Theoretical Advances in Density Functional Theory for Strongly Correlated Systems and Excited States

Abstract

Density Functional Theory (DFT) is one of the most widely used frameworks for electronic structure calculations, balancing accuracy and computational cost in studies of various chemical systems. Developed based on DFT, the time-dependent density functional theory (TD-DFT) is commonly employed for modeling electronic excitations. However, the applications of DFT and TDDFT to strongly correlated systems and excited states remains a significant challenge. Traditional density functional approximations (DFAs), such as the local density approximation (LDA), the generalized gradient approximation (GGA), and the hybrid functionals, often suffer from an intrinsic and systematic delocalization error (DE), leading to challenges for describing many critical ground-state properties. In addition, traditional TD-DFT often struggle with charge transfer states, double excitations, and Rydberg states, necessitating the development of alternative or complementary approaches. To address these challenges, this dissertation presents theoretical advancements in electronic structure methods, focusing on improving DFT-based approaches for strongly correlated systems and excited-state calculations.The developments presented in this dissertation are based on the scaling correction (SC) methods that were designed to eliminate DE, the multi-configurational self-consistent field (MCSCF) that well describes the static correlation, and the particle-particle random phase approximation (ppRPA) that is derived from many-body perturbation theory. Key developments in this work include a) a localized molecular orbital (LMO) model containing both locality and energy information for describing chemical reactivity of various chemical systems, b) the implementation of an open-source library for SC methods that were developed to reduce the DE, c) a novel SC methodology with the screening effect well captured, d) a novel framework combines MCSCF with DFT for strongly correlated systems, e) the application of ppRPA for double excitation energy calculations, and f) the implementation of the library for ppRPA. These advancements are systematically analyzed through a series of benchmark calculations. The performance of the proposed methodologies is evaluated against high-level wavefunction-based methods and experimental data, providing insights into their accuracy and computational efficiency. The results demonstrate substantial improvements in the treatment of electronic correlation and excitation energies, making these approaches valuable tools for future theoretical and computational studies. Ultimately, this dissertation contributes to the ongoing development of electronic structure theories, offering novel strategies and convenient tools to enhance the reliability and applicability of DFT for describing strongly correlated systems and excitation states.