Table S1. Data of experimental (Expt.) and theoretical vertical detachment energies (VDEs) of the ground-state ${\mathrm{Mg}}_n^{-}$ (n = 3–8), for six different functionals. The structures have been optimized at the def2-TZVP level, for the calculations the def2-TZVPD basis set was used. All energies are given in eV. The experimental VDEs were extracted from previously reported work.¹

Table S2. Vertical detachment energies (VDE), HOMO−LUMO gaps (E_HL, in eV), average binding energies (E_b, in eV), and the secondry energy differences Δ₂E (in eV) of the ground-state ${\mathrm{Mg}}_n^{-}$ (n = 3–30) clusters.

Figure S1. Simulated photoelectron spectra of ${\mathrm{Mg}}_n^{-}$ (n = 3–8) cluster anions from the lowest energy structure found at a given functional (red lines) with the def2-TZVPD basis set, with the experimental ones (blue ones)¹ for comparison.

Figure S2. Low-lying structures of ${\mathrm{Mg}}_n^{-}$ (n = 11–20) clusters. For each structure, the total energy difference (eV) and the symmetry with respect to the lowest-energy isomer in main text are given.

Figure S3. Low-lying structures of ${\mathrm{Mg}}_n^{-}$ (n = 21–30) clusters. For each structure, the total energy difference (eV) and the symmetry with respect to the lowest-energy isomer in main text are given.