The structure and stability of magic carbon clusters observed in graphene chemical vapor deposition growth on Ru(0001) and Rh(111) surfaces.

To improve the atomically controlled growth of graphene by chemical vapor deposition (CVD), understanding the evolution from various carbon species to a graphene nucleus on various catalyst surfaces is essential. Experimentally, an ultrastable carbon cluster on Ru(0001) and Rh(111) surfaces was observed, while its structure and formation process were still under debate. Using ab initio calculations and kinetic analyses, we disclose a specific type of carbon cluster, composed of a C21  core and a few dangling C atoms, which is exceptional stable in a size range from 21 to 27 C atoms. The most stable one of them, an isomer of C24 characterized by three dangling C atoms attached to the C21 core (denoted as C21-3C), is the most promising candidate of the experimental observation. The ultrastability of C21-3C originates from both the stable core and the appropriate passivation of the dangling carbon atoms by the catalyst surface.