in preparative scale [e.g. 3.30 g of N-(1,3-diphenylallyl)-4-nitroaniline]. The catalyst could be reused up to 15 cycles without loss of activity, proving its robustness.

We investigate here the lowest-energy (spin-conserving) excitation energies for the set of He-Ne atoms, with the family of nonempirical PBE, PBE0, PBE0-1/3, PBE0-DH, PBE-CIDH, PBE-QIDH, and PBE0-2 functionals, after employing a wide variety of basis sets systematically approaching the basis set limit: def2-nVP(D), cc-pVnZ, aug-cc-pVnZ, and d-aug-cc-pVnZ. We find that an accuracy (ie, mean unsigned error) of 0.3 to 0.4 eV for time-dependent density functional theory (DFT) atomic excitation energies can be robustly achieved with modern double-hybrid methods, which are also stable with respect to the addition of a double set of diffuse functions, contrarily to hybrid versions, in agreement with recent findings employing sophisticated multiconfigurational DFT methods. K E Y W O R D S atomic excitation energies, diffuse basis functions, double-hybrid density functionals | INTRODUCTIONExcited-state studies continue to be a topic of the most interest, [1][2][3] not only because the underlying theory intrinsically presents challenges for its implementation in common codes but also due to the interplay and large number of factors affecting the final results in molecular and real systems. Whereas ground-state properties still receive much more attention in the ongoing development of density functional theory (DFT) (eg, for built-in datasets and the associated benchmarking of density functional approximations [4,5] ) the applications to atoms are recently emerging as an alternative for the benchmarking of DFT for excited states too. [6][7][8] This is facilitated by the reasonable computational cost of atomic calculations compared to more complex systems, together with the lack of geometry-induced and environmental issues often difficulting the adequate comparison between various theoretical methods.We thus apply here a set of recently developed minimally empirical models, with the time-dependent density functional theory (TD-DFT) formalism, to the lowest-energy and spin-conserving (ΔS = 0) excited-state of atoms from He to Ne. This study aims also at complementing historical studies employing more sophisticated methods, [9][10][11][12][13] as well as shedding light about the performance of some last-generation DFT methods (ie, double-hybrid [DH] functionals) from the fifth rung of the Jacob's ladder. However, dealing with atomic excitation energies unfortunately brings nonnegligible (and severe) basis set issues, due to the presence of valence and Rydberg states, and the challenge they present for an accurate excited-state description in all cases. For instance, it has been recently shown [8] how adding diffuse basis functions to state-of-the-art hybrid functionals dramatically deteriorates the results for standard TD-DFT calculations, with unreasonable errors reaching up to 1.5 to 2.5 eV with respect to experimental values [14] for first-and second-row atoms. Note that the recently developed multiconfigurational pair-density functional theory [15] (MC-PDFT) was instead not affected of such basis set dependence, which clear...