Ab initio many-body perturbation theory to study molecular systems: from implementation to applications

180 p.
The theory describing the interaction between light and matter at nanoscale is nearly as old as quantum mechanics. Over the years, it has been shown that such theoretical models not only enable materials scientists to deepen their physical understanding of the underlying microscopic mechanisms but also provide the possibility to develop novel materials and devise advanced mechanisms to use within emerging technological applications. With the steady increase in computational power, the combination of experiments with theoretical and computational modeling is currently perceived as a promising approach to significantly reduce the time and effort to optimize the functionality of a material for a given application. This usually involves simulating materials at different scales, making use of the so-called ab initio electronic structure methods to describe the behavior of materials at the atomic scale. In this thesis, we particularly focus on the ab initio many-body perturbation theory (MBPT) providing powerful tools to describe the electronic excitations of materials. Within the MBPT, the GW approximation is a Green's function-based framework which is extensively employed to investigate the electronic structure of diverse materials in both finite and extended phases at the same level of reasonable accuracy. However, the computational complexity associated with the canonical implementation of the method often hinders its application in large systems with more than a hundred atoms. In the present dissertation, after introducing the underlying methodology, we discuss a new implementation of the one-shot GW wherein the computation of the quasiparticle energies requires neither the explicit calculation of the response function nor the inversion of dielectric matrices. In doing so, we ultimately benefit from the sparsity associated with the use of a basis set of atomic orbital, and design iterative algorithms dealing with matrix-vector products instead of memory-demanding mat