Fig. 2: Theoretical optical absorption fingerprints of surface holes.

a, Surface Pourbaix diagram of the α-Fe₂O₃(0001) surface in contact with liquid water, with the potential E referenced to the RHE. The different colours represent different hydrogen coverages, ranging from 0 ML coverage to 1 ML coverage (see Supplementary Note 6 for further details). The dashed line indicates the estimated position of the VBM edge. b–d, Isosurfaces of the lowest-unoccupied molecular orbital showing the location of the hole at the haematite/water interface when both an electron and a proton have been removed from a surface hydroxy group, with the hole shared between a surface O and a subsurface Fe, formally denoted *O¹⁻ (b), when only an electron has been removed, leading to an Fe(IV) subsurface species (c), and when an electron has been removed from bulk haematite, leading to a bulk Fe(IV) species (d). Red, brown and white spheres represent O, Fe and H atoms, respectively. e–g, TDDFT-computed optical absorption spectra of the α-Fe₂O₃(0001)/water interface, where the hole has been created by a PCET, leading to the formation of an *O¹⁻ species (e), the interface where the hole has been created by the removal of an electron, leading to the formation of a subsurface Fe(IV) species (f), and bulk haematite, where the hole has been created by the removal of an electron, leading to the formation of an Fe(IV) species (g). The spectra are averages of snapshots extracted from FPMD. The red curve is the spectrum of the pristine surface, the black line is the spectrum of the oxidized surface and the blue curve is the difference between the black and red curves, multiplied by an arbitrary factor; the grey vertical line at 650 nm indicates the position of the peak in the experimental optical spectra associated with the long-lived surface holes.