Theoretical Study On Doped Indium Clusters And (TiO₂)_n Clusters

In recent years, studies on clusters have focused on two major topics. On one hand, clusters are considered to be bridge connecting single atom and bulk system, and the trend in the evolution of their structures and properties with cluster size is systematically examined, which contributes gretaly to deepening our understanding of the growth modes and the underlying microscopic mechanisms of matter from micro- toward macro-scale. On the other hand, magic clusters with exceptional stability, sometimes called superatoms, are extensively searched for, which are expected to act as building blocks in developing cluster-assembled nanostructured materials with special structures and properties.As a powerful analysis tool, theoretical study can provide valuable insight into the microscopic mechanism underlying the experimantal observations, and can explore problems that are not accessible under experimental conditions currently available. One of the major objectives in these studies is to determine the energetically most stable structures of the clusters. With the rapid progress in computer modeling techniques and high performance supercomputers, first-principles-based density functional theory (DFT) has become the prevailing theoretical method in condensed matter physics, quantum chemistry and material science. In this dissertation, the geometric and electronic properties of the doped indium clusters and the structures and photoelectron spectroscopy of (TiO2)n clusters are studied by means of density functional theory.In chapter 1, the fundamental concepts of clusters are briefly introduced, including the definition and important effects of clusters, and magic clusters, etc. Then, an overview is given on the current status and open problems in the study of indium- and aluminium-based clusters as well as titanium oxide clusters.In chapter 2, the development in quantum chemistry, the basic framework of DFT and its recent progress are briefly introduced. For DFT, emphasis is paid on the establishment of the basic theory, and the search for a better exchange-correlation functional. Since the accurate form of the exchange-correlation functional is not available up to date, many approximate types of exchange-correlation functionals have been proposed, from the earliest local density functionals (LDF), to generalized gradient functionals (GGA) and hybrid density functionls, and the more recent self-interaction correction and many types of new and more complicated density functionals. All of these enable DFT to provide more and more accurate results. The chapter ends with an introduction to some popular computer modeling codes. Chapter 3 deals with the doped In12X (X=C, Si, Ge, Sn) clusters. In this section, a systematic investigation is performed on the geometric and electronic properties of neutral and anionic In12X (X=C, Si, Ge, Sn) clusters by BLYP and B3LYP density functional methods. The most stable structures of neutral and anionic In12C clusters are found to be of Cs symmetry, while all other In12X (X=Si, Ge, and Sn) clusters have pseudo Dsh structures in both the neutral and anionic charge states. For all In12X (X=C, Si, Ge, Sn) clusters, our calculated adiabatic electron affinities (AEAs) agree well with the experimental data, which indicates that the geometries we optimized for neutral and anionic In12X (X=C, Si, Ge, Sn) clusters are reasonable candidates as the ground-state structures of these clusters. In addition, we found that the energy gaps between the HOMO (highest occupied molecular orbital) and LUMO (the lowest unoccupied molecular orbital) for the neutral In12X (X=C, Si, Ge, Sn) clusters are considerably larger than their anionic counterparts at the BLYP level, implying that the neutral clustes may have remarkably high chemical stability. The calculation of cluster magnetism shows that the magnetic moments of the neutral In12X (X=C, Si, Ge, Sn) clusters are all zero. We thus infer that the electronic structures for these neutral clusters should have closed electronic shells. Further analysis on the electronic structure of the clusters and the partial densities of states for the indium atoms in the clusters indicates that there is strong hybridization between the s and p orbitals of the indium atoms. Therefore the indium atoms in the neutral In12X (X=C, Si, Ge, Sn) clusters should be trivalent. According to the Jellium model, the neutral In12X (X=C, Si, Ge, Sn) clusters would have the electronic configuration of 1s21p61d102s21f142p6, which forms a closed electronic shell and the clusters are thus very stable.In chapter 4, we focus on the geometric and electronic properties of the doped InnM (n=11-15, M=Li, Na, K) clusters. A detailed computational study is carried out to examine the magic stability of InnM clusters using density-functional methods. For all InnM clusters, the M atom is found to be preferably adsorbed on a hollow site and bond to four indium atoms of the Inn cage. Very similar size dependence is observed between InnM and AlnM in electronic properties, including the average binding energy per atom, the HOMO-LUMO gap, the vertical ionization potential (VEA) and the adiabatic electron affinity (AEA). Especially, the In13M cluster is characterized by an electronic shell closure with enhanced stability, a considerably larger HOMO-LUMO gap, higher vertical ionization potential, and lower adiabatic electron affinity as compared with adjacent In12M and In14M clusters, leading to an extraordinarily high stability of the In13M cluster. All of these properties are characteristic of a magic cluster and can be well understood by the Jellium model. Therefore, we strongly suggest that In13M be magic clusters and be promising as building blocks in developing cluster-assembled nanomaterials. Examination of the electron-density distribution and natural bonding orbital (NBO) analysis both lead to the conclusion that the interaction between In13 and M atom is ionic. Further calculation indicates that the AEA of In13 is close to that of an iodine atom, suggesting that In13M could be regarded as an ionic'molecules'in which the In13 subunit would behave like a halogen atom.In chapter 5, we focus on the assignment of photoelectron spectra of the (TiO2)n (n=1-3) clusters. In this portion, using LDF, GGA and time-dependent density functional (TDDFT) methods, we have performed a comprehensive investigation of the (TiO2)n (n=1-3) clusters on their structural and electronic properties, VEA and AEA, excited states, and correlated the calculated excitation energies to the experimental photoelectron spectra (PES). For (TiO2)n clusters with n=1 and 3, we determined their ground-state geometries to be C2v and Cs structures in the neutral and anionic charge states, respectively. For neutral (TiO2)2, the most stable structure has C2h symmetry. For anionic (TiO2)2, two isomers with C2h and C2v symmetries are found to be nearly isoenergetic at the LSDA and CCSD (T) levels. Therefore, they are both competitive candidates for the ground-state structure of (TiO2)2-. Further comparison with experimental data is needed to identify which of these two structures will correspond to the one observed in experiment. To this end, we proceeded to calculate the VEA and AEA values of the clusters. For TiO2 and (TiO2)3, the calculated VEA and AEA values agree well with experimental data. For (TiO2)2, the VEA and AEA obtained with the C2v structure agree well with the experimental data, while those with the C2h structure do not. Thus, we infer that the C2v isomer of (TiO2)2- would correspond to the structure from which the photoexcitation in experimental PES takes place. TDDFT is used to determine the excited states of (TiO2)n (n=1-3) and the calculated excitation energies are in good agreement with the experimental PES, confirming that the ground-state structure of (TiO2)2- corresponds to the C2v one. Therefore, our assignment of PES is reasonable and TDDFT proves to be a good method to calculate the excited states of such clusters.