In this work, novel two-dimensional BC$$_2$$
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X (X = N, P, As) monolayers with X atoms out of the B–C plane, are predicted by means of the density functional theory. The structural, electronic, optical, photocatalytic and thermoelectric properties of the BC$$_2$$
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X monolayers have been investigated. Stability evaluation of the BC$$_2$$
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X single-layers is carried out by phonon dispersion, ab-initio molecular dynamics (AIMD) simulation, elastic stability, and cohesive energies study. The mechanical properties reveal all monolayers considered are stable and have brittle nature. The band structure calculations using the HSE06 functional reveal that the BC$$_2$$
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N, BC$$_2$$
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P and BC$$_2$$
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As are semiconducting monolayers with indirect bandgaps of 2.68 eV, 1.77 eV and 1.21 eV, respectively. The absorption spectra demonstrate large absorption coefficients of the BC$$_2$$
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X monolayers in the ultraviolet range of electromagnetic spectrum. Furthermore, we disclose the BC$$_2$$
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N and BC$$_2$$
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P monolayers are potentially good candidates for photocatalytic water splitting. The electrical conductivity of BC$$_2$$
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X is very small and slightly increases by raising the temperature. Electron doping may yield greater electric productivity of the studied monolayers than hole doping, as indicated by the larger power factor in the n-doped region compared to the p-type region. These results suggest that BC$$_2$$
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X (X = N, P, As) monolayers represent a new promising class of 2DMs for electronic, optical and energy conversion systems.