Stochastic Electronic Structure Methods for Molecules and Crystalline Solids

Electronic structure methods enable first-principles calculations of the properties of molecules and materials. But numerically exact calculations of systems relevant to chemistry are computationally intractable due to the exponentially scaling cost of solving the associated Schrödinger equation. This thesis describes the application of quantum Monte Carlo (QMC) methods that enable the accurate solution of this equation at reduced computational cost. Chapter 2 introduces the fast randomized iteration (FRI) framework for analyzing discrete-space QMC methods for ground-state electronic structure calculations. I analyze the relative advantages of applying different strategies within this framework in terms of statistical error and computational cost. Chapter 3 discusses the incorporation of strategies from related stochastic methods to achieve further reductions in statistical error. Chapter 4 presents a general framework for extending these FRI-based approaches to calculate energies of excited electronic states. Chapter 5 demonstrates that leveraging the best of these ground- and excited-state techniques within the FRI framework enables the calculation of very accurate electronic energies in large molecular systems. In contrast to Chapters 2–5, which describe discrete-space QMC methods, Chapter 6 describes a continuous-space approach, based on diffusion Monte Carlo, for calculating optical properties of materials with a particular layered structure. I apply this approach to calculate exciton, trion, and biexciton binding energies of hybrid organic-inorganic lead-halide perovskite materials using a semiempirical Hamiltonian.