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

Abstract

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.