In this thesis, two important niobium-oxygen systems are studied. The first system is the NbO "nanocrystal" termination of Nb(110). A new model to explain this structure based on a monolayer of oxygen covering the surface with a subtle reconstruction is proposed. In the model, part of the surface reconstructs to form a fourfold absorption site that the oxygen sinks into, while the remainder of the surface adopts a NbO(111)-like hexagonal structure with threefold coordinated oxygen. DFT calculations of this model demonstrate strong agreement across a wide variety of experimental techniques including STM, STS, LEED, and XPS. The second system studied is NbO2. It is found that first principles Hubbard U and Hund's J parameters can be determined for the Nb 4d and O 2p subspaces through a simple linear response method. The inclusion of a correction based on these parameters in bulk calculations is found to improve agreement with experimental measurements for the band gap and O 2p band width, but fall short when describing the Nb 4d band width. XPS and UPS experiments indicate metallic behaviour at the surface, which is confirmed through slab calculations. These slab calculations, including U and J corrections, finally provide a theory which predicts the correct Nb 4d band width. This indicates that the essential physics of NbO2 can be captured within DFT+U+J, when accounting for the modification of the electronic structure near the surface.

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