  Single photon emitters in hexagonal boron nitride have been extensively
studied recently. Although unambiguous identification of the emitters is still
under intense research, carbon related defects are believed to play a vital
role for the emitter producing zero-phonon-lines in the range of $1.6$ to
$2.2$~eV. In this study, we systematically investigate two configurations of
carbon-vacancy defects, VNCB and CNVB, by means of density functional theory
calculations. We calculated the reaction barrier energies from one defect to
the other to determine relative stability. We find the barrier energies are
charge dependent and CNVB could easily transform to VNCB in neutral and
positive charge states while it is stable when negatively charged. Formation
energy calculations show that the VNCB is the dominant defect over CNVB.
However, neither VNCB nor CNVB has suitable fluorescence spectra that could
reproduce the observed ones. Our results indicate that the origin of the
$1.6$-to-$2.2$-eV emitters should be other carbon-related configurations.
