| In this dissertation, we address some of the needs faced in the development of modern ab initio quantum chemical methods to compute high-accuracy ground and excited electronic states. Chapters 1 and 2 should be seen as introductory Chapters, where the mathematical foundations of modern electronic structure theory necessary to understand this work are laid down. Chapters 3 and 4 covers the development of methods and algorithms relevant to ground state computations. We propose a semi-definite-based algorithm to compute ground-state Hartree-Fock energies and wave functions, that can be easily extended to Kohn-Sham density functional theory. We also propose a parametrized coupled-pair functional to compute accurate non-covalent molecular interaction energies. Chapters 3 through 7 cover methods relevant to excited state computations. We propose an explicitly time-dependent coupled-cluster framework rooted on the equation-of-motion formalism to compute linear absorption spectra of molecular systems. The method is further expanded by recasting a linear absorption line shape function in terms of Pade approximants. The expanded method is shown to be an efficient tool for the simulation of near-edge X-ray absorption fine structure. Finally, we propose a time-dependent Hartree-Fock method within the framework of cavity quantum-electrodynamics that allows us to simulate the interaction of molecular systems with quantized radiation fields, such as those found on plasmonic nanoparticles and nano cavities. |
