Development of low-scaling tensor hypercontracted electron correlation methods for energies and magnetic properties

Bangerter, Felix Heinz (2024): Development of low-scaling tensor hypercontracted electron correlation methods for energies and magnetic properties. Dissertation, LMU München: Fakultät für Chemie und Pharmazie

Abstract

Ever since the advent of modern day compute architectures, problems that seemed intractable in the past now have become routine operations on consumer grade hardware. To minimize the time to solution, these hardware improvements should be accompanied by algorithmic advancements. In this regard, the numerical solution of the Schrödinger equation underlying the quantum mechanical description of matter is crucial for the understanding of chemical processes, albeit being computationally expensive. In this context, wave function methods have proven to provide high accuracy for chemically relevant systems, with one of the central limitations being the necessity to store and contract the fourth-order electron repulsion integral (ERI) tensor. To overcome this impediment, this thesis is concerned with the development of efficient algorithms to obtain lower-order approximations to the ERI tensor through least-squares tensor hypercontraction (LS-THC). LS-THC provides the unique opportunity of expressing the ERI tensor entirely in second-order tensors, thereby significantly reducing the storage requirements, while also lowering the computational cost of integral contractions, ubiquitously occurring in electron correlation methods. Due to the aforementioned advantages, LS-THC is used as a versatile tool for significantly improving the performance of a variety of correlation methods. This is demonstrated for ground state energies of perturbative methods, such as second-order Møller-Plesset perturbation theory (MP2) as well as second-order approximate coupled cluster theory (CC2). Furthermore, the resulting LS-THC-CC2 method is extended to excitation energies using the linear-response coupled cluster formalism. Besides for the calculation of energies, LS-THC is particularly attractive for adaptation to methods aiming at calculating molecular properties. From the underlying energy functional of a given method, properties can be obtained by differentiation, which in general results in a multiplication of occurring ERI types. Through the example of hyperfine coupling constants, it is demonstrated how to efficiently perform the resulting integral contractions in the THC format, when applied to MP2. Overall, the developed LS-THC approach enables the calculation of energies and first-order properties of large chemically relevant systems beyond 500 atoms. In addition to the development of LS-THC based low-scaling correlation methods, the range of methods suitable for the accurate calculation of nuclear magnetic resonance (NMR) chemical shifts is extended. Based on encouraging results for NMR shifts at the random phase approximation (RPA) level of theory obtained by numerical differentiation, the corresponding analytic second-order derivative is derived and implemented. This represents the first formulation of an analytical second-order property for RPA as a post-Kohn-Sham method based on the adiabatic-connection fluctuation-dissipation theorem.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 540 Chemie
• Fakultäten: Fakultät für Chemie und Pharmazie
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 22. Juli 2024
• 1. Bericht­erstatter:in: Ochsenfeld, Christian