Do DFT-based calculations always result in integer-charge ions in electrolytes?

The well-established phenomenon of solute atom dissolution from metal surfaces and their conversion into ions, with integer charges, as electrode potential increases has long been recognized. However, a critical question arises regarding the capability of Density Functional Theory (DFT) computations in predicting ions with integer charge states, given their reliance on probabilistic electron representations. This study introduces a more sophisticated perspective through comprehensive first-principles/continuum calculations, exploring the dissolution and deposition processes of 22 distinct metal elements across a broad range of applied electrode potentials. The outcomes illuminate three distinct dissolution models for various metals, thus offering fresh insights into this intricate phenomenon. Firstly, solute atoms exhibit an integer charge state following an integer-valence jump, aligning with classical understandings. Secondly, solute atoms attain an eventual integer valence, yet their charge state increases in a non-integer manner during dissolution. Lastly, we observe solute atoms exhibiting a non-integer charge state, challenging classical understandings. Furthermore, we propose a theoretical criterion for determining the selection of ion valence during electrode dissolution under applied potential. This discovery provides a novel perspective on our understanding of ion charge states.