Electronic many-body effects govern aqueous redox thermodynamics, yet their roles in transition metal redox chemistry remain poorly understood. Here, we systematically compare density functional theory and random phase approximation (RPA)-based methods using statistically converged first-principles free-energy calculations. We show that density functional errors correlate strongly with the self-interaction error and are substantially reduced when the straight-line condition is satisfied. In contrast, RPA-based methods exhibit substantial errors that show no clear correlation with self-interaction error. Combined analyses using beyond-RPA methods and correlated wave-function calculations show that complete second-order correlation, infinite summation of ring diagrams, renormalized single excitations, and empirically optimized functionals of the RPA response each fail, individually, to yield accurate redox levels, a trend consistently observed from isolated ions to clusters and the bulk solution, highlighting the need for balanced higher-order correlations for localized $d$-electron systems in solution.

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• Electrochemistry
• Electronic structure
• Density functional calculations
• Machine learning
• Molecular dynamics