Weak interactions including van der Waals force, - electron attraction and H-bonding are important in vast systems such as solution, biology, catalytic procedure, and adsorption or desorption on surface and crystal packing. H-bonds are the source of specific properties of associated liquids, with water being the most popular among them. It relates particularly to biological systems, such as molecular recognition that could be a basis for the creation of life, formation of higher order structures of peptides and nucleic acids, and biochemical processes, in particular the enzymes catalyzed. The - electron attraction plays an important role in the determination of geometry structures of molecules composed of aromatic groups, such as protein folding, heterocyclic molecule with high fluorescence yield applied in organic light-emitting diodes and the carbon nanotube biosensor interaction with biological molecules. In the physisorption type self assembly on metal or semiconductor surface, the weak attraction force is the main attribution to the binding energy. Theoretical studies on these systems should include the weak dispersion energy, which is hard to treat using the conventional Hartree-Fock approach or the density functional theory. This thesis used a self-consistent charge density functional tight-binding (DFTB) approach, complemented by an empirical London dispersion correction (DFTB-D) to study several interesting weak interaction systems. First, the structures and energetics of small water clusters (H2O)n (n=1-6) and their adsorption behavior on graphite surface are discussed. Comparing the results predicted by the DFTB-D and MP2 methods on small water clusters (H2O)n, n=2-6, and fused benzene (fbz)mH2O, it is revealed that the DFTB-D method is reasonably reliable and efficient. The results using DFTB-D method indicates that the water dimer maintains its original structure when adsorbed on a graphite surface. The cyclic trimer, tetramer, and pentamer also maintain their cyclic geometries when they interact with a graphite surface, regardless of their assumed starting orientations. For the hexamer, it is interesting that with the influence of a graphite sheet, the highest energy of the local minimum structure S6 will change to that of the more stable Book-like structure when its starting orientation is perpendicular to the graphite surface. With a special orientation, a Bag structure will also change to a Prism structure. However, most of the starting orientations relative to the graphite surface will keep the water clusters as their original skeleton structure but with a slight distortion. The graphite surface always keeps a perfect planar structure. The binding energy of the water cluster with a graphite surface is only dependent on the number of water molecules that are in the hydrogen bond length range, about 3.0 Å, but it is independent of the water cluster size. These physically adsorbed water clusters show little change in their IR peak position and leave an almost perfect graphite surface. For the methanol cluster adsorbed on graphite surface, its behavior is very similar to the water cluster regarding the binding energy and geometry structure, although the larger size methyl group contributes more attraction energy with graphite surface. After having reexamined the validity and efficiency of DFTB-D method in weak interaction system, we applied the method to study the high fluorescence quantum yield materials, 1,4-bis(benzothiazole-vinyl)benzene (BT) and 2,2,2-(1,3,5-phenylene)tris- [1-phenyl-1H-benzimidazole] (TPBI), which are of promising applications in organic light-emitting diodes devices. It is found that the isolated planar BT molecule will be distorted when it interacts with TPBI through the vdW force. The geometry distortion of BT and its interaction with TPBI are found to play an important role in the luminescence. The distortion of the BT molecule is activated by the TPBI molecule and results blue luminescence around 475 nm. The weak vdW attraction between BT and TPBI adsorbed on graphite surface is found to be slightly larger than that between each of them and the HOPG substrate. The separation of the TPBI + BT mixture on graphite surface is energetically preferred. This fact can partly explain the migration and agglomeration at elevated temperatures, which is believed to be one cause of device degradation. The interaction of biosystems and carbon molecules has attracted considerable attention in recent years. This is partly associated with the practical interest in carbon nanotubes (CNTs), which have much promise in biosensor technology and other applications. The cyclic voltammetry (CV) experiment about the interaction between the CNT and the deep-embedded active group of the redox coenzyme has been reported. It is found that the peak current of the electroactive Flavin adenine dinucleotide (FAD) at single-walled carbon nanotube (SWNT)/GCE (glassy carbon electrodes) is almost 22 times as large as that found at the bare GCE. By using the DFTB-D method, it is shown that the flavin and adenine group of FAD are attracted to the CNT surface but remain at the physisorption distance when FAD interacted with CNT. The configuration with the FAD long axis perpendicular or parallel to the semiconducting (10,0) and metallic (5,5) tube axis are almost energetically degenerated. The density of states (DOS) and projected DOS (PDOS) show that in FAD/(10,0) system, FAD flavin group contributes more components in the band structure at Fermi energy, which enhances its electronic transfer as observed in the CV experiment. The calculations demonstrate that even in the cases of physisorption interaction there is a noticeable influence of the CNT electronic structure and mobility. Self-assembly is a critical and necessary process in living organisms and plays a very important role in chemistry and material science. Now this process has been employed in the so-called “bottom-up” strategy for nanofabrication. Self-assembled monolayers (SAMs) with controlled structure and function are promising candidates in molecular electronic devices, lubrication, wetting, sensors and catalysis. Therefore, understanding the principle of two-dimensional molecular arrangement is the prerequisite for nanodevice development. The structure of SAMs is dominated by molecule-substrate interaction and intermolecular action. Based on the STM studies on the two carboxylic substituted thiophene derivatives, thiophene-2-carboxylic acid (TCA) and thiophene-2,5- dicarboxylic acid (TDA) on Au(111) surface and highly oriented pyrolytic graphite (HOPG), it was observed that the 2D supramolecular self-assemblies of TCA and TDA are highly substrate dependent. Theoretical prediction indicates that the molecule-substrate interaction plays a more important role than intermolecular interaction. While the interaction between molecule and HOPG is weaker, the intermolecular action plays an equal important role as the molecule-substrate interaction for the formation and stability of assembled monolayer.