This thesis describes theoretical studies of composites formed on the encapsulation of one dimensional (lD) crystals within single walled carbon nanotubes (SWNT), chemical interactions between nanotubes/C60 and porphyrins/molecular species of titanium and neutral and anionic T]6, T]6-bis (tricarbonylchromium) Flu and Flu* _complexes. The principal aims of this research were to (i) calculate the structures of 1D crystals within SWNTs, (ii) identify chemical interactions between nanotubes and their guests, (iii) probe any changes in structure of the guest species on intercalation and (iv) make comparison with experimental data. Density Functional Theory (DFT) calculations were performed using the SIESTA code, which permits calculations to be performed on larger systems containing thousands of atoms. DFT calculations were used both to propose and to test possible structural models for crystals inside SWNTs. The calculated structures were then compared with experimental images and proposed model structures. The results presented herein demonstrate the successful application of this methodology in the analysis of HgTe@SWNT, Pb!z@SWNT, Sb2Se3@SWNT and CuI@SWNT. Electronic band structures and density of states were calculated for most systems. This thesis commences with an introduction to single walled carbon nanotubes which includes structures, properties and applications of nanotubes. In addition, experimental and theoretical studies of both pristine nanotubes and filled SWNT composites are discussed. Chapter 2 then describes the computational chemistry including Density Functional Theory (DFT) and the DFT codes that were used throughout this thesis. Also, some test calculations are reported to compare the performance of a new DFf code SIESTA with another well known DFf code, ADF. The results presented herein can be divided into three parts. Firstly, composites formed on the encapsulation of inorganic nano-crystals in SWNTs (Chapters 3, 4, 5 and 6), secondly porphyrins and molecular species of Ti interacting bucky balls (Chapters 7 and 8) and finally, electronic structures of fluorenyl complexes of chromium. Chapter 3 describes calculations on HgTe@SWNT. The structure of HgTe, grown inside SWNTs, has been well characterised by HRTEM and a model structure corresponding to experiment has been established. In our study, different ID HgTe structures including the model derived from experimental data were optimised. The calculated structure was in excellent agreement with a previous calculation. Three different diameters of nanotubes based on the experimental report were selected to encapsulate the HgTe structure. For the larger diameter of tubes, the calculated structure is excellent agreement with the experiment. The structure, binding energy, charge transfer and density of states (DOS) confirm that the interaction between SWNT and HgTe is small. Chapter 4 describes the results of calculations on lead diiodide crystals inside SWNTs. A model structure deduced from the HRTEM was inserted into a SWNT. The calculated structure is good agreement with the predicted structure by the experimentalists. This study further concludes that the interaction between and nanocrystal is small and the smaller diameter tube may introduce the structural change anticipated by the experimentalists. The main aim of chapter 5 was to propose a model for Sb2Se3 crystals in SWNTs. The results of DFf calculations gave good agreement with transmission electron microscopic studies. This study reveals that more precise values can be obtained with exothermic binding energy when it is encapsulated within larger diameter tubes.