In this study, density functional theory (DFT)-based calculation has been performed on activated carbon sheet doped with silicon atom. In a two-dimensional activated carbon sheet, carbon atoms are replaced by silicon atom and the structural and electronic properties are investigated. The result of structural analysis explains the depth of an activated carbon (AC) sheet, total width as well as changes in the bond lengths with the doping of Siatoms. AcSi$_1$ (single silicon-doped activated carbon) and AcSi$_2$ (double silicon-doped activated carbon) exhibit lesser binding energy than pristine AC sheet and AcSi$_3$ (triple silicon-doped activated carbon). The result of the projected density of states (PDOS) explains s–p hybridisation of all the systems. The analysis of crystal orbital overlap population (COOP) explains the antibonding states in all the systems. There is also a probability to get higher values of transport properties in pristine sheet and AcSi$_3$ sheet rather than in AcSi$_1$ and AcSi$_2$ sheets.

In an attempt to analyse how the properties evolve with the cluster size, we report the results of a first principle density functional study on the electronic structures and properties of (BCN)$_x$ clusters (where x = 1 to 5) as well as (BCN)$_{12}$ nanotube. We have investigated geometries of (BCN)$_x$ and their isomers at the B3LYP/6-311G(d) level of theory and their vibrational as well as optical spectra. Their relative stability is discussed by calculating the binding energies. The electronic properties of (BCN)$_x$ clusters and the nanotube are analysed by the frontier orbitals and density of state curves. The frontier orbital energy gap of (BCN)$_{12}$ nanotube is found to be comparable to carbon nanotube but much small as compared to BN nanotube. Various electronic parameters of (BCN)$_x$ clusters have been calculated and their variation with the increase in x has been analysed. The study should be useful in the design of hybrid BCN-based nanostructures for possible applications analogous to purely carbon-based nanostructures.