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Two-dimensional semiconductor materials with proper band gap can expand the optical absorption into visible and even infrared regions and have been proposed as the photocatalytic candidates for clean energy conversion and environmental pollution. Based on density functional theory, we investigate a new family of two-dimensional materials halogen-substituted graphdiyne (H-GDY, H=F, Cl, Br, and I). H-GDY is a new porous carbon-rich framework composed of 1,3,5-trihalogen benzene rings and butadiyne linkages. These H-GDY monolayers possess excellent mechanical, dynamic and thermal stabilities as demonstrated by elastic constant, cohesive energy, ab initio molecular dynamics simulation, and phonon dispersion. More significantly, these H-GDY monolayers are nonmagnetic semiconductors with wide-band-gap energy of 3.13, 2.82, 2.80, and 2.70 eV for F-GDY, Cl-GDY, Br-GDY, and I-GDY, and display good optical absorption in the visible region. Furthermore, all these H-GDY monolayers have suitable band edge for full water-splitting. Our theoretical investigation not only broaden GDY family, but also provides promising photocatalysts for water-splitting. [ABSTRACT FROM AUTHOR]