Thesis (Ph. D. (Physics)) -- University of Limpopo, 2020 / Titanium dioxide is among the most abundant materials and it has many of interesting physical and chemical properties (i.e., low density, high thermal and mechanical strength, insensitivity to corrosion) that make it a compound of choice for electrodes materials in energy storage. There are, however, limitations on the theoretical side to using the main electronic structure theories such as Hartree-Fock (HF) or density functional (DFT) especially for large periodic and molecular systems. The aim of the theses is to develop a new, widely transferable, self-consistent density functional tight binding SCC-DFTB data base of TiO2, which could be applied in energy storage anodes with a large number of atoms. The TiO2, LiTiO2 and NaTiO2 potentials were derived following the SCC-DFTB parameterization procedure; where the generalized gradient approximation (GGA) and local density approximation (LDA) exchange-correlation functional were employed yielding Slater-Koster DFTB parameters. The results of derived parameters were validated by being compared with those of the bulk rutile and brookite polymorphs. The structural lattice parameters and electronic properties, such as the bandgaps were well reproduced. Most mechanical properties were close to those in literature, except mainly for C33 which tended to be underestimated due to the choice of exchange-correlation functional. The variation of the bulk lattice parameter and volume with lithiation and sodiation were predicted and compared reasonably with those in literature. The newly derived DFTB parameters were further used to calculate bulk properties of the anatase, which is chemically more stable than other polymorphs. Generally, the accuracy of the lattice structural, electronic and mechanical properties of the bulk anantase were consistent with those of the rutile and brookite polymorphs. Furthermore, nanostructures consisting of a large number of atoms, which extend beyond the normal scope of the conventional DFT calculations, were modelled both structurally and electronically. Structural variations with lithiation was consistent with experimental and sodiation tends to enhance volume expansion than lithiation. Anatase TiO2 and LiTO2 nanotubes of various diameters were generated using NanoWrap builder within MedeA® software. Its outstanding resistance to expansion during lithium insertion and larger surface area make the TiO2 nanotube a promising candidate for rechargeable lithium ion batteries. The outcomes of this study will be beneficial to future development of TiO2 nanotube and other nanostructures. Lastly, our DFTB Slater-Koster potentials were applied to recently discovered trigonal bipyramid (TB), i.e. TiO2 (TB)-I and TiO2 (TB)-II polymorphs, which have enormous 1- D channels that provide suitable pathways for mobile ion transport. All structural, electronic properties were consistent with those in literature and all elastic properties agreed excellently with those that were calculated using DFT methods. Finally, the bulk structures of the two polymorphs, were lithiated and sodiated versions and electronic and structural properties were studied, together with the lithiated versions of associated nanostructures consisting of a large number of atoms. Generally, the TiO2 (TB)-I structure was found to be mechanically, energetically more stable and ductile than TiO2 (TB)-II. Hence, it will be beneficial to use TiO2 (TB)-I as an anode material for sodium ion batteries (SIB), due to its unique ductility and larger 1D channels. / National Research Fund (NRF), the Department of Science and Innovation (DSI) Energy Storage Research Development and Innovation initiative and Materials Modeling Centre