Theoretical and Computational Studies on Growth Patterns of Silicon and Germanium Clusters and Reaction Mechanisms of Metal/Oxygen

Abstract: Nano- semiconductor materials are an important member of the nanomaterial family. When the size of materials is reduced to a nano-scale, it will show a lot of marvellous physical and chemical properties. The main goals of nanomaterial research are to synthesize, design, and analyze the micro-structural materials with special functions. Clusters, as a transition state from molecular to macroscopic materials, have attracted much attention and interest in both theoretical and experimental studies. The structural and property changes of clusters with cluster size can reflect the micro to macro transformation at some extent. In recent years, the studies of clusters have got rapid development.In this thesis, we have investigated semiconductor silicon and germanium clusters using the genetic algorithm (GA) with TB (tight-binding) method and density functional theory (DFT) calculations. We try to determine the most stable geometries of Si and Ge clusters, and explore their growth patterns. The energies, HOMO-LUMO gaps, occupations on HOMO shells, densities of states, ionization potentials, IR vibrational spectra, fragmentation behaviors, and mobilities of cluster ions have been studied. On other hand, the reaction mechanisms of Ti, Na with O2 were investigated at the MP2/6-311+G(d) level. We try to understand the optimal reaction pathways of alkali and transitional metal atoms with O2, and the effect of a negative charge on the reaction barriers and pathways.The main results are listed as follows:(1) We performed an unbiased search for low-energy structures of medium-sized neutral Sin and Gen clusters (n = 25 ~ 33) using a genetic algorithm (GA) coupled with tight-binding (TB) interatomic potentials. The structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Sin and Gen clusters of n = 25 ~ 29 as compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Sin and Gen (n = 29 ~ 33) and their relative stabilities, and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Sin (n = 25 ~ 33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE calculated results. In the size range of 25 ~ 33, the corresponding Gen clusters hold the prolate growth pattern. The changes of small cluster structures from the free standing states to the building blocks of large clusters, were also studied.(2) The lowest-energy structures of Ge2-Ge33 have been optimized using DFT method. The properties of the germanium clusters including binding energies, second differences in energy, HOMO-LOMO gaps, and especially fragmentation energies and fragmentation behaviors have been studied. Our calculation results show that Ge6, Ge7, and Ge10 species display large abundances in the fragmentation products. According to the large fragmentation energies of the small germanium clusters with n≤11 and the small fragmentation energies of the medium-sized clusters with 11 < n≤33, we can conclude that the germanium clusters with 11 < n≤33 can be easily dissociated into small stable germanium clusters. Such dissociations would occur successively until the sizes of fragmentation products are reduced to n≤11. The present calculated results and analyses are consistent with the experimental observations of photo-ionization mass spectra. (3) We have performed DFT calculations to study the structure and stability of the Si70 cluster. The results from the density functional theory (DFT) calculation with BLYP exchange-correlation functional suggest that a bulk-fragment Si70 isomer is the most stable structure, in contrast to the cage structure of Si60, showing that the transition from cage structure to bulk-like motif for silicon clusters would require only about 70 atoms. In addition, an endohedral fullerene of Si16@Si54 was found to be competitive to bulk-like Si70 if the PBE functional is used. The calculated density of states, IR vibration spectra, ionization potential (IP) and inverse motilities were also calculated and discussed.(4) The reaction mechanisms of Ti, Na with O2 were investigated at the MP2/6-311+G(d) level. Ti and Na atom were assumed to approach O2 in the manner of horizontally or vertically with respect to the O-O bond, respectively. The binding energy and the charge curves for each reaction pathway have been analyzed in detail, to validate the optimal reaction mode. The vertical pathway is shown to be more favorable than the horizontal one. Both neutral Ti/Na + O2 and anionic (Ti/Na + O2)– systems were considered. The reaction of metal atom (Ti and Na) with O2 is easier for negatively charged system (Ti/Na + O2)– than for the neutral Ti/Na+O2. Meanwhile, the calculated results show that Ti atom prefers to react with the singlet O2 in both neutral and negatively charged systems. Na is easy to react with the singlet O2 in the neutral system, but with triplet O2 in negatively charged system. The potential energy surfaces of Ti with O2 reaction were also calculated at CCSD(T)/6-311++G(3df)//MP2/6-311+G(d) for Ti + O2 and (Ti + O2)– systems…
Key words: Theoretical Calculations; Semiconductor Clusters; Stable Structures; Growth Patterns; Electronic Properties; Reaction Mechanisms of Metal with O_2

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