Stability of hydrogenated group-IV nanostructures: magic structures of diamond nanocrystals and Silicon quantum dots

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We have developed an effective model to investigate the energetic stability of hydrogenated group-IV nanostructures, followed by validations from first-principles calculations. It is found that the Hamiltonian of XₘHₙ (X=C, Si, Ge and Sn) can be expressed analytically by a linear combination of the atom numbers (m, n), indicating a dominating contribution of X-X and X-H local interactions. As a result, we explain the stable nanostructures observed experimentally, and provide a reliable and efficient technique of searching the magic structures of diamond nanocrystals(Dia-NCs) and Silicon quantum dots(SiQDs).