Doubly excited character or static correlation of the reference state in the controversial 2¹A_g state of trans-butadiene?

Butadiene is the simplest polyene and has long served as a model system for many chemical and spectroscopic properties. However, this small molecule has presented significant challenges to theoretical chemistry. The 2¹A_g state, which is dark but photochemically important, is a prime source of this difficulty. Previous studies attributed the notorious difficulty in treating this state to strong double excitation character of the 2¹A_g state, which prevents the application of linear response (LR) methods. Therefore, one would require methods with much higher computational cost, especially for the analogues of this state in longer polyenes, and consequently studies of longer polyenes are very limited. In the present work, we argue that the difficulty stems more significantly from the inherently multiconfigurational character of the ground state. In addition, we validate the possibility of employing LR time-dependent density functional theory to investigate such a state with reasonable accuracy.