  The formation of conducting channels of Ti${}_4$O${}_7$ inside
TiO${}_2$-based memristors is believed to be the origin for the change in
electric resistivity of these devices. While the properties of the bulk
materials are reasonably known, the interface between them has not been studied
up to now mostly due to their different crystalline structures. In this work we
present a way to match the interfaces between TiO${}_2$ and Ti${}_4$O${}_7$ and
subsequently the band offset between these materials is obtained from density
functional theory based calculations. The results show that while the valence
band is located at the Ti${}_4$O${}_7$, the conduction band is found at the
TiO${}_2$ structure, resulting into a type II interface. In this case, the
Ti${}_4$O${}_7$ would act as a donor to the TiO${}_2$ matrix.
