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 t2g occupancies of Ti3+ and Ti4+ cations is large and gives direct evidence for charge ordering. Ti 4s and 4p states make a large contribution to the static "screening" of the total 3d charge difference. This effective charge screening leads to complete loss of the disproportionation between the charges at 3+ and 4+ Ti sites. The occupied t2g states of Ti3+ cations are predominantly of dxy character and form a spin-singlet molecular orbital via strong direct antiferromagnetic exchange coupling between neighboring Ti(1) and Ti(3) sites, whereas the role of superexchange is found to be negligible.
@article{arxiv.cond-mat/0508378,
title = {Charge order and spin-singlet pairs formation in Ti4O7},
author = {I. Leonov and A. N. Yaresko and V. N. Antonov and U. Schwingenschlögl and V. Eyert and V. I. Anisimov},
journal= {arXiv preprint arXiv:cond-mat/0508378},
year = {2007}
}