  In some topological insulators, such as graphene and WTe$_2$, band inversion
originates from chemical bonding and space group symmetry, in contrast to
materials such as Bi$_2$Se$_3$, where the band inversion derives from
relativistic effects in the atoms. In the former, band inversion is susceptible
to changes of the chemical environment, e.g. by defects, while the latter are
less affected by defects due to the larger energy scale associated with atomic
relativistic effects. Motivated by recent experiments, we study the effect of
Te-vacancies and Te-adatoms on the electronic properties of WTe$_2$. We find
that the Te-vacancies have a formation energy of $2.21$ eV, while the formation
energy of the Te-adatoms is much lower with $0.72$ eV. The vacancies strongly
influence the band structure and we present evidence that band inversion is
already reversed at the nominal composition of WTe$_{1.97}$. In contrast, we
show that the adatoms do not change the electronic structure in the vicinity of
the Fermi level and thus the topological properties. Our findings indicate that
Te-adatoms should be present in thin films that are grown in a Te-rich
environment, and we suggest that they have been observed in scanning tunneling
microscopy experiments.
