  In this work we undertake the problem of a transition metal impurity in an
oxide. We present an ab-initio study of the relaxations introduced in TiO2 when
a Cd impurity replaces substitutionally a Ti atom. Using the Full-Potential
Linearized-Augmented-Plane-Wave method we obtain relaxed structures for
different charge states of the impurity and computed the electric-field
gradients (EFGs) at the Cd site. We find that EFGs, and also relaxations, are
dependent on the charge state of the impurity. This dependence is very
remarkable in the case of the EFG and is explained analyzing the electronic
structure of the studied system. We predict fairly anisotropic relaxations for
the nearest oxygen neighbors of the Cd impurity. The experimental confirmation
of this prediction and a brief report of these calculations have recently been
presented [P.R.L. 89, 55503 (2002)]. Our results for relaxations and EFGs are
in clear contradiction with previous studies of this system that assumed
isotropic relaxations and point out that no simple model is viable to describe
relaxations and the EFG at Cd in TiO2 even approximately.
