  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
X$_{m}$H$_{n}$ (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).
