Ab initio electronic structure calculation of hollandite vanadate   K$_2$V$_8$O$_{16}$
  An \textit{ab initio} electronic structure calculation based on the generalized gradient approximation in the density functional theory is carried out to study the basic electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$. We find that the states near the Fermi energy consist predominantly of the three $t_{2g}$-orbital components and the hybridization with oxygen $2p$ orbitals is small. The $d_{yz}$ and $d_{zx}$ orbitals are exactly degenerate and are lifted from the $d_{xy}$ orbital. The calculated band dispersion and Fermi surface indicate that the system is not purely one-dimensional but the coupling between the VO double chains is important. Comparison with available experimental data suggests the importance of electron correlations in this system. 
M. Sakamaki, S. Horiuchi, T. Konishi, Y. Ohta