  The theoretical framework, which is built from the first-principles results,
is successfully developed for investigating emergent two-dimensional (2D)
materials, as it is clearly illustrated by carbon substitution in silicene.
Computer coding with the aid of VASP in conjunction with data analysis from the
multi-orbital hybridizations [spin configurations] are thoroughly identified
from the optimal honeycomb lattices, the atom-dominated energy spectra, and the
spatial charge density distributions. The atom and orbital-decomposed van Hove
singularities [the net magnetic moments], being very sensitive to the
concentration and arrangements of guest atoms. All the binary 2D silicon-carbon
compounds belong to the finite- or zero-gap semiconductors, corresponding to
the thoroughly/strongly/slightly modified Dirac-cone structures near the Fermi
level. Additionally, there are frequent {\pi} and {\sigma} band crossings, but
less anti-crossing behaviors. Apparently, our results indicate the well-defined
{\pi} and {\sigma} bondings.
