In this paper, we report a first principles molecular dynamics (FPMD) study of the acid–base chemistry of gibbsite. With FPMD based vertical energy gap technique, the acidity constants of the sites on the basal surface (i.e. (0 0 1)) and the edge surface (1 0 0) are derived and the results overall indicate that triple bond; length of mdashl(OH2)2 groups on the edge surface are the major acidic sites. The free-energy calculation indicates that both the 6-fold (i.e. triple bond; length of mdashAl(OH2)2) and 5-fold (i.e. triple bond; length of mdashAl(OH2)) coordination states of edge Al atoms are probable with the former being much more stable. The 6-fold forms have very similar 1st and 2nd acidity constants in 9.0–10.0, which agrees with the experimental PZC (point of zero charge) range. The 5-fold forms have a very low pKa of about 2.0, which indicates that its common form is triple bond; length of mdashAl(OH) within normal pH range. The doubly coordinated site (i.e. triple bond; length of mdashAl2(OH)) on the edge surface has a very high pKa of about 13.0, indicating that the proton dissociation rarely happens. For the basal surface, the hydroxyl groups almost do not have contribution to the acid–base chemistry of gibbsite. On this surface, some OHs keep orientation parallel to the surface and therefore they can only perform as proton acceptors. However, their protonated states have very low pKas of around 1.3. The other OHs have an extremely high pKa (about 22.0), indicating no dissociation in common pH. Overall, this study provides atomic-scale understanding on the acid–base chemistry of gibbsite and the derived interfacial structures and acidity constants form a basis for future research on the interfacial processes of Al–hydroxides.