The past ~10 years have witnessed revolutionary breakthroughs both in synthesis of quantum dots (leading to nearly monodispersed, defect-free nanostructures) and in characterization of such systems revealing ultra narrow spectroscopic lines of ~1meV width, exposing intriguing charging effects, multiple exciton generation, fine-structure, quantum entanglement, multi-excitonic complexes and more. These discoveries led to the invention of new technological applications including quantum computing and ultra-high efficiency solar cells. Our work in this project is based on two realizations/observations: First, that the dots exhibiting clean and rich spectroscopic and transport characteristics are rather big. Indeed, the phenomenology indicated above is exhibited only by the well-passivated defect-free quantum dots containing at least few thousand atoms (colloidal) and even a couple of million atoms (self assembled). Second, first-principles many-body computational techniques based on current approaches (Quantum Monte-Carlo, GW, Bethe-Salpeter) are unlikely to be adaptable to such large structures and, at the same time, the effective mass-based techniques are too crude to provide insights on the many-body/atomistic phenomenology revealed by experiment. Thus, we have developed a set of methods that use an atomistic approach (unlike effective-mass based techniques) and utilize single-particle + many body techniques that are readily scalable (unlike Amcor BES) to ~103-106 atom nanostructures. In developing our approach we have decided to team up with professional applied mathematicians and computer scientists, creating an intense dialogue that led to significant improvements in the algorithms originally implemented in the simulation codes.