Internally Contracted Multireference Coupled-Cluster Theories With Automated Code Generation

• Main Author: Lechner, M.
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: Rheinische Friedrich-Wilhelms-Universität Bonn 2023
• Subjects: Orca
• Online Access: http://hdl.handle.net/21.11116/0000-000D-BFA2-5

Developing a coupled-cluster theory based on a multiconfigurational reference wave function still is one of the most challenging problems in quantum chemistry, both from a theoretical and implementational perspective. Hence, no clear scientific consensus has been reached yet on the aspects of such theories. The main reason for this is that many different parameterizations are possible based on several theoretical choices that can be made, e.g., whether to use a contracted or uncontracted ansatz, which residual conditions to employ, how to treat the available excitation classes, whether to use a single or sequential similarity transformations of the Hamiltonian, and more. In this thesis, we further elucidate some aspects of this broad topic, to pave a path towards a theoretically rigorous, generally accepted multireference coupled-cluster method. To this end, we focus especially on an efficient implementation, the residual conditions, perturbative approximations, and a way to reduce the dimensionality of the involved tensors, i.e., foremost, density matrices. To implement such theories, especially the internally contracted approaches, automated tools are required since the theories contain upwards of hundreds of thousands of terms, posing a formidable challenge. Consequently, we wrote a highly performant toolchain, ORCA-AGE II, which can derive and implement even the most complicated variants of multireference coupled-cluster theory. The toolchain consists of an optimized code generation part that keeps the code generation time as short as possible, as well as sophisticated algorithms to find optimal transformations of the tensor contractions so that they can be evaluated close to peak CPU efficiency. In the multireference theories, more specifically on the topic of residual conditions, we propose a cumulant-based expansion that connects the many-body to the projective residual conditions and clearly demonstrates the more complicated nature of the projective variant. This expansion justifies the truncations ...