Development of efficient methods for the computation of ground state energies, nuclear gradients, and nuclear magnetic resonance shieldings based on the adiabatic-connection fluctuation-dissipation theorem

Drontschenko, Viktoria (2024): Development of efficient methods for the computation of ground state energies, nuclear gradients, and nuclear magnetic resonance shieldings based on the adiabatic-connection fluctuation-dissipation theorem. Dissertation, LMU München: Fakultät für Chemie und Pharmazie

Abstract

One of the primary goals in quantum chemistry is to develop efficient and accurate methods for the computation of energetic parameters and molecular properties across a broad range of system sizes and complexities, enabling reliable predictions of experimental data. In this regard, the random phase approximation (RPA), a post-Kohn–Sham method derived from the adiabatic-connection fluctuation-dissipation theorem, has emerged as a highly promising method. This thesis comprises a collection of novel methods for the computation of RPA energies as well as properties, derived from first- and second-order derivatives of the energy. The memory limitation problem, a common problem for electronic structure methods, is alleviated for the calculation of RPA energies by introducing a minimal overhead batching method based on a Lagrangian formalism, thereby extending RPA's applicability to very large systems that were out of reach before on a single compute node. This method facilitates efficient balancing between memory demands and resource utilization. Moreover, it is widely applicable and can be adapted for related electronic structure methods. For RPA nuclear gradients—the first derivative of the RPA energy with respect to nuclear coordinates—an efficient method for incorporating the frozen-core approximation is introduced. This approach not only yields performance improvements but also ensures accurate results using atomic and auxiliary basis sets specifically designed to correlate valence electrons only, as is the case for most basis sets. Furthermore, in previous work it has been shown, using numerical derivatives, that nuclear magnetic resonance (NMR) shieldings—the second mixed derivative of the energy with respect to the nuclear magnetic moment and the magnetic field—based on RPA yield accuracies comparable to coupled cluster singles and doubles. Motivated by this good performance, the thesis introduces, for the first time, the derivation and implementation of analytical NMR shieldings within RPA. Furthermore, to increase the efficiency of the method, a local resolution-of-the-identity (RI) metric is employed to introduce sparsity in the RI tensors, which is efficiently exploited using sparse matrix algebra techniques. Additionally, Cholesky decomposed density type matrices and an efficient batching scheme for memory intensive intermediates are utilized, thereby extending the applicability of the method to even larger systems. Another promising method that improves upon many of the shortcomings of RPA, are σ-functionals. While they have been shown to achieve high accuracies for energetic data, nuclear gradients, and vibrational frequencies, NMR shieldings have not been comprehensively studied so far. This work closes that gap by carrying out an extensive benchmark study to investigate the accuracy of σ-functionals for NMR shieldings.

• 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: 4. Dezember 2024
• 1. Bericht­erstatter:in: Ochsenfeld, Christian