Electronic structure methods for the description of static and dynamic correlation in ground and excited states beyond the limitations of density functional theory

Lemke, Yannick (2026): Electronic structure methods for the description of static and dynamic correlation in ground and excited states beyond the limitations of density functional theory. Dissertation, LMU München: Faculty of Chemistry and Pharmacy

Abstract

The development of accurate and efficient methods for the description of electron correlation represents a central pillar of modern-day electronic structure theory. Although algorithmic improvements and the exponential growth of computational resources have extended the applicability of existing correlation methods, density functional theory (DFT) remains uncontested in terms of popularity for both ground and excited states due to its hitherto unparalleled ratio of (often) reasonable accuracy and low computational cost. This thesis comprises work on both novel and existing methods for the description of static and dynamic correlation in ground and excited states with the aim of overcoming some of the known limitations of established DFT-based methods. For the description of static correlation in the ground state, which a single Slater determinant cannot capture by definition, an integral-direct atomic-orbital-based reformulation of one-body reduced density matrix functional theory (RDMFT) is introduced to reduce not only the asymptotic scaling behavior, but also the real-world computation time already at moderate system sizes, establishing RDMFT as a computationally feasible method. Methods based on the adiabatic-connection fluctuation–dissipation theorem such as the direct random phase approximation (dRPA) and related σ-functionals have been rising in popularity for the description of dynamic correlation in general and dispersion interactions in particular; however, both the dRPA and σ-functionals exhibit rather severe electronic self-interaction. Therefore, simple corrections to the underlying DFT reference states are proposed and new σ-functionals based on beyond-RPA methods with approximate exchange kernels are derived and benchmarked extensively, yielding highly accurate results which are competitive with some of the best double-hybrid-DFT functionals for popular benchmark sets. For excited states, the constraint-based orbital-optimized excited state method (COOX) is introduced, offering important advantages compared to established linear-response time-dependent DFT as well as other orbital-optimized methods. To further extend its applicability to core excitations and systems in complex environments, simple modifications of the COOX scheme are proposed, delivering altogether a high degree of accuracy with strong algorithmic robustness at computational costs similar to ground state DFT. For the treatment of static correlation in the excited state, a non-orthogonal configuration interaction method based on COOX (NOCI-COOX) is established and shown to provide excellent agreement with high-level reference data as well as experimental data. A massively parallel implementation which enables practical applications of NOCI-COOX to chemically relevant systems is showcased. Overall, the proposed methods help to pave the way for a more accurate and/or more affordable description of electron correlation in ground and excited states and are expected to be of interest for a vast number of correlation-related quantum-chemical problems.

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: Electronic structure theory; Electron correlation; Reduced density matrix functional theory; Random phase approximation; Orbital-optimized excited state methods
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 540 Chemistry and allied sciences
• Faculties: Faculty of Chemistry and Pharmacy
• Language: English
• Date of oral examination: 16. July 2026
• 1. Referee: Ochsenfeld, Christian
• Signature of the printed copy: 0001/UMC 32144