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Structure and stability of small H clusters on graphene

The structure and stability of small hydrogen clusters adsorbed on graphene is studied by means of Density Functional Theory (DFT) calculations. Clusters containing up to six H atoms are investigated systematically -- the clusters having either all H atoms on one side of the graphene sheet (\textit{cis}-clusters) or having the H atoms on both sides in an alternating manner (\textit{trans}-cluster). The most stable cis-clusters found have H atoms in ortho- and para-positions with respect to each other (two H's on neighboring or diagonally opposite carbon positions within one carbon hexagon) while the most stable trans-clusters found have H atoms in ortho-trans-positions with respect to each other (two H's on neighboring carbon positions, but on opposite sides of the graphene). Very stable trans-clusters with 13-22 H atoms were identified by optimizing the number of H atoms in ortho-trans-positions and thereby the number of closed, H-covered carbon hexagons. For the cis-clusters, the associative H$_2$ desorption was investigated. Generally, the desorption with the lowest activation energy proceeds via para-cis-dimer states, i.e.\ involving somewhere in the H clusters two H atoms that are positioned on opposite sites within one carbon hexagon. H$_2$ desorption from clusters lacking such H pairs is calculated to occur via hydrogen diffusion causing the formation of para-cis-dimer states. Studying the diffusion events showed a strong dependence of the diffusion energy barriers on the reaction energies and a general odd-even dependence on the number of H atoms in the cis-clusters.