How to show a band structure for water?
do Couto et al have published an article [1] characterizing the density of states (band structure) of water using DFT theory combined with MC sampling. Extrapolating from clusters to bulk water, the HOMO-LUMO gap is 8.55 eV (Table 3). 

From the abstract:


  By extrapolating the results for larger clusters the threshold energy
  for photoelectron emission is $9.6±0.15 eV$ free clusters and
  $10.58±0.10 eV$ embedded clusters. Our results  for  the  electron 
  affinity $V_0=−0.17±0.05 eV$ and  adiabatic  band  gap
  $E_{G,Ad}=6.83±0.05 eV$ of liquid water are in excellent agreement
  with recent information from theoretical and experimental works.


From the introduction: 


  It is generally accepted that water canbe  described  as  a  very 
  large  band-gap  amorphous semiconductor.11,17 However, it is not
  obvious that the band-gap of liquid water can be uniquely associated
  with an optical vertical excitation process, where the gap is
  defined simply as the highest occupied molecular orbital-lowest
  unoccupied molecular orbital HOMO-LUMO energy difference. As recently pointed out 
  by Coeet  al.,3 the reactive nature of electronically excited water
  molecules,18 the reorganization of water molecules around charged
  species in liquid phase, and the observed photophysics of anionic
  defects known as the anion problem 4 strongly indicate that an
  adiabatic route can be defined for accessing the conduction-band edge
  in liquid phase. Moreover, given that the time scale ofthe solvent
  relaxation is much larger than the vertical process, the adiabatic
  band gap of liquid water cannot be determined vertically. 


Reference
[1] Cabral do Couto, Estácio, and Costa Cabral J. Chem. Phys.123, 0545102005