Charge order and spin-singlet pair formation in Ti₄O₇

Charge ordering in the low-temperature triclinic structure of titanium oxide (Ti₄O₇) is investigated using the local density approximation (LDA)+U method. Although the total 3d charge separation is rather small, an orbital order parameter defined as the difference between t _2g occupancies of Ti³⁺ and Ti⁴⁺ cations is large and gives direct evidence for charge ordering. Strong covalency of O2p-Ti3d σ-type bonds, which results in partial occupation of Ti e _g states, leads to almost complete loss of the disproportionation between the charges at 3+and 4+Ti sites. The occupied t_2g states of Ti³⁺ cations are predominantly of d_xy character and form a spin-singlet molecular orbital via strong direct antiferromagnetic exchange coupling between neighbouring Ti(1) and Ti(3) sites, whereas the role of superexchange is found to be negligible.