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 inter
face 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.
