Excitons in Hematite Fe₂O₃: Short-Time Dynamics from TD-DFT and Non-Adiabatic Dynamics Theories

We present a first-principles study of the short-time dynamics of excitons in hematite Fe₂O₃. We used time-dependent density functional theory (TD-DFT) with an underlying DFT+U treatment of electron interactions to characterize the electronic structure of excitons and nonadiabatic molecular dynamics theory (NA-MD) to determine their recombination (electronic ground-state recovery) and relaxation dynamics. Decoherence-corrected trajectory surface hopping approaches in NA-MD simulations yielded recovery times of ∼1.1 to 1.8 ns and “higher-lying” exciton relaxation times of ∼60 to 70 fs, in accord with experimentally derived lifetimes. With hematite phonons in the range of ∼100 to 700 cm^-1, higher-lying excitons relax within one or two oscillations of the phonons before getting trapped into an electron-hole pair Exc-3 structure on the first excited state potential energy surface. This structure resembles already a pair of polarons (electron polaron plus hole polaron) with associated lattice distortions three (3) basal planes away. On longer time scales, the electron-hole bipolaronic pair hops to structures Exc-5, then Exc-7, then Exc-9, ... with the electron polaron and hole polaron separated by 5, 7, 9, ... basal planes in a process of charge separation. The largest frequency phonon ∼672 cm^-1 for the Exc-3 exciton structure is associated with the electron polaron moiety of the exciton. This phonon is a good candidate for giving rise to the recently observed and reported postexcitation transient IR absorption peak.