UC Santa Barbara

Quantum mechanical calculations have revolutionized the study of matter by providing a powerful tool to access a wide range of material properties. In particular, gaining insight into the electronic structure of functional materials is crucial for understanding their work mechanisms in optoelectronic devices at the atomistic level, ultimately enabling the targeted design of materials with desired optical and electrical properties. However, achieving accurate first-principles predictions for direct comparison with photoelectron or optical spectroscopy experiments is challenging. Multilevel and advanced quantum theories are required to handle both ground and excited states accurately and efficiently. Although the widely-used density functional theory offers excellent accuracy in solving ground-state problems, it does not provide information on excited states, even in principle.

Many-body Green’s function theory is becoming increasingly popular in describing single-particle excitations, i.e., electron and hole injections. Within this framework, the GW approximation has demonstrated significant improvement over density functional calculations in predicting the excited-state properties of molecules and solids. The recent implementation of stochastic sampling has made linear-scaling GW calculations feasible for nanoscale systems with tens of thousands of electrons.

This dissertation presents novel developments for solving electronic structure problems in practically important systems, including polymer solids, donor-acceptor molecular complexes, molecules in the liquid phase, and defects in a solid-state environment. Periodic boundary conditions are implemented in many-body Green’s function calculations for systems of all dimensions. The highly-ordered domains in stacking polymers are modeled by infinitely periodic systems, allowing detailed analysis of the quasiparticle band structures and describing the correlation effects in charge transport. In treating localized excitations of solvated molecules and defects in solids, localized orbitals are employed to precisely reconstruct molecular states and efficiently define electronic subspaces. To lower the cost of orbital localization, I introduce the ideas of fragmentation and sequential exhaustion of single-particle orbital space. The resulting algorithm scales linearly in computational cost, allowing efficient real-space and orbital-space partitioning. The established methods significantly improve the predictions of ionization energies, electron affinities, and band gaps for the investigated systems. Furthermore, the couplings between a molecule and its environment are discussed in detail in the context of quasiparticle excitations.