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We have investigated the structural properties and dynamical stability ofC$_3$N$_2$ hosting hydrogen as a guest atom. The calculations were performedusing the density functional theory (DFT) as implemented in Quantum espressocode. The generalized gradient approximation approach was used throughout thecalculations presented here. We find that the guest atom leaves the latticeconstant of the host almost unchanged. We, therefore, noted that C$_3$N$_2$remains dynamically stable when a single guest atom is inserted into itscage-like structure. We also established that the guest vibrational modes arelow-lying modes that lower the acoustic bandwidth of C$_3$N$_2$.

Ab initio study of structural properties and dynamical stability of C$_3$N$_2$ encapsulating H guest atom