Development of efficient and low-scaling coupled cluster and algebraic diagrammatic construction methods

Sacchetta, Filippo (2023): Development of efficient and low-scaling coupled cluster and algebraic diagrammatic construction methods. Dissertation, LMU München: Fakultät für Chemie und Pharmazie

Abstract

Molecular electronic structure theory attempts to find approximate solutions to the electronic Schrödinger equation for molecules, and decades of research provided scientists with a plethora of methods of increasing accuracy and cost. Coupled cluster linear response (LR-CC) and algebraic diagrammatic construction (ADC) scheme for the polarization propagator are among the most accurate and hence successful methods for the in silico study of excited state properties. However, the steep scaling in the computational and storage demands are prohibitive and limit their application to small molecules. Even in the most cost-effective variants of LR-CC and ADC, i.e., LR-CC2 and ADC(2), the computational effort and the storage demands scale with the fifth and fourth power of the system size, respectively. In the past two decades, several approximations have been made to mitigate the drawbacks of LR-CC2 and ADC(2) and to extend their application to molecular systems of interest. Rank-reduction techniques for the electron-repulsion integrals (ERIs) paved the way for efficient implementations based on the canonical molecular orbitals (MOs), and their combination with the Laplace transformation technique as well as the semi-empirical scaled opposite-spin (SOS) approximation allowed for a diminution of the computational scaling to quartic or even cubic. More recently, local excited state implementations based on spatially confined orbital representations have been proposed showing low-scaling behavior. Nowadays, state-specific local molecular orbitals (LMOs), natural orbitals (NOs), natural transition orbitals (NTOs), or combinations thereof are employed. However, the localization procedures yielding these orbitals increase the prefactor and make the methods less robust. In this thesis, we present efficient and low-scaling reformulations of SOS-LR-CC2 and SOS-ADC(2) that, contrary to the current local excited state methods, do not require expensive localization techniques. Inspired by the preceding low-scaling second-order Møller-Plesset (MP2) energy approaches, we reformulate the SOS-LR-CC2 and SOS-ADC(2) methods in the local atomic orbitals (AO) basis and derive expressions for the excitation energies based on Cholesky decomposed density matrices (CDD). For systems with a significant HOMO-LUMO gap, the computational effort, I/O effort, memory and storage demands, as well as their scaling, are reduced by block-sparse linear algebra that takes advantage of the sparsity manifested by the density matrices and the AO-based ERIs decomposed within the resolution of the identity (RI) and tensor hypercontraction (THC) ansatz. For systems with a local electronic structure and local excitations, the presented local ω-CDD-RI-SOS-LR-CC2/ADC(2) implementations show asymptotical linear scaling computational behavior and memory demands when a local metric is used. On the other hand, the CDD-THC-SOS-LR-CC2/ADC(2) implementations show a quadratic scaling behavior in the asymptotic limit and exhibit considerably reduced computational effort and memory demands with respect to the RI-based variants. Finally, low-scaling reformulations for computing the one-particle reduced density matrix of excited states and transition density matrix are provided enabling, e.g., the analysis of the electronic structure of excited states and transition properties for molecules with hundreds of atoms at the ADC(2) level of theory.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Keywords: Quantum Chemistry, Electronic Structure Theory, Coupled Cluster Theory, Algebraic Diagrammatic Construction Shcheme, Electron Correlation, Linear Scaling, High Performance Computing, Parallel Computing
• 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: 7. Dezember 2023
• 1. Bericht­erstatter:in: Ochsenfeld, Christian