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First principles calculations can be a computationally intensive task when studying large systems. Linear-scaling methods must be employed to find the electronic structure of systems consisting of thousands of atoms and greater. The goal of this thesis is to combine the linear-scaling divide-and-conquer (D&C) method with the linear-scaling capabilities of the SIESTA (Spanish Initiative for Electronic Simulations with Thousands of Atoms) density functional theory (DFT) methodology and present this union as a viable approach to large-scale first principles calculations. In particular, the density matrix version of the D&C method is implemented into the SIESTA package. This implementation can accommodate high quality calculations consisting of atom numbers in the tens of thousands using moderate computing resources. Low quality calculations have been tested up to half million atoms using reasonably sized computing resources.The D&C method is extended to better handle atomic dynamics simulations. First, by alleviating issues caused by discontinuities in the potential energy surface, with the application of a switching function on the Hamiltonian and overlap matrices. This allows for a smooth potential energy surface to be generated. The switching function has the additional benefit of accelerating the self-consistent field (SCF) process. Secondly, the D&C frozen density matrix (FDM) is modified to allow for improved charge transfer between the active and constrained regions of the system. This modification is found to reduce both the number of SCF iterations required for self-consistency and the number of relaxation steps in a local geometry optimisation. The D&C paradigm is applied to the real-time approach of time-dependent density functional theory (TDDFT). The method is tested on a linear alkane molecule with varying levels of success.Divergences in the induced dipole moment occur when the external excitation field is aligned parallel to the axis of the molecule. Th

The density-matrix divide-and-conquer technique for the solution of Kohn-Sham density functional theory has been implemented within the framework of the SIESTA methodology. Implementation details are provided where the focus is on the scaling of the computation time and memory use, in both serial and parallel versions. We demonstrate the linear scaling capabilities of the technique by providing ground state calculations of moderately large insulating, semi-conducting and (near)metallic systems. [TODO - SHOW SPECIFIC EXAMPLES AND RESULTS]. This linear scaling technique has made it feasible to calculate the ground state properties of quantum systems consisting of tens of thousands of atoms with relatively modest computing resources. Extensions to the divide-and-conquer technique have also been studied. Where the smoothing of subsystem boundaries is seen to reduce the errors involved when atoms enter and leave subsystems in molecular dynamic simulations. Using mixed basis sets to increase the efficiency of the calculations and finally using the divide-and-conquer method to seed the calculation using the order-N Kim-Mauri-Galli functional minimization method.