Low-Lying ππ* Excited States in Five-Membered Ring Heterocycles: A Continuing Challenge.

The lowest electronically excited ππ* states of conjugated hydrocarbons, as well as related heterocyclic compounds, pose a significant challenge for quantum chemical calculations. The difficulty arises from the need to achieve a balanced description of excited states with markedly different electronic characters, such as bright vs dark, ionic vs covalent, and singly vs doubly excited states. Here, we focus on the low-lying ππ* states of five-member-ring heterocycles, such as furan, pyrrole and thiophene. We analyze the origins of the diverse excited-state characters from both molecular orbital and valence bond theory perspectives, employing pseudosymmetry arguments to bridge the two viewpoints and drawing comparisons with the ππ* excited states of the cis-butadiene and benzene model systems. We further discuss the critical role of electronic correlation in obtaining a balanced description of excited states and explain why it is difficult, or sometimes impossible, to achieve high accuracy with commonly used electronic-structure approximations. As an illustration, we focus on results from standard time-dependent density functional theory approximations, as well as a series of algebraic diagrammatic construction methods with systematically improvable correlation levels through perturbative truncation schemes. Finally, we address the origins and implications of valence-Rydberg mixing, which arguably remains an open question in excited-state quantum chemistry.