The electron bandstructure for vanadium (bcc) was calculated using the program Quantum Espresso (version 5.3.0) in Winmostar (version 8.034). A bandstructure calculation always calculates a finite number of bands. Usually these are the bands around the Fermi energy. For energies further away from the Fermi energy, bands will be missing. To check that the bandstructure is correct in the range that is plotted, make two calculations including different numbers of bands and only plot the energies where both calculations overlap.
For some k values the bands are degenerate but six bands can distinguished between N and Γ. These are the five 3d bands and the 4s band. The 4s orbitals have the most overlap between neighboring atoms so the 4s band has largest band width. The band with a minimum at Γ is the 4s band. This can also be seen in the density of states where the contribution of the 4s band has a free-electron-like form $\sqrt{E}$ and the 3d bands cause peaks in the density of states clustered in energy.
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