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

Electronic properties of water clusters ( H 2 O ) 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 3 a 1 and 1 b 1 valence bands. When long-ranged polarization effects are taken into account by the introduction of embedding charges, the DOS associated with 3 a 1 orbitals is significantly enhanced. In agreement with valence-band photoelectron spectra of liquid water, the 1 b 1 , 3 a 1 , and 1 b 2 electron binding energies in water aggregates are redshifted by ∼ 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 ( 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.