Role of c-axis pairs in V2O3 from the band-structure point of view

The common interpretation of the LDA band structure of V${}_2$O${}_3$ is that the apparent splitting of the $a_{1g}$ band into a low intensity structure deep below the Fermi energy and a high intensity feature above it, is due to the bonding-antibonding coupling of the vertical V-V pair. Using tight-binding fitting to --as well as first-principles NMTO downfolding of-- the spin-up LDA+U $a_{1g}$ band, we show that there are other hopping integrals which are equally important for the band shape as the integral for hopping between the partners of the pair.