Cluster science is devoted to understanding the size dependent changes in fundamental properties of materials, bridging the gap between isolated molecules or small molecules and bulk phases. With the vast application prospects of nanoparticles, understanding the atomic aggregation process, configuration, and stability has become an important goal for experimental and theoretical researches. New physical and chemical properties emerge when the size of a material becomes smaller and smaller, and down to nanoscale. Illustrating the evolution from the molecular to bulk behavior with increasing the cluster size is very important for understanding nanotechnology principles and applications, especially for material selection and their design. Both silicon oxide and titanium dioxide are important materials for various applications. Silicon is the second most abundant element on earth, commonly occurring as oxide. Because of its natural abundance, it has already been exploited for numerous applications. Furthermore, silicon oxide shows immense potential for applications in electronic devices, optics, glass, thin film synthesis and so on. Silicon monoxide clusters have drawn a surge of research interests soon after the uncovering of the crucial role played by small (SiO)n clusters in inducing the formation of silicon nanowires (SiNWs) at the initial stages. [N. Wang, Y. H. Tang, et al. Physical Review B 1998, 58, R16024] Titanium dioxide is an important material for various applications including electronic devices, polluting compounds decomposition, medical bio-engineering, solar energy conversion and water dissociation. Therefore, deep researches of the clusters of silicon oxide and titanium dioxide are very necessary. In this thesis, we study the electronic and vibrational properties of the stable isomers of (SiO)n(0,±) (n=2-7) clusters and the energetics of dissociative adsorption of water on small TiO2 clusters. In chapter 1, we first introduce the research background about nanomaterials. We discuss the novel properties of nanomaterials as well as their promising potential applications. Nanoclusters are very important for understanding the formation of the initial stage of different materials and nanoclusters also have some special properties which are far better than other materials. Here, we focused on the research of silicon oxide and titanium oxide clusters by first reviewing the latest research results on silicon oxide and titanium oxide nanomaterials. In chapter 2, we introduce the basic theory of quantum physics, quantum chemistry calculations, and related computational methods, such as Hartree-Fock theory, perturbation theory. We also introduce the density functional theory (DFT), theory of molecular orbital and density of states. The theory of vibrational spectrum calculations is discussed with focus on infrared spectrum and Raman spectrum in this chapter. And we further discussed the important applications of vibrational spectra in experimental and theoretical researches. In chapter 3, DFT based first-principles calculations have been performed to explore the stable configurations, electronic structures, and vibrational spectra of neutral and charged silicon monoxide clusters (SiO)n(0,±) (n=2-7), which act as precursors in the synthesis of silicon nanowires. Adiabatic electron affinity (AEA), vertical electron affinity (VEA), adiabatic ionization potential (AIP) and vertical ionization potential (VIP) have been calculated to compare with the available experimental results and provide useful information for the future experiment. Our theoretical results of AEA and VEA confirm the findings of photoelectron spectroscopy [J. S. Anderson and J. S. Odgen, J. Chem. Phys. 1969, 51, 4189]. The calculated vibrational spectra along with IR absorption intensities and Raman activities provide unique spectral information on the chemical bonding, which can be used for comparison with experiments. As the number of SiO units n increases, infrared (IR) spectra of (SiO)n± and Raman spectra of (SiO)n- showed evident blue shift and Raman spectra of (SiO)n demonstrated red shift. Moreover, our results reveal that most of the neutral silicon monoxide clusters have strong IR intensities and weak Raman activities, while most of the anionic counterparts have relatively weak IR intensities and strong Raman activities respectively. Our calculated IR and Raman spectra of (SiO)n+ (n=3-5) agree well with the previous findings [E. Garand, D. Goebbert, et al. Phys. Chem. Chem. Phys. 2008, 10, 1502]. The possible coexisting low-lying isomers of some (SiO)n(0,±) species were also studied to show their contributions to the IR and Raman spectra. The geometry of small clusters TinOm (n=2, m=1-4; n=3-4, m=n-2n) were calculated using DFT in chapter 4. The IR and Raman spectra of the global minima of TinOm (n=2,m=1-4; n=3-4, m=n-2n) were investigated by theoretical calculation. Our results showed that the IR spectra of TinOm (m≠2n) clusters mainly distribute at the range of 600-900cm-1 and Raman spectra of TinOm (m≠2n) clusters mainly distribute at the range of 300-800cm-1; as for TinOm (m=2n) clusters, both their IR and Raman spectra mainly locate at the range of 700-1100 cm-1. The novel structures we reported can provide the basis for further studies of the effect of nanostructure on adsorption, photochemistry, and nucleation of small titanium oxide material. In chapter 5, we performed systematic first principles calculations based on DFT to probe the energetics of dissociation of water molecules on small (TiO2)n (n=3, 4, 6, 8, and 10) clusters. We found that the (TiO2)n clusters have a strong ability to adsorb water molecules and the dissociative adsorption of water molecules on the surface of (TiO2)n clusters with a three-step process is energetically more favorable than the same on the surfaces of titanium oxide. Owing to the steric effect, the number of water molecules dissociating on (TiO2)n cluster surface varies inversely with the cluster size. Reaction profile and the selected intermediate states for water dissociation on (TiO2)n clusters were given and were compared with the published results of water dissociation on rutile TiO2 (110). Our results suggested that the larger the size of (TiO2)n clusters, the smaller the energy barriers in water dissociation process. The most important thing is that the process of H2O dissociation on the surface TiO2 (110) is reversible [Y. Du, N. A. Deskins, et al. Physical Review Letters 2009, 102, 096102], while the process of H2O dissociation on the surface of (TiO2)n clusters is irreversible according to our investigation. Charged titanium dioxide clusters have the strong ability to adsorb and dissociate water molecules similar to neutral ones. Moreover, IR and Raman spectra of water molecule, (TiO2)6 and the stable configuration of water molecule molecularly or dissociatively adsorbed on (TiO2)6 were performed in order to provide useful data for a direct and meaningful comparison with experimental results. Our research results indicate a higher efficiency of small clusters of titanium oxide in dissociating water molecules than its low index surfaces of bulk terminated. In chapter 6, a conclusion of the whole thesis will be given.