Excited states exhibiting double excitation character are notoriously di cult to model using conventional singlereference methods, such as adiabatic time-dependent density-functional theory (TD-DFT) or equation-of-motion coupled cluster (EOM-CC). In addition, these states are typical experimentally "dark" making their detection in photo-absorption spectra very challenging. Nonetheless, they play a key role in the faithful description of many physical, chemical, and biological processes. In the present work, we provide accurate reference excitation energies for transitions involving a substantial amount of double excitation using a series of increasingly large di use-containing atomic basis sets. Our set gathers 20 vertical transitions from 14 small-and medium-size molecules (acrolein, benzene, beryllium atom, butadiene, carbon dimer and trimer, ethylene, formaldehyde, glyoxal, hexatriene, nitrosomethane, nitroxyl, pyrazine, and tetrazine). Depending on the size of the molecule, selected con guration interaction (sCI) and/or multicon gurational (CASSCF, CASPT2, (X)MS-CASPT2 and NEVPT2) calculations are performed in order to obtain reliable estimates of the vertical transition energies. In addition, coupled cluster approaches including at least contributions from iterative triples (such as CC3, CCSDT, CCSDTQ, and CCSDTQP) are assessed. Our results clearly evidence that the error in CC methods is intimately related to the amount of double excitation character of the transition. For "pure" double excitations (i.e. for transitions which do not mix with single excitations), the error in CC3 can easily reach 1 eV, while it goes down to few tenths of an eV for more common transitions (like in trans-butadiene) involving a signi cant amount of singles. As expected, CC approaches including quadruples yield highly accurate results for any type of transitions. e quality of the excitation energies obtained with multicon gurational methods is harder to predict. We have found that the overall accuracy of these methods is highly dependent of both the system and the selected active space. e inclusion of the σ and σ orbitals in the active space, even for transitions involving mostly π and π orbitals, is mandatory in order to reach high accuracy. A theoretical best estimate (TBE) is reported for each transition. We believe that these reference data will be valuable for future methodological developments aiming at accurately describing double excitations. TOC graphical abstract arXiv:1811.12861v1 [physics.chem-ph] 30 Nov 2018

We describe our efforts of the past few years to create a large set of more than 500 highly accurate vertical excitation energies of various natures (π → π*, n → π*, double excitation, Rydberg, singlet, doublet, triplet, etc.) in small‐ and medium‐sized molecules. These values have been obtained using an incremental strategy which consists in combining high‐order coupled cluster and selected configuration interaction calculations using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspects of the so‐called QUEST database of vertical excitations is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating theoretical cross comparisons. Following this composite protocol, we have been able to produce theoretical best estimates (TBEs) with the aug‐cc‐pVTZ basis set for each of these transitions, as well as basis set corrected TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug‐cc‐pVTZ have been employed to benchmark a large number of (lower‐order) wave function methods such as CIS(D), ADC(2), CC2, STEOM‐CCSD, CCSD, CCSDR(3), CCSDT‐3, ADC(3), CC3, NEVPT2, and so on (including spin‐scaled variants). In order to gather the huge amount of data produced during the QUEST project, we have created a website (https://lcpq.github.io/QUESTDB_website) where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, and so on. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited‐state methods. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods