## 3 Results
### X-ray Absorption Near Edge Spectroscopy (XANES)  
Operando Mn and Fe K-edge XANES spectra for the electrode at D\({}_{0}\), C\({}_{1}\), and D\({}_{1}\) states of charge are presented in Figure 2. The high variability in the Mn K-edge spectral shape and the low modifications occurring at the Fe K-edge are in line with previous work done on this material [11,12]. The Mn edge shifts towards higher energies during charge (C\({}_{1}\)) as the Mn ions are oxidized from the divalent to the trivalent oxidation state. A similar trend is recorded also for the Fe edge (see Figure S2 for the magnified XANES portion), showing a higher threshold energy at C\({}_{1}\) as a result of the Fe oxidation during ion-release (Fe\({}^{\text{II}}\)\(\rightarrow\) Fe\({}^{\text{III}}\)). The ion-uptake during the following discharge (see spectra for D\({}_{1}\)) triggers the reduction of both Mn and Fe centers, resulting in their spectral shapes almost coinciding with those seen at D\({}_{0}\). We anticipate here that the difference between D\({}_{0}\) and D\({}_{1}\) spectra is relevant for the remaining part of the discussion revolving around the MCR-ALS analysis.  
To make a further comparison between the dataset recorded in this work and the earlier one [11], Figure 3 highlights the differences and analogies between the most relevant states of charge for both edges. The pristine state in Reference [11] (pref) and the discharged state (D\({}_{0}\)) in the present dataset were used to compare the initial states of charge for MnHCF. As the Fe K-edge is modified only slightly, the differences between all the states of charge at the Fe edge do not appear significant (cf. Panels b, d, f), although Figure S3 underlines a non-perfect match between the considered pairs. On the other hand,  
Figure 1: Voltage profiles upon galvanostatic charge-discharge of a manganese hexacyanoferrate (MnHCF) electrode subjected to anomalous pre-cycling (red curve). For comparison, the behavior of a pristine electrode (data from ref. [11]) is also shown (blue curve). Also shown is the labeling of a few selected states of charge (see text).  
Figure 2: Spectra at the Mn and Fe K-edges for D\({}_{0}\), C\({}_{1}\), and D\({}_{1}\) states of charge.  
the Mn K-edge shows major dissimilarities between pristine, charged, and discharged states (Panels a, c, and e, respectively). In particular, D\({}_{0}\) and D\({}_{1}\) significantly differ from P\({}^{\text{ref}}\) and D\({}^{\text{ref}}\), respectively, while the charged states, i.e., C\({}_{1}\) and C\({}^{\text{ref}}\), match fairly well. The D\({}_{0}\) and P\({}^{\text{ref}}\) spectra are different, as expected (Panel a), due to the anomalous electrochemical pre-treatment. Despite the different initial states of charge, C\({}_{1}\) and C\({}^{\text{ref}}\) appear almost identical (Panel c), giving further insight into the electronic and structural stability of MnHCF as the ion-release occurs. The consecutive discharge process gives as a result different spectral shapes, especially if the white line intensity is taken into consideration (Panel e); however, the signal modulation of the D\({}_{1}\) and D\({}^{\text{ref}}\) samples coincides, as opposed to D\({}_{0}\)/P\({}^{\text{ref}}\) comparison (Panel a). The local structure around the Mn site is, therefore, not much affected by the anomalous pre-treatment, with the only exception being the very initial state not reflecting the much lower coulombic efficiency highlighted by the electrochemical results in Figure 1.