SUPPORTING INFORMATION (comparison to data about gas phase, free-standing, Ag nanoclusters from the literature). First of all, we applied our calculation methods for calculation of the absorption (or excitation of luminescence) spectra of simplest Ag nanoclusters dispersed in the gas phase, such as dimers, trimers and tetramers. The results of our calculations are listed in the Table, where the experimental data from the previous literature is shown for comparison with our calculation results. The distances between the Ag atoms comprising the respective Ag nanoclusters have been optimized using DFT method with LCwPBE/Aug-cc-pVTZ-PP functional/basic set; and the optimized distances are post-signed in Fig.S1 of this Section. In the particular case of the free-standing gas phase tetramer Ag42+, which has a 3-dimensional structure, the optimized geometry was a tetrahedron, as shown in Figure S1. Therefore, we applied our computing methods for calculation of parameters of the gas phase Ag42+ nanoclusters in a tetrahedron shape; note a rhomb shape for a Ag42+ nanocluster was argued above to occur when this tetramer was dispersed in the lattice of the oxyfluoride glass host. Noteworthy, we have found the rhomb structure for a free-standing gas phase Ag42+ nanocluster is not structurally stable. Table. Energy of the lowest singlet excited state of free-standing (gas phase) Ag20 dimer, Ag2+ dimer, Ag3+ trimer and Ag42+ tetramer. Experimental data are taken from the Ref. [22]; theoretical data are taken from Refs. [16-21]. Our calculation data are shown in the right column. Ag cluster Ag20 Ag2+ Data from literature Theoretical Experimental work data [22] Refs. [16-21] 2.85 2.87 No data 3.15 This work calculation LC-wPBE/ Aug-cc-pVTZCASPT2 PP 3.06 2.88 3.11 2.88 Ag3+ No data 4.11 4.10 3.98 Ag42+ No data No data 4.91 4.91 Ag Ag 2.66 Å 2.54 Å Ag 2.72 Å Ag Ag 2.78 Å Ag 2.66 Å 2.66 Å Ag Ag Ag Ag20 Ag2+ Ag Ag Ag3+ Figure S1. Geometries of Ag20, Ag2+, Ag3+ and Ag42+ which are optimized using DFT method with LC-wPBE/Aug-cc-pVTZ-PP functional/basic set. Ag42+