  We investigate Ge mixing at the Si(001) surface and characterize the $2\times
N$ Si(001) reconstruction by means of hybrid quantum and molecular mechanics
calculations (QM/MM). Avoiding fake elastic dampening, this scheme allows to
correctly take into account long range deformation induced by reconstruted and
defective surfaces. We focus in particular on the dimer vacancy line (DVL) and
its interaction with Ge adatoms. We first show that calculated formation
energies for these defects are highly dependent on the choice of chemical
potential and that the latter must be chosen carefully. Characterizing the
effect of the DVL on the deformation field, we also find that the DVL favors Ge
segregation in the fourth layer close to the DVL. Using the
activation-relaxation technique (ART nouveau) and QM/MM, we show that a complex
diffusion path permits the substitution of the Ge atom in the fourth layer,
with barriers compatible with mixing observed at intermediate temperature.
