Benchmarking Electronic-Structure Methods for the Description of Dark Transitions in Carbonyls at and Beyond the Franck-Condon Point.

Herein, we propose a comprehensive benchmark of electronic-structure methods to describe dark transitions, that is, transitions to excited electronic states characterized by a near-zero oscillator strength. This type of electronic state is particularly important for the photochemistry of molecules containing carbonyl groups, such as atmospheric volatile organic compounds (VOCs). The oscillator strength characterizing a dark transition can change dramatically by a slight alteration of the molecular geometry around its ground-state equilibrium, the so-called non-Condon effects. Hence, testing the performance of electronic-structure methods for dark transitions requires considering molecules at their Franck-Condon point (i.e., equilibrium geometry), but also beyond the Franck-Condon point. Our benchmark focuses on various electronic-structure methods─LR-TDDFT(/TDA), ADC(2), CC2, EOM-CCSD, CC2/3, XMS-CASPT2─with CC3/aug-cc-pVTZ serving as a theoretical best estimate. These techniques are tested against a set of 16 carbonyl-containing VOCs at their equilibrium geometry. We then assess the performance of these methods to describe the dark transition of acetaldehyde beyond its Franck-Condon point by (i) distorting the molecule toward its S