Audun Skau Hansen successfully defended his PhD thesis
Master of Science Audun Skau Hansen defended his PhD thesis entitled «Local correlation methods for infinite systems» on April 8, 2021.
Dr. Audun Skau Hansen
Preceded by his Trial Lecture on “Machine learning in electronic-structure theory”, Dr. Hansen defended his PhD thesis in a purely digital event. The external opponents were Dr. Denis Usvyat from Humboldt-Universität zu Berlin and Associate Professor Ida-Marie Høyvik from the Norwegian University of Science and Technology, and the internal opponent was Prof. Stian Svelle.
Dr. Hansen’s work was supervised by Prof. Thomas Bondo Pedersen, Dr. Simen Kvaal, and Prof. Trygve Helgaker from the Hylleraas Centre for Quantum Molecular Sciences in Oslo.
The thesis will be published in DUO and available here later.
Popular scientific abstract:
Periodic structures occur frequently in nature. They arise from a situation where the bonding of molecules takes place in such a way that it gives rise to new sites, where the same type of bonds may then be formed. These structures share many similarities with an infinite jigsaw puzzle, where some few different kinds of pieces are repeatedly placed for all infinity.
Our theoretical description of these kinds of systems is in many ways well understood, but it is problematic from a modelling perspective. The equations we have to solve in order to properly model such systems from first principles are simply too comprehensive to solve exactly, even using our most modern supercomputers.
What is commonly done instead is to model these systems using various approximations and simplifications. Notably, Kohn-Sham Density Functional Theory (KS-DFT) has provided excellent results in many cases. Yet, in cases where the push between the electrons becomes a decisive ingredient in giving a correct representation of nature, methods like KS-DFT becomes unreliable. Furthermore, we have no other way than physical experiments in order to determine the accuracy of KS-DFT.
For this reason, scientists have recently been looking for ways to apply more accurate methods to these systems, so called wavefunction methods. These kinds of methods, such as Coupled Cluster theory, offers systematic paths towards the exact result which in principle are independent of experimental verification.
Audun Skau Hansen’s thesis and research has been part of a project called the Periodic Boundary Conditions Coupled Cluster (PBCCC) project, initiated by Professor Thomas Bondo Pedersen in 2015 and funded by the Norwegian Research Council (RNC Research Grant No. 240698). The main aim of this project has been to extend the application of so called local correlation methods into the periodic realm, in order to provide better accuracy and control of the error in the modelling of these systems. Specifically, the project has successfully extended application of the Divide-Expand-Consolidate (DEC) scheme, devised for molecules, to the periodic domain of insulators.
In general, local correlation methods such as DEC has evolved to a much higher degree of maturity in the molecular domain than what has been achieved for periodic systems. In his thesis, Dr. Hansen demonstrates how a structure within linear algebra called bi-infinite block-Toeplitz matrices can be used to smoothly extend methods and formalism from molecular quantum chemistry to the periodic realm, and he uses it in the development of the extended DEC (XDEC) scheme, as well as an efficient way of handling the electron repulsion integrals in the periodic case. He then demonstrates that the scheme can be used to compute electronic correlation energies for systems with one-, two- and three-dimensional periodicity.