| Carbon clusters, comprising aggregates up to several carbon atoms,and C70 particles, and carbon nanotubes, have diverse interests in astrophysics and in material science. Recently, experimental and theoretical studies on carbon clusters have attracted a considerable attention, and significant progresses have been made in synthesis and characterization of carbon clusters and in investigation of their physical and chemical performances. With research deepening, fundamental questions concerning carbon clusters, such as formation mechanism of C60 and carbon nanotubes and identification of DIBs carriers, etc, become increasing important.In the present work, structures, stabilities, and spectroscopic features of carbon clusters have been investigated by quantum chemistry calculations. Our work will focus in three aspects:1. Theoretical study on linear carbon chainsNew developments in matrix isolation spectroscopy have led to spectroscopic characterization of mass-selected carbon clusters HCnH, C2nH and C2n-1N in the gas phase. Among the numerous observed bands, only a few bands of specific species were assigned, both experimentally and theoretically. A precise understanding of these electronic spectra remains open. Using DFT calculations, we optimized geometries of carbon chains in their ground states, and calculated their vibrational frequencies. Vertical excitation energies for the transition of HC2nH (n=l-5) and for the transition of HC2n+1H (n=2-5) have been calculated by the time-dependent density functional theory and ab initio second order multiconfiguration perturbation method. On the basis of present calculations, explicit size-dependent expressions for the wavelength of excitation energies in linear polyynes are suggested. Present calculations show that the odd-numbered polyynes has a linear dependence as =A + Bn, while there is a nonlinear size dependence for the even-numbered polyynes:Such analytical -n relationships work very well for prediction of electronic excitation energies in linear polyynes. Further analyses reveal that such significant difference in spectroscopic feature of both series can be ascribed to distinct bonding features between the ground and excited states in the odd- and even-numbered polyynes.Similar theoretical treatments are extended to C2nH and C2n-1N, the size dependence of vertical excitation energies for transitions of C2nH and C2n-1N have been discussed.Static longitudinal polarizabilities of HC2nH and HC2n+1H have been calculated by ab initio Hartree-Fock and B3LYP methods with several basis sets. On the basis of HF calculations, simple exponential and logarithmic expressions are proposed for the size dependences of longitudinal polarizabilities of polyynes HC2nH and HC2n+iH. The logarithmic expression is A(n) = anln(bn2+c). In comparison with other theoretical treatments, it is found that the logarithmic expression has better extrapolation behavior than the exponential one A{n) = anb.Density functional theory calculations with the B3LYP functional are used to study the structure and stabilities of C5H2 isomers and possible isomerization mechanisms on the triplet and singlet potential energy surfaces. Calculated results show that isomerization of C5H2 is likely to occur on the triplet potential energy surface while direct conversions of the singlet C5H2 isomers via 1,3-hydrogen migration transition states are extremely difficult dynamically.2. The optimization of carbon clusters with genetic algorithm (GA)Geometrical optimization of Cn (n=2-30) has been performed with a GA method. A modified Brenner's potential energy surface (PES) of carbon species, which omits the conjugate-compensation term F(ij,k) in the original form, is employed in the present study. Our results show that Cn is a linear chain for n<5, and a single ring from C6 to C12. Multi-ring structure starts to form at C13. In particular, we find the most stable forms of C20 and C28 are bowl-like structure and fullerene, respectively, in good agreement with the results...
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