## 4 Conclusions  
The hydrogen economy comprises a broad spectrum of technologies, including solid oxide cells (SOC), which rely on oxygen ion transport in ceramic materials. Catalytic materials with fast kinetics for the involved reactions (ORR/OER) must possess high ionic and electronic conductivity. Such MIEC properties were recently discovered in YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.56}\), which led to the present DFT investigation. The computational results herein have shown that the idealized YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.5}\) compound presents a remarkable oxygen diffusion coefficient (predicted 1.28 \(\times\) 10\({}^{-7}\) cm\({}^{2}\)/s at 500 \({}^{\circ}\)C) and attractive activation energy (Ea = 0.37 eV), which buttress the low ASR value (0.08 \(\Omega\) cm\({}^{2}\) at 973 K) reported for the YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.56}\) phase [15]. The AIMD calculations confirm that oxygen diffusion is anisotropic, taking place in the _ab_ plane of the FeO\({}_{1+\delta}\) layers. In addition, the DFT results support a good electronic conductivity in the YFSCO materials, in line with previous experimental and computational findings. Although the MIEC properties can be anticipated from the DFT calculations, other requirements for OER/ORR catalysis (such as chemical and mechanical stability over cycling) must be experimentally examined.  
It is worth remarking that, depending on the annealing history/oxygen content, anti-site disorder can exist, which is to say, Cu/Fe mixing can take place in the YSCFO system [19; 20; 42; 43]. It is therefore foreseeable that anti-site defects could influence the diffusion mechanism that, in the idealized oxides, takes place exclusively in the FeO\({}_{1+\delta}\) layer. Further computational investigations will address the influence of anti-site defects in the MIEC properties of the YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7+\delta}\) (0 \(<\delta<\) 1) system.  
Conceptualization, E.M.A.-d.D.; methodology, M.G.-T.; software, M.G.-T.; validation, M.G.-T.; formal analysis, M.G.-T.; investigation, E.M.A.-d.D. and M.G.-T.; data curation, M.G.-T.; writing--original draft preparation, E.M.A.-d.D. and M.G.-T.; visualization, M.G.-T.; supervision, E.M.A.-d.D.; project administration, E.M.A.-d.D.; funding acquisition, E.M.A.-d.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the MCIN/AEI/10.13039/501100011033--\"ERDF A way of making Europe\" across the project ECSAWE-PID2022-139501 OB-C22. Authors are also thankful for funding from MCIN/AEI/10.13039/501100011033--\"NextGenerationEU\"/PRTR (project TED2021-130452B-C21) and the Universidad Complutense de Madrid (FEI-EU-22-01-4129585).  
Not applicable.  
Figure 5: (**a**) Crystal structure of the most stable model found for YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.55}\) (2a\({}_{\rm p}\)\(\times\) 2a\({}_{\rm p}\)\(\times\) 3a\({}_{\rm p}\) supercell). Color code: Fe in brown, Cu in blue, Sr in green, Y in grey, and O in red. (**b**) MSD at 1400 K for the YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.55}\). The MSD of the added O in the Y plane is depicted as a blue line, and the MSD for the O3 (FeO\({}_{1.75}\) plane) in the structure is shown in black. (**c**) Calculated atom projected DOS for the YSr\({}_{2}\)FeCu\({}_{2}\)O\({}_{7.75}\).  
Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request.  
Computational resources from the MALTA-cluster (Universidad de Oviedo) and I2 Basque are acknowledged. The authors thank the contributions of [PERSON] to the study of the \(\mathrm{YSr_{2}Cu_{2}FeO_{7.5}}\) phase.  
The authors declare no conflicts of interest.