Ab initio Electronic Structure of Liquid Water

Abstract

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio pathintegral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at −9.4 and −0.5 eV with respect to the vacuum level, respectively. DOI: 10.1103/PhysRevLett.117.186401 Liquid water is such a ubiquitous substance that it has been the subject of upsurging research efforts for the past 30 years. Of particular importance is the electronic structure of liquid water, the significance of which has been recently highlighted in clean-energy technologies through semiconductor-assisted artificial photosynthesis [1,2]. A good understanding of the electronic structure of water is a prerequisite toward the design of photocatalytic systems with high catalytic activity.The extended hydrogen-bond network of liquid water gives rise to the formation of electronic bands. The valence band maximum (VBM) is characterized by the localized 2p z electrons of O atoms. The conduction band minimum (CBM) derives from the antibonding orbitals of O-H bonds, and is at variance much more extended. Experimentally determined positions of these band edge states have yet to reach a consensus. Early ultraviolet (UV) photoemission experiments by Delahay and collaborators reported photoemission threshold energies of 9.3 [3] and 10.06 eV [4]. More recent work by Winter et al. employed the liquid microjet technique and found a threshold energy of 9.9 eV [5]. For the unoccupied states, inverse photoemission and photoionization measurements placed the CBM at −1.2 eV with respect to the vacuum level [6,7]. This value was later revised to −0.74 eV, in light of the observation that excess electrons in liquid water could be initially captured in a localized trap state below the actual CBM [8]. Altogether, these measurements allude to a band gap of 8.7 eV, but associated with a sizable uncertainty of AE0.6 eV.To shed light on the electronic structure of water, it is necessary to resort to a fully ab initio method, which avoids the use of experimental input. Ab initio molecular dynamics (MD) simulations based on Kohn-Sham density-functional theory (DFT) have been extensively carried out to understand the structural and dynamical properties of water and of aqueous solutions. It is well recognized that the use of semilocal density functionals precludes a faithful description of the electronic structure and the predicted band gap of liquid water is apparently too small [9,10]. Hybrid functionals improve the description of the electronic structure [10], but the mixing parameter of the Fock exchange is not known a priori without the input from experiment ...

Ab initio theory and modeling of water

“…The widths and intensities of peaks in the computed DOS are also, respectively, narrower and higher than those in the experimental DOS. In fact, DFT is not rigorous for photoemission spectra and does not include lifetime broadening; NQEs, however, can additionally broaden the DOS, bringing the resulting widths and intensities in closer agreement with the experiment (44). NQEs can be accounted for within the Feynman discretized path-integral approach (27,35,44).…”

Nuclear quantum effects of light and heavy water studied by all-electron first principles path integral simulations

“…This delicate inconsistency might be improved by the use of more elaborate exchange-correlation functionals such as the hybrid functionals. 19,20 However, such a PIMD calculation will require a huge computational effort, especially in the present calculation scheme employing the all-electron PAW scheme and the explicit imaginary-time representation based on Suzuki-Trotter expansion. On the other hand, the third peak of the oxygen-hydrogen radial distribution and the second peak of the hydrogen-hydrogen radial distribution are slightly shortened in agreement with the experimental observation.…”

“…2), van der Waals corrections 9,13,14,[25][26][27][28] (for a recent review, see also, e.g., Ref. 2), or post Hartree-Fock theories 13,[17][18][19]29,30 used instead. Meanwhile other errors may arise from sampling issues, 31,32 small system sizes, 6,31 the choice of pseudopotentials(see, e.g., Ref.…”

“…Thereafter first principles PIMD simulations were used to study the structure of liquid H 2 O, the structure of H 2 O and D 2 O in the liquid-vapor interface, 47,48 and the fractionation ratio of H 2 O and D 2 O of liquid and vapor. 49,50 In recent first principles PIMD simulations of liquid H 2 O, the focus was on the nuclear quantum effect on the hydrogen bond structure and its impact on the electronic structure, 19,20 etc. However "on-the-fly" first principles PIMD simulations on the structural isotope effect of H 2 O and D 2 O in the bulk liquid phase have not been presented since the first report in 2003.…”

Decisive role of nuclear quantum effects on surface mediated water dissociation at finite temperature

“…Anharmonic connections among different minima in the potential energy surface call for approaches beyond the harmonic approximation. Moreover, the structural, dynamic, and electronic properties of water are known to be heavily affected by the quantum nature of the nuclei even at room temperature [7][8][9][10][11][12][13][14] . In fact, nuclear quantum effects (NQE) have also been shown, through several experiments and a few theoretical works, to play a crucial role in the behaviour of organic adsorbates on metallic surfaces [15][16][17][18][19][20][21][22][23][24] .…”