Dichroism of Crystalline Materials through First-Principles Calculations

The electronic circular dichroism (ECD) of crystalline materials is governed by physical effects that are absent in isolated-molecule theory. Bloch-state delocalization makes position-operator matrix elements ill-defined and requires Berry-connection formulations of the periodic optical-activity response, while excitonic effects redistribute oscillator strength across the band gap. This Perspective critically surveys the hierarchy of first-principles methods that have been established to address these challenges. Molecular-cluster time-dependent density functional theory (TDDFT) provides chemical intuition and mechanistic insight but cannot represent the complete periodic response and can underestimate long-range crystal field effects. Periodic independent-particle calculations incorporate the crystalline environment and band-geometric response, whereas self-consistent coupled-perturbed approaches additionally include crystal-orbital relaxation. Adaptive Brillouin-zone sampling can accelerate convergence for localized one-particle contributions, although nonuniform meshes complicate momentum conservation in the correlated treatments. GW-BSE provides a rigorous framework for excitonic optical activity, whereas maximally localized Wannier function interpolation efficiently converges the DFT-level periodic quantities used to analyze the band-geometric response. A generally validated workflow that combines the BSE-level excitonic response with all geometric and interpolation ingredients has not yet been established. Finally, we discuss open challenges including fully relativistic treatments of chiral rare-earth halide perovskites and single-crystal anisotropy measurements.