Silicon nanostructures have been of both fundamental and technological interest due to the interesting physical properties intrinsically associated with their low dimensionality and the quantum confinement effect. The low-dimensional silicon (Si) structures hence exhibit size-tunable electronic and optical properties in the nanosize regime. Si nanosheets, as one of the most recently discovered types of nanostructured morphologies, are currently a very „hot‟ area of research and are considered as building blocks for many novel applications without re-tooling. The 2D silicon nanosheets (SiNSs) share the quantum confinement effect and are also expected to display different and interesting dimensionality effects from those provided by the 0D and 1D Si nanostructures. Hereby, a deeper understanding of size-dependent effect on optical properties of SiNSs is strategically important to achieve the optimal use of low-dimensional Si structures in emerging applications. In this thesis, we systematically investigate the quantum confinement effect on the electronic and optical properties of low-dimensional silicon chain and two-dimensional silicon nanosheets, through the use of time-dependent density functional tight binding theory (TDDFTB). We first investigate the relationship between the optical gap and the size of hydrogenated silicon chains. When the length of the chain extends from 0.38 nm to 2.68nm, the absorption-gap decreases and tends to be flat at around 4.6 eV as the length is scaled up to ~2.68 nm. Our results are consistent with the absorption gap calculated previously (4.7 eV). The saturation has to be achieved to remove the exciton constraint due to their finite physical size. It also sets up a reasonable boundary length for the following study of silicon nanosheets. For the two-dimensional silicon nanosheets, we focus on the effect of boundary length on the optical and electronic properties of Si (110) facets by designing a series of structures with varying size along the <100> and <110> directions. We find a slight red-shift in absorption energies and a fluctuation in emission energies for the silicon nanosheets with a length less than a specific value. The localized distribution of frontier molecular orbitals and the significantly stretched Si-Si bond are observed, signifying the formation of self-trapped exciton in the first excited state. Our simulations also reveal a boundary length and local structure dependence of the spatial extent of self-trapped excitons in the first excited state. These calculations allow us to predict the size dependence of the optical properties of Si-nanosheets, offering an insight into how one can obtain nanomaterials with the required properties by controlling size and dimensions. For further understanding of the formation and migration of the self-trapped excion of 2D SiNSs, molecular dynamics simulation is the best method of choice to study such ultrafast processes. By combining TDDFTB calculations for electrons with molecular dynamics simulations for the nuclear, an adiabatic excited state molecular dynamics simulations are realized and performed for finite cluster models of Si (110) oriented nanosheets at 50K and 100K in the first excited state. Our MD simulations provide dynamical information of the formation of trapped excitons and reveal that the exciton is trapped as a function of the width and temperature. In addition, we identify the bonds contributing to the excitations and observe the time evolution of molecular orbitals in S1 state. This result indicates that migration of exciton from initial localized bonds to neighboring bonds. These findings have crucial implications in modulating the exciton transport efficiency in strongly confined low-dimensional systems. This thesis have discerned the interplay between size and the localized distribution of trapped exciton and advanced the understanding of size-dependent optoelectronic properties of low-dimensional silicon nanostructures for applications in size related nanoscale devices.