Effect of Charge and Solvation Shell on Non-Radiative Decay Processes in s-Block Cationic Metal Ion Water Clusters

A molecular cluster's inner valence ionized state undergoes autoionization, which is nonlocal by nature. In a molecular system, when the inner valence's ionization potential (IP) is higher than the double ionization energy (DIP), it is energetically favorable for the initially ionized system to emit a secondary electron and reach a final state which is lower in energy. This relaxation usually happens via intermolecular coulombic decay (ICD) or electron transfer-mediated decay (ETMD). We have choosen the Na$^+$-(H$_2$O)$_{n=1-5}$ and Mg$^{2+}$-(H$_2$O)$_{m=1-5}$ cluster as the test systems. These systems are also found in the human body, which makes this study important. We have calculated the IP, DIP values, and the lifetime of Na-2s and Mg-2s temporary bound states (TBSs) in these clusters to study the effect of solvation on IP, DIP, and the lifetime of Na-2s and Mg-2s TBSs. We observe a considerable increase (96\%) in the lifetime of the Na-2s TBS in the second solvated shell structure in Na$^+$-(H$_ 2$O)$_{n=2}$ compared to the first solvated one. However, the increase in the lifetime of the Mg-2s state in the second solvation shell is only 33\%. We have revealed the different factors that affect the lifetime of TBSs and which type of decay process (ICD or ETMD) is dominant. We have shown how the charge of metal ions and increased water molecules affect the decay rate. We have shown that the decay of Mg-2p is also possible in all magnesium-water clusters, but it is not valid for the decay of Na-2p.