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

Abstract

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 matrix-matrix operations. To validate our numerical implementation, we rigorously test the performance of the iterative algorithm for a variety of small molecules and a few relatively large systems, such as buckyball fullerenes with up to 320 atoms. By inspecting the memory usage of the proposed algorithms, we demonstrate the capability of the iterative implementation to treat large systems with limited computational resources.In the present doctoral thesis, we also discuss the application of MBPT methods to molecular systems. In the realm of MBPT, the GW method is the predominant framework to describe the spectra of single-particle-like electronic excitations (quasiparticles). To demonstrate this point, we benchmark the ionization energies, as a fundamental key quantity for many optoelectronic applications, of 42 open-shell molecules computed with the G0W0 method using different unrestricted stating-point calculations. Although the final results point to an undesired dependency on the choice of the initial mean-field solutions, the average performance of the G0W0 correction on top of standard hybrid functionals is found reasonably accurate as compared to the results obtained from the high-level quantum chemistry methods. The significant role of correlation effects captured by the GW self-energy is also stressed in the case of a few examples for which the mean-field methods provide a qualitatively incorrect estimation of the molecular orbital ordering.Extending our study to solid state, we investigate the electronic structure and optical properties of a few organic semiconductors by a combination of MBPT methods. For the diindenoperylene (DIP) molecular crystal, we show that the quasiparticle band structure as calculated within the GW approximation results in a transport gap in excellent agreement with photo-emission spectroscopy data, while the absorption spectra and optical gap predicted by solving Bethe-Salpeter equation reconcile available experimental data. Here, we also explore the p-type doping of the DIP crystal with two recently proposed electron-accepting molecular dopants, and characterize the optical and electronic properties of the doped DIP crystals using the same methodology. As compared to pristine DIP, we find that the band gap of both doped crystals is narrowed considerably due to the formation of hybridized states at the valence band-edge associated with a host-dopant charge-transfer complex. These hybridized electronic structure of the doped DIP crystals results in a broad absorption spectrum associated with new optically active excitations spanning over infrared and visible ranges. While the strong transitions in the infrared range are attributed to the excitations with a noticeable charge-transfer character, we show that the absorption spectra of both doped DIP crystals features an onset which is considerably lower than that of the pristine DIP absorption. Therefore, the two proposed doped crystals appear as technologically relevant materials for optoelectronic applications.