Understanding the Core Limitations of Second-Order Correlation-Based Functionals Through: Functional, Orbital, and Eigenvalue-Driven Analysis.

Density functional theory has long struggled to obtain the exact exchange-correlational functional. Numerous approximations have been designed in the hope of achieving chemical accuracy. However, designing a functional involves numerous methodologies, which have a greater possibility for error accumulation if the functionals are poorly formulated. This study aims to investigate the performance and limitations of second-order correlation functionals within the framework of density functional theory. Specifically, we focus on three major classes of density functional approximations that incorporate second-order energy expressions: ab initio (primarily Görling-Levy) functionals, adiabatic connection models, and double-hybrid functionals. The principal objectives of this research are to evaluate the accuracy of second-order correlation functionals, to understand how the choice of reference orbitals and eigenvalues affects the performance of these functionals, to identify the intrinsic limitations of second-order energy expressions, especially when using arbitrary orbitals or noncanonical configurations, and to propose strategies for improving their accuracy. By addressing these questions, we aim to provide deeper insights into the factors governing the accuracy of second-order correlation functionals, thereby guiding future functional development.