## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**GDE before O\({}_{2}\) Starvation**} \\ \hline Condition & Path & R [Å] & CN & \(\sigma^{2}\) [Å\({}^{2}\)] & E\({}_{0}\) [eV] & R-Factor \({}^{*}\) \\ \hline \multirow{4}{*}{ORR} & Mn-O\({}_{\text{ads}}\) & 1.620 \(\pm\) 0.019 & **1.0** & \multirow{4}{*}{0.006 \(\pm\) 5 \(\times\) 10\({}^{-4}\)} & \multirow{4}{*}{0.003 \(\pm\) 6 \(\times\) 10\({}^{-4}\)} & \\  & Mn-O\({}_{\text{lattice}}\) & 1.896 \(\pm\) 0.003 & 7.6 \(\pm\) 0.3 & & \\  & Mn-Mn\({}_{\text{edge}}\) & 2.878 \(\pm\) 0.004 & **4.9** & & \\  & Mn-Mn\({}_{\text{corner}}\) & 3.439 \(\pm\) 0.007 & **3.7** & & \\ \hline \multirow{4}{*}{OER} & Mn-O\({}_{\text{ads}}\) & 1.777 \(\pm\) 0.027 & **1.0** & \multirow{4}{*}{0.003 \(\pm\) 6 \(\times\) 10\({}^{-4}\)} & \multirow{4}{*}{0.004} \\  & Mn-O\({}_{\text{lattice}}\) & 1.906 \(\pm\) 0.004 & 5.7 \(\pm\) 0.5 & & \\  & Mn-Mn\({}_{\text{edge}}\) & 2.879 \(\pm\) 0.004 & **4.9** & & \\  & Mn-Mn\({}_{\text{corner}}\) & 3.442 \(\pm\) 0.008 & **3.7** & & \\ \hline \multicolumn{6}{c}{**GDE after O\({}_{2}\) starvation**} \\ \hline Condition & Path & R [Å] & CN & \(\sigma^{2}\) [Å\({}^{2}\)] & E\({}_{0}\) [eV] & R-Factor \({}^{*}\) \\ \hline \multirow{4}{*}{ORR} & Mn-O\({}_{\text{ads}}\) & 1.699 \(\pm\) 0.027 & **1.0** & \multirow{4}{*}{0.003 \(\pm\) 8 \(\times\) 10\({}^{-4}\)} & \multirow{4}{*}{0.008} \\  & Mn-O\({}_{\text{lattice}}\) & 1.892 \(\pm\) 0.004 & 5.8 \(\pm\) 0.5 & & \\  & Mn-Mn\({}_{\text{edge}}\) & 2.869 \(\pm\) 0.006 & **6.3** & & \\  & Mn-Mn\({}_{\text{corner}}\) & 3.421 \(\pm\) 0.081 & **0.5** & & \\ \hline \multirow{4}{*}{OER} & Mn-O\({}_{\text{ads}}\) & 1.768 \(\pm\) 0.040 & **1.0** & \multirow{4}{*}{0.002 \(\pm\) 1.1 \(\times\) 10\({}^{-3}\)} & \multirow{4}{*}{0.014} \\  & Mn-O\({}_{\text{lattice}}\) & 1.907 \(\pm\) 0.009 & 4.7 \(\pm\) 0.9 & & \\ \cline{1-1}  & Mn-Mn\({}_{\text{corner}}\) & 2.875 \(\pm\) 0.010 & **6.3** & & 6553.8 \(\pm\) 1.3 & \\ \cline{1-1}  & Mn-Mn\({}_{\text{corner}}\) & 3.464 \(\pm\) 0.097 & **0.5** & & \\ \hline \hline \end{tabular}  
* Constrained parameters, fixed at the averaged value, are indicated in **bold**.
* Paths with similar adsorber-scatterer interactions (i.e., Mn-O\({}_{\text{ads}}\) and Mn-O\({}_{\text{lattice}}\) or Mn-Mn\({}_{\text{edge}}\) and Mn-Mn\({}_{\text{corner}}\)) share the same mean-squared relative displacements: \(\sigma^{2}_{\text{Mn-Mn}_{\text{edge}}\) & \(\sigma^{2}_{\text{Mn-Mn}_{\text{edge}}\) & \(\text{Mn-Mn}_{\text{Human}}\), respectively. In all curve fitting processes, the goodness of fit was estimated by calculating the averaged R-factor, defined as \(\frac{\sum_{i=1}^{3}\left[\sum_{i=1}^{N}\left(\sum_{i=1}^{N}\left(\sum_{i=1}^{N} \left(\hat{x}_{i}\cdot X_{\text{data}_{i}}\right)^{i}\right)^{i}\right]^{2} \right]/\left[\sum_{i=1}^{N}\left(\hat{x}_{i}\cdot X_{\text{data}_{i}}\right)^{i} \right]^{2}\right]}{3}\).  
\end{table} 
Table 1: Results of non-linear least-squares fittings for the operando EXAFS spectra shown in Figure 4b for electrodes before and after partial O\({}_{2}\) starvation, measured under different electrochemical conditions. Fitting was performed for the following ranges of wavenumbers and radial distances: k = 3.0–15 Å\({}^{-1}\) and R = 1.25–3.2 Å.  
Figure 4: **(a)** Schematic (rendered with the open source software VESTA [18]) showing the crystal lattice of \(\alpha\)-MnO\({}_{2}\). **(b)** EXAFS spectra in the R-space (black solid line) and curve fitting (red solid line) of the Mn K-edge for GDE before (left) and after partial O\({}_{2}\) starvation (right) without (left) under OER (top) and ORR (bottom) current loads, as indicated in the figure. (c) Mn-O\({}_{\text{lattice}}\) coordination number and (d) edge energy E\({}_{0}\) as a function of applied condition. Figure 5: Determination of the \(\alpha\)-MnO\({}_{2}\) oxidation state at ORR (blue) and OER (red) conditions before (squared dots) and after (circular dots) partial O\({}_{2}\) starvation of the GDE, using the Mn K-edge energy shift of the reference Mn compounds. See text for details.