Stable hydrogenated graphene edge types: Normal and reconstructed Klein edges

Hydrogenated graphene edges are assumed to be either armchair, zigzag, or a combination of the two. We show that the zigzag is not the most stable fully hydrogenated edge structure along the < 2 (1) over bar(1) over bar0 > direction. Instead hydrogenated Klein and reconstructed Klein based edges are found to be energetically more favorable, with stabilities approaching that of armchair edges. These new structures unify graphene edge topology, the most stable flat hydrogenated graphene edges always consisting of pairwise bonded C2H4 edge groups, irrespective of the edge orientation. When edge rippling is included, CH3 edge groups are most stable. These new fundamental hydrogen-terminated edges have important implications for graphene edge imaging and spectroscopy, as well as mechanisms for graphene growth, nanotube cutting, and nanoribbon formation and behavior.