Atomically thin MoS2 has emerged to be promising for photocatalytic water splitting benefiting from its suitable geometrical and electronic structure for light harvesting. A better understanding of how water molecules affect the band edge levels of MoS2 is critical for promoting the interfacial reactivity. Here we determine the structures of water monolayers on MoS2 using global optimizations achieved by molecular dynamics in combination with local minimization. It is shown that cyclic water clusters are formed on surface through hydrogen-bonding network. The absolute band edge positions are explored taking into account the derivative discontinuity of the exchange-correlation functional. Shifts in band edges are observed with the increase in H2O coverage while band gaps tend to be slightly decreased. In particular, the band alignment relative to water redox potentials has been investigated in detail. We find that the dimer configuration is likely to suppress the hydrogen evolution reaction (HER), while the polygon clusters lift the conduction band by 0.2-0.7 eV and thus they would enhance HER. This effect is explained in terms of the linear dependence of band edge offset on interface electric dipole arising from water assemblies.

We present an ab initio study on quasiparticle (QP) excitations and excitonic effects in two-dimensional (2D) GaN based on density-functional theory and many-body perturbation theory. We calculate the QP band structure using GW approximation, which generates an indirect band gap of 4.83 eV (K→Γ) for 2D GaN, opening up 1.24 eV with respect to its bulk counterpart. It is shown that the success of plasmon-pole approximation in treating the 2D material benefits considerably from error cancellation. On the other hand, much better gaps, comparable to GW ones, could be obtained by correcting the Kohn–Sham gap with a derivative discontinuity of the exchange–correlation functional at much lower computational cost. To evaluate excitonic effects, we solve the Bethe–Salpeter equation (BSE) starting from Kohn–Sham eigenvalues with a scissors operator to open the single-particle gap. This approach yields an exciton binding energy of 1.23 eV in 2D GaN, which is in good agreement with the highly demanding GW-BSE results. The enhanced excitonic effects due to reduced dimensionality are discussed by comparing the optical spectra from BSE calculations with that by random-phase approximation (RPA) for both the monolayer and bulk GaN in wurtzite phase. Additionally, we find that the spin–orbit splitting of excitonic peaks is noticeable in 2D GaN but buried in the bulk crystal.