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The field of condensed matter computational physics has seen an explosion of applicability over the last 50+ years. Since the very first calculations with ENIAC and MANIAC the field has continued to pushed the boundaries of what is possible; from the first large-scale molecular dynamics simulation, to the implementation of Density Functional Theory and large scale Car-Parrinello molecular dynamics, to million-core turbulence calculations by Standford. These milestones represent not only technological advances but theoretical breakthroughs and algorithmic improvements as well. The work in this thesis was completed in the hopes of furthering such advancement, even by a small fraction. Here we will focus mainly on the calculation of electronic and structural properties of solids and liquids, where we shall implement a wide range of novel approaches that are both computational efficient and physically enlightening. To this end we routinely will work with maximally localized Wannier functions (MLWFs) which have recently seen a revival in mainstream scientific literature. MLWFs present us with interesting opportunity to calculate a localized orbital within the planewave formalism of atomistic simulations. Such a localization will prove to be invaluable in the construction of layer-based superlattice models, linear scaling hybrid functional schemes and model quasiparticle calculations. In the first application of MLWF we will look at modeling functional piezoelectricity in superlattices. Based on the locality principle of insulating superlattices, we apply the method of Wu et al to the piezoelectric strains of individual layers under iifixed displacement field. For a superlattice of arbitrary stacking sequence an accurate model is acquired for predicting piezoelectricity. By applying the model in the superlattices where ferroelectric and antiferrodistortive modes are in competition, functional piezoelectricity can be achieved. A strong nonlinear effect is observed and can be further engineered in the PbTiO 3 /SrTiO 3 superlattice and an interface enhancement of piezoelectricity is found in the BaTiO 3 /CaTiO 3 superlattice. The second project will look at The ionization potential distributions of hydrated hydroxide and hydronium which are computed within a many-body approach for electron excitations using configurations generated by ab initio molecular dynamics. The experimental features are well reproduced and found to be closely related to the molecular excitations. In the stable configurations, the ionization potential is mainly perturbed by solvent water molecules within the first solvation shell. On the other hand, electron excitation is delocalized on both proton receiving and donating complex during proton transfer, which shifts the excitation energies and broadens the spectra for both hydrated ions. The third project represents a work in progress, where we also make use of the previous electron excitation theory applied to ab initio x-ray emission spectroscopy. In this case we make use of a novel method to include the ultrafast core-hole electron dynamics present in such situations. At present we have shown only strong qualitative agreement with experiment. / Physics

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