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