The electronic structure of liquid water within density-functional theory

In the last decade, computational studies of liquid water have mostly concentrated on ground-state properties. However, recent spectroscopic measurements have been used to infer the structure of water, and the interpretation of optical and x-ray spectra requires accurate theoretical models of excited electronic states, not only of the ground state. To this end, we investigate the electronic properties of water at ambient conditions using ab initio density-functional theory within the generalized gradient approximation (DFT/GGA), focusing on the unoccupied subspace of Kohn-Sham eigenstates. We generate long (250ps) classical trajectories for large supercells, up to 256 molecules, from which uncorrelated configurations of water molecules are extracted for use in DFT/GGA calculations of the electronic structure. We find that the density of occupied states of this molecular liquid is well described with 32-molecule supercells using a single k point (k=0) to approximate integration over the first Brillouin zone. However, the description of the unoccupied electronic density of states (u-EDOS) is sensitive to finite size effects. Small, 32-molecule supercell calculations, using the Γ-point approximation, yield a spuriously isolated state above the Fermi level. Nevertheless, the more accurate u-EDOS of large, 256-molecule supercells may be reproduced using smaller supercells and increased k-point sampling. This indicates that the electronic structure of molecular liquids such as water is relatively insensitive to the long-range disorder in the molecular structure. These results have important implications for efficiently increasing the accuracy of spectral calculations for water and other molecular liquids.