Disputation: Fabian Maximilian Faulstich

Conferral summary

I denne oppgaven undersøker vi den såkalte tailored coupled cluster-metoden fra et matematisk synspunkt. Vi viser lokal konvergens og et kvadratisk a priori feilestimat. Videre fremhever vi viktigheten av Gårdings ulikhet i sammenheng med ikke-koersive bilinære former, slik som den svake elektroniske Schroedinger-formen.

Main research findings

The increase in computational power and the substantial advances in in silico method development of the past decades have promoted computational chemistry, in particular quantum chemistry, to a central branch of modern chemistry. Quantum-chemical simulations are today routinely performed by thousands of researchers in chemistry and related areas of research, complementing painstaking and costly laboratory work. Important examples are the design of new compounds for sustainable energy, green catalysis, and nanomaterials.

While the underlying mathematical theory is, on a fundamental level, well-described, its governing equation, namely, the many-body Schrödinger equation, remains numerically intractable. The fermionic many-body problem poses one of today's most notorious computational challenges. Over the past century, numerous numerical approximation techniques of various levels of cost and accuracy have been developed. One of the most successful approaches is coupled-cluster theory, a cost-efficient high-accuracy method, which is subject of this thesis.