By first-principles calculations, we have performed extensive studies for the structures of Pb on Si(111) at low coverage. Relative stabilities between these low coverage phases were compared and comparison with scanning tunneling microscopy (STM) experiments were made. By tight-binding molecular dynamics simulations, we discovered that there are significant atomic rearrangements at the Pb/Si interface of the Pb islands on Si(111), which can lead to a change in the electronic structures of ultra-thin Pb films predicted by quantum size effect. In particular, the electronic behavior of nano-scale Moire pattern observed in STM for ultra-thin Pb films on Si(111) support our results. By first-principles calculations, the energetics and dynamical rocking behavior of Pb and Sn dimers on Si(100) were studied. We concluded that Pb and Sn dimers and dimer chains on Si(100) observed in STM experiments are composed of pure metal dimers instead of mixed Pb-Si or Sn-Si dimers due to a lack of favorable intermixing channel. The diffusion of Pb adatoms and dimers on Si(100) surface were studied as well. A construction of a minimal basis set of highly localized quasiatomic orbitals (QUAMBOs) for Mo were described. By using the first-principles eigenstates as input, the orbitals are constructed to look similar to the free-atomic orbitals, but are able to deform to adapt to the bonding environment and reproduce the occupied-states electronic properties of the system from which the orbitals are derived. The QUAMBOs can be used to analyze the chemical bonding for the self-consistent eigenstates obtained from first-principles calculations. We also performed a global optimization study on the structure of [110]-oriented H-passivated Si nanowires using a genetic algorithm. We found that the structures of H-passivated Si nanowires are bulk-like down to sub-nanometer wire dimensions. And structural motifs of "magic" nanowires were recognized with chain-like and hexagonal-shaped cross sections. The first type of magic nanowires has not been experimentally observed yet due to its small diameter, but our model for Si nanowires with hexagonal cross section has consistent dimensions and simulated STM images with the smallest nanowires observed experimentally.