The Kohn-Sham density of states and band gap of water: from small clusters to liquid water.

Electronic properties of water clusters (H2O)(n), with n=2, 4, 8, 10, 15, 20, and 30 molecules were investigated by sequential Monte Carlo/density-functional theory (DFT) calculations. DFT calculations were carried out over uncorrelated configurations generated by Monte Carlo simulations of liquid water with a reparametrized exchange-correlation functional that reproduces the experimental information on the electronic properties (first ionization energy and highest occupied molecular orbital-lowest unoccupied molecular orbital gap) of the water dimer. The dependence of electronic properties on the cluster size (n) shows that the density of states (DOS) of small water clusters (n>10) exhibits the same basic features that are typical of larger aggregates, such as the mixing of the 3a1 and 1b1 valence bands. When long-ranged polarization effects are taken into account by the introduction of embedding charges, the DOS associated with 3a1 orbitals is significantly enhanced. In agreement with valence-band photoelectron spectra of liquid water, the 1b1, 3a1, and 1b2 electron binding energies in water aggregates are redshifted by approximately 1 eV relative to the isolated molecule. 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 (V0=-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.