  A recent study associate carbon with single photon emitters (SPEs) in
hexagonal boron nitride (h-BN). This observation, together with the high
mobility of carbon in h-BN suggest the existence of SPEs based on carbon
clusters. Here, by means of density-functional theory calculations we studied
clusters of substitutional carbon atoms up to tetramers in hexagonal boron
nitride. Two different conformations of neutral carbon trimers have zero-point
line energies and shifts of the phonon sideband compatible with typical
photoluminescence spectra. Moreover, some conformations of two small C clusters
next to each other result in photoluminescence spectra similar to those found
in experiments. We also showed that vacancies are unable to reproduce the
typical features of the phonon sideband observed in most measurements due to
the large spectral weight of low-energy breathing modes, ubiquitous in such
defects.
