The structural, electronic, optical, and photocatalytic properties of out-of-plane and in-plane heterostructures of transition metal dichalcogenides are investigated by (hybrid) first principles calculations. The out-of-plane heterostructures are found to be indirect band gap semiconductors with type-II band alignment. Direct band gaps can be achieved by moderate tensile strain in specific cases. The excitonic peaks show blueshifts as compared to the parent monolayer systems, whereas redshifts

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... ccur when the chalcogen atoms are exchanged along the series S-Se-Te. Strong absorption from infrared to visible light as well as excellent photocatalytic properties can be achieved.