  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 Ti$^{3+}$ and
Ti$^{4+}$ 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 Ti$^{3+}$ cations are predominantly of $d_{xy}$ 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.
