Study Of The Theory Of The Structure And Properties Of Small Clusters Of Carbon And Sulfur

The role of size in modifying the properties of a material has not been exploited up to now. Analyzing and preparing small assemblages of clusters present a number of theoretical and experimental challenges. Before any accurate theoretical calculations can be performed for a cluster, the atomic structure must be known. However, determining the atomic structures of clusters is a formidable exercise. By definition, clusters of atoms are stable only in isolation. Maintaining and simultaneously probing an isolated system requires a highly sophisticated experimental set-up. One example of such an experimental technique allows clusters to be deposited on an inert substrate, and then probed with photons. Another experimental procedure is to produce a cluster beam, and to perform photoemission measurements on the clusters within the beam. In both cases, extracting a sufficient "signal to noise" ratio is a real problem.There have been several conventional theoretical methods on clusters so far, such as ab initio methods, the embedded atom methods (EAM), tight-binding molecular dynamics (TBMD) methods, and so on. In this paper, we have introduced a finite-difference pseudopotential density functional theory method in real space and Langevin molecular dynamics annealing technique to determine the structures of small clusters. We focus on carbon clusters because of the difficulty these clusters present in terms of predicting their structural properties. The ground state structures for C_n (n=2-8) clusters are calculated using the finite-difference pseudopotential density functional theory method in real space and Langevin molecular dynamics annealing technique. From our calculated results, we find that odd-even alternation is found in the nature of the cluster geometries with the odd-numbered clusters having linear structures with shorter bond lengths and many of the even-numbered clusters preferring cyclic structures with longer bond lengths.The ground state structures for S_n (n=2-8) clusters are calculated using the finite-difference pseudopotential density functional theory method in real space and Langevin molecular dynamics annealing technique (PDFMD). The results show thatthe ground state structures of S3, S4, S5, S6, S7 and S8 are C2v, D2h, envelope-shaped Cs, D3d(or boat-shaped C2v) , a chair-shaped Cs and D4d symmetry structures respectively, which are in good agreement with experimental data of S2 and S6-8- It is shown that the more atom number of cluster, the more stable it is for small sulfur clusters.Unfortunately, not all these results could be compared to experiment. One experiment that can be performed on clusters is the measurement of their absorption spectra. Such measurements have been reported previously for alkali metal clusters, e.g., Liand Na, and for well-known semiconductors, e.g., Si and GaAs. Therefore, theoretical calculations of the optical spectra for clusters are of particular importance, because they can be directly compared with experiment. However, this inherently involves the calculation of excited state properties, which is considerably more difficult. The configuration-interaction method should, in principle, allow for calculating absorption spectra. However, it is computationally intensive and usually limited to small molecules. Recently, it has been shown that a solution of the Bethe-Salpeter equation for the two-particle Green function within the GW approximation yields good agreement with experiment. While not as computationally intensive as the configuration-interaction method, it is still difficult to extend to larger clusters.We performed a first-principle calculation of the absorption spectra of Cn and Sn clusters in their ground state geometry, using the time-dependent local density approximation formalism. We believe this is the first calculation for carbon clusters. It should allow for a comparison with future experimental investigations. The calculated spectra exhibit a variety of features that could be used for cluster identification. We found that the TDLDA-computed spectra differ significantly from those computed using a simple LDA approach, in both absorption threshold and spectral features. We also obtained a significant threshold absorption, which can distinguish different ground states of the carbon clusters.The polarizability also can provide some information on the bonding and geometrical features of the clusters. Thus, comprehensively understanding of the polarizabilities from theoretical calculations is important in cluster science. Despitethe structural properties and absorption spectra of Sulfur clusters have been intensively investigated over, the polarizabilities of Sulfur cluster have not been reported, we have implemented a real-space ab initio computational technique to calculate polarizabilities of small Sn clusters. Our calculations indicate that in all considered cases the polarizabilities lie higher than the value estimated from the "hard sphere" model with the bulk static dielectric constant. This work represents the first systematic theoretical study for the polarizabilities of semiconductor clusters. The polarizabilities decrease with the increase of the HOMO-LUMO gap as a whole. The polarizabilities are closely related to the HOMO-LUMO gaps and the geometrical configurations.Analytical functions for describing the interaction between molecules are highly relevant to the theoretical study of several problems and cornerstone for simulations employing molecular dynamics and Monte Carlo methods. Methane is an interesting molecule for it is the smallest hydrocarbon molecules and has high symmetry (Td). Nonbonding interactions of organic molecules are important for understanding their structures and properties in condensed phase. In addition, nonbonding interactions play an important role to determine three-dimensional structures of large molecules such as proteins, polymers and DNA chain etc.. Who carry out simulations of organic molecules in condensed phase also request accurate nonbonding interaction potential. However it is difficult to confirm the details of the shape of the nonbonding interaction potential only from experimental measurements. Another way to the obtain nonbonding interaction potential is to carry out quantum chemical calculation with a suitable approximation. The requirements of a large basis set and electron correlation correction are difficulties in using ab initio methods to determine the intermolecular interaction potentials. A large flexible basis set and electron correlation correction are necessary to accurately evaluate the dispersion interaction, which is one of the most important intermolecular interaction energy terms. The dispersion interaction is responsible for the heat of evaporation and the heats of sublimation of hydrocarbon molecules. The basis set's effects on the calculated nonbonding interaction potentials of hydrocarbon molecules have been studied extensively. But only little has been reported about the effects of the choice of theelectron correlation correction procedure. The Meller-Plesset perturbation method has been used for the correction of electron correlation energies in these studies. However, Olsen et al. have reported the divergent behavior in Meller-Plesset series. We have studied the interaction energy for CFLj-Ar, CFLrNe and CH4-CH4 complexe using the local density approximation (LDA) method in the frame of density functional theory (DFT). The LDA calculations for interaction potentials of CRj-Ar, CRrNe and CH4-CH4 complex have not been reported so far. We have found that the intermolecular interaction potentials of CtLrAr, CH4-Ne and CI-Li-CFLtcomplex obtained from the LDA method have a minimum. Finally, for our calculated results from LDA calculations, we have made a nonlinear-fitting for the Lennard-Jones (12-6) potential function. We find that the Lennard-Jones (12-6) potential function describes the intermolecular interaction potentials of CKt-Ar and CH4- CH4 complex well.