In this thesis, we study surface chemistry of colloidal quantum dots and nanoscale friction of graphene by investigating their surface properties using first-principles density-functional theory calculations. For colloidal quantum dots, our calculation results show that cation-rich surfaces are necessary for proper ligand-surface coordination to be stabilized. In addition to ligand-surface coordination, the cation-rich surface stabilization is affected by steric hindrance between coordinating ligands. For IV-VI colloidal quantum dots, the steric hindrance between passivating ligands has influence on shape transition from oleate-capped octahedron to cuboctahedron truncated with (100) surface that prone to surface oxidation. The shape transition leads to size-dependent air-stability of IV-VI colloidal quantum dots. For graphene, we examine nanoscale friction properties of chemically modified graphene, epitaxial graphene on SiC(0001), and water-intercalated graphene on mica. By calculating elastic properties of graphene and investigating 3D/2D contact through first-principles calculations and contact mechanics theory, we find that nanoscale frictional energy of graphene is mainly dissipated by out-of-plane bending deformation of graphene and shear deformations between graphene and substrate. In addition, for water-intercalated graphene, we propose that the increased friction by water layer is attributed to phonon excitation enhancement and improved energy transfer based on calculated phonon properties.