20:T4c3,Quasiparticle band structures and optical properties of MoS${}_{2}$, MoSe${}_{2}$, MoTe${}_{2}$, WS${}_{2}$, and WSe${}_{2}$ monolayers are studied using the GW approximation in conjunction with the Bethe-Salpeter equation (BSE). The inclusion of two-particle excitations in the BSE approach reveals the presence of two strongly bound excitons ($A$ and $B$) below the quasiparticle absorption onset arising from vertical transitions between a spin-orbit-split valence band and the conduction band at the $K$ point of the Brillouin zone. The transition energies for monolayer MoS${}_{2}$, in particular, are shown to be in excellent agreement with available absorption and photoluminescence measurements. Excitation energies for the remaining monolayers are predicted to lie in the range of 1--2 eV. Systematic trends are identified for quasiparticle band gaps, transition energies, and exciton binding energies within as well as across the Mo and W families of dichalcogenides. Overall, the results suggest that quantum confinement of carriers within monolayers can be exploited in conjunction with chemical composition to tune the optoelectronic properties of layered transition-metal dichalcogenides at the nanoscale.21:T47a,Two-dimensional (2D) materials with the vertical intrinsic electric fields show great promise in inhibiting the recombination of photogenerated carriers and widening light absorption region for the photocatalytic applications. For the first time, we investigated the potential feasibility of the experimentally attainable 2D M₂X₃ (M = Al, Ga, In; X = S, Se, Te) family featuring out-of-plane ferroelectricity used in photocatalytic water splitting. By using first-principles calculations, all the nine members of 2D M₂X₃ are verified to be available photocatalysts for overall water splitting. The predicted solar-to-hydrogen efficiency of Al₂Te₃, Ga₂Se₃, Ga₂Te₃, In₂S₃, In₂Se₃, and In₂Te₃ are larger than 10%. Excitingly, In₂Te₃ is manifested to be an infrared-light driven photocatalyst, and its solar-to-hydrogen efficiency limit using the full solar spectrum even reaches up to 32.1%, which breaks the conventional theoretical efficiency limit.

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