  Hexagonal boron nitride (h-BN) is a promising platform for quantum
information processing due to its potential to host optically active defects
with attractive optical and spin properties. Recent studies suggest that carbon
trimers might be the defect responsible for single-photon emission in the
visible spectral range in h-BN. In this theoretical study, we combine group
theory together with density functional theory (DFT) calculations to predict
the properties of the neutral $\text{C}_\text{2}\text{C}_\text{N}$ carbon
trimer defect. We find the multi-electron states of this defect along with
possible radiative and non-radiative transitions assisted by the spin-orbit and
the spin-spin interactions. We also investigate the Hamiltonian for external
magnetic field and ground-state hyperfine interactions. Lastly, we use the
results of our investigation in a Lindblad master equation model to predict an
optically detected magnetic resonance (ODMR) signal and the $g^2(\tau)$
correlation function. Our findings can have important outcomes in quantum
information applications such as quantum repeaters used in quantum networks and
quantum sensing.
