Fig. 2: Comparison between experimental and simulated XAS spectra.

a Experimental KLL AM decay, partial-electron-yield XAS recorded in the vicinity of the aqueous Na⁺, Mg²⁺, and Al³⁺ cation 1s ionization thresholds (the spectra are based on the 2D plots, see Fig. 3). The vertical dashed lines indicate the 1s ionization energies (1s IEs). b Calculated XAS for a single structure of the [M(H₂O)₆]ⁿ⁺ clusters at the SRC2-R2 level with a cc-pCVTZ basis set on the cations and a cc-pVTZ basis set on the water molecules in a polarizable continuum. Each calculated spectral point was broadened by 0.28 eV for Na⁺, 0.43 eV for Mg²⁺, and 0.44 eV for Al³⁺. The gray bars show the oscillator strengths and the colored bars show the weights of the local contributions to the excited states. The most intense transitions are accompanied by corresponding NTOs as insets (purple—Na⁺, green—Mg²⁺, and orange—Al³⁺). c XAS spectra calculated for a set of 50 structures of [M(H₂O)₆]ⁿ⁺ clusters. d XAS spectra calculated for a set of 50 structures of \({[{{{\rm{M}}}}{({{{{\rm{H}}}}}_{2}{{{\rm{O}}}})}_{18}]}^{n+}\) clusters. The filled areas in panels (c) and (d) show the contribution of the local excited states to the overall spectrum.