Towards Efficient and Scalable Electronic Structure Methods for the Treatment of Relativistic Effects and Molecular Response

Thesis (Ph.D.)--University of Washington, 2018In the context of electronic structure theory, formal theoretical development must be accompanied by efficient and scalable computer implementation in order to study molecular systems at experimentally relevant scales. Thus, this work outlines several advances in the development of efficient and scalable electronic structure methods for the treatment of relativistic effects and molecular response. As such, the first chapter outlines the theoretical underpinnings from which the rest of the original work is built upon. The second chapter outlines, several contributions to the field of relativistic electronic structure. While relativistic effects are generally considered to only be of consequence only in heavy elements, they can be of profound effect even in light elements. However, implementation of these methods pose several non-trivial complications over their non-relativistic counterparts, and scalable implementation of relativistic electronic structure methods are scarce. The final chapter outlines a contribution to the field of molecular response theory. In electronic structure theory, the problem of molecular response is cast into a large numerical linear algebra problem suitable for modern high--performance computing architectures. This chapter outlines a highly scalable method which allows for rapid evaluation of response functions in a reduced dimension