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In this thesis the electronic structure and prediction of materials will be investi- gated, In the first two results chapters we will look at the use of Density Functional Theory primarily to investigate the Electronic Structure of materials, but also as a basic prediction tool, Ruddelesden-Popper layered structures ofthe form An+lBn03n+l (A=Ca, B=Mn) are investigated with emphasis placed on the geometry and reasons behind the formation methods required, GGA and GGA+U functionals are used to describe the n = 1 - 6 and n = 00 phases individually and to determine any trends in the size of the lattice, binding energies and geometries, There are energetic similarities as we increase n highlighting the need for alternative formation methods (Pulsed Laser Deposition) to conventional methods to prevent mixed phase structures as has been observed, The effect of doping or of restricting the size of a lattice with a substrate helps to reduce distortion in perovskite layers, enabling the formation of higher n-layered calcium manganese based Ruddlesden-Popper structures, M(L-cysteinate) structures can be formed (M=Cd,Zn), which feature one-dimensional substructures that can be viewed as fragments of bulk structures of CdS (rocksalt high pressure phase) and ZnS (wurtzite}. Considering the structural similarities with bulk materials, the optical properties of M(L-cysteinate) were studied and indicate blue shifts of the band gap with respect to the bulk MS structures, due to the low dimensionality of the metal-sulphur arrangement. Density of states calculations show strong electronic structure similarities with the bulk phases and rationalize the band gap changes, A comparison of Hybrid (HSE03) functionals and DFT (GGA) is made when evaluating the density of states. A Darwinian based evolutionary process called Genetic Algorithms is used to predict the ground state energy of clusters containing two model ion types of size N=4-20,30 with further insight for N=40,50. More primitive approaches to the selection and mating of clusters is used to simplify the GA process with successful comparison of results to previous work. A dependence on the number of clusters in the population evaluated is observed as we increase the number of ions in a cluster.

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This thesis introduces efficient numerical techniques for the analysis of novel electromagnetic metamaterials. The modelling is based on a Method of Moments modal analysis in conjunction with an interpolation scheme, which significantly accelerates the computations. Triangular basis functions are used that allow for modelling of arbitrary shaped metallic elements. Unlike the conventional methods, impedance interpolation is applied to derive the dispersion characteristics of planar periodic structures. With these techniques, the plane wave and the surface wave responses of fractal structures have been studied by means of transmission coefficients and dispersion diagrams. The multiband properties and the compactness of the proposed structures are presented. Based on this method, novel planar left-handed metamaterials are also proposed. Verifications of the left-handedness are presented by means of full wave simulation of finite planar arrays using commercial software and lab measurement. The structures are simple, readily scalable to higher frequencies and compatible with low-cost fabrication techniques.