  Apart from the most studied tin-oxide compounds, SnO and SnO2, intermediate
states have been claimed to exist for more than a hundred years. In addition to
the known homologous series (Seko et al., Phys. Rev. Lett. 100, 045702 (2008)),
we here predict the existence of several new compounds with an O concentration
between 50 % (SnO) and 67 % (SnO2). All these intermediate compounds are
constructed from removing one or more (101) oxygen layers of SnO2. Since the
van der Waals (vdW) interaction is known to be important for the Sn-Sn
interlayer distances, we use a vdW-corrected functional, and compare these
results with results obtained with PBE and hybrid functionals. We present the
electronic properties of the intermediate structures and we observe a decrease
of the band gap when (i) the O concentration increases and (ii) more SnO-like
units are present for a given concentration. The contribution of the different
atoms to the valence and conduction band is also investigated.
