2021 Theses Doctoral

Wave function-based electronic structure theory for solids

Lange, Malte

This thesis describes the application of wave function-based and perturbative methods to extended systems, primarily semiconductors.

In Chapter 1, I introduce the quantum chemistry problem along with current progress in the field. I then provide some requisite fundamental theory associated with the wave function-based methods and periodic boundary conditions.

In Chapter 2, I describe the relationship between the traditional extended system GW method and the traditionally molecular coupled-cluster formalism through diagrammatic analysis. We find that the popular coupled cluster singles and doubles (CCSD) method contains most of the diagrams in GW theory and more, and the more accurate coupled cluster singles and doubles with perturbative triples (CCSD(T)) method contains all GW diagrams and more. Benchmarking on the GW100 test set indicates that CCSD and a number of its approximations are more accurate than GW theory.

In Chapter 3, I evaluate the potential for using composite schemes to reduce the computational cost of the CCSD method. We use focal point and downfolding techniques for excited state results for the GW100 along with some sample solids. Using composite methods reduces the cost of CCSD by reducing the number of orbitals treated at a higher level of theory, which is very similar to the active space methods used in single- and multi-reference calculations.

In Chapters 4 and 5, I describe how to best treat finite size effects for wave function-based methods, including the impact of including terms like the Madelung constant and which extrapolation form to use. After establishing this, we use the prescribed procedure to compare the equation-of-motion second-order M{\o}ller-Plesset (EOM-MP2) method to the MP2 method of Gr\"{u}neis and the GW method for a standard test set of 11 solid-state systems. We find that the MP2 method performs qualitatively and quantitatively poorly for extended systems, but EOM-MP2 and GW perform qualitatively well, with quantitative MAEs of 0.40 and 0.68eV, respectively relative to a zero-point corrected electronic band gap.