| Metal oxide clusters play an important role in clusters science. The transition metal oxide clusters have been studied since decades, owing to their chemical and physical properties, and their diverse practical applications in inorganic chemistry, catalysis chemistry and electrochemistry. Recently, with the development of actinide chemistry and treatment of nuclear waste, a lot of experimental data about actinide(An) oxide clusters were reported. However, because of the strong relativistic effect and complicated electronic correlation, a deeper theoretical understanding of actinide oxide clusters was unclear. Therefore, in this dissertation we focused on the theoretical studies on geometry structure, electronic structure and chemical bonding in actinide oxide clusters. By using relativistic density functional theory and chemical bonding analysis methods, the relationship between chemical bonding and cluster topology was explored.The AnO22+ / +(An = U, Np, Pu, Am, Cm) is the simplest molecule in actinide oxide, the calculations showed that with atomic number of An element increases, the radii of 5f and 6d orbital became more contract and the bond strength of An-O became more weaken, thus, a turning point was discovered in the change curve of An-O bond length. For dinuclear actinide oxide clusters, the cation effect in geometry structure of clusters was characterized, theoretical results showed that the O22 played a bridge role in hexavalent cluster while the multicenter bond of U-O-U-O connected the two U atoms in pentavalent cluster. The geometry structure, electronic structure and multicenter bonding of hexanulcear clusters [M6(OH) 4O4] L12(M = Ti, Zr, Hf, Rf, Ce,Th, Pa, U, Np, Pu, Am, Cm) were investigated, our calculations revealed that the lowest energy geometry structure of clusters was Td structure, 3 center bond was found in OH-M-M while 4 center bond was found in O-M-M-M, and the origin of the stability of clusters is attributed to the multicenter bonds.We extended our studies to six hexanuclear polyoxometalates [M6O19]2- of the six-valence-electron metals including the d-elements M = Cr, Mo, W, Sg from group 6and the f-elements M = Nd, U. It was shown that the Oh Lindqvist structure of the isolated [M6O19]2- units with hexavalent M elements was only stable for the three heavy transition metals M = Mo, W and Sg. The calculated results suggested that for the 4d, 5d,and 6d metals, the M-(n-1) d radial maxima of Mo, W and Sg overlap and interact well with the dative O-2p lobes of the ligands, giving rise to appreciable σπ overlap bonding that stabilizes the octahedral geometry. In contrast, the M-(n-1)d AOs of Nd and U were radially too diffuse, while the Cr-3d, Nd-4f and U-5f AOs were too contracted for efficient double-sided oxygen interaction, so that weak perturbative interactions of 2nd order Jahn-Teller type determine the structure. Finally, the most stable structures from[(U6O19]2-to [U6O19]8-were determined, and the dependence of the structure on the oxidation state of the metal atoms were investigated. |