## 1 Introduction  
Hydrogen is considered the energy vector of the future. However, its sustainability depends on a broad range of technologies capable of producing clean hydrogen that is subsequently used to produce energy [1]. Technologies based on oxide ion transport (solid oxide cells, SOC) are expected to play a significant role: solid oxide electrolysis cells (SOEC) produce hydrogen from water electrolysis, while solid oxide fuel cells (SOFC) combine hydrogen and oxygen to form water [2]. The effective catalysis of the oxygen evolution reaction (OER) in SOEC and the oxygen reduction reaction (ORR) in SOFC have raised the necessity of designing and developing catalyst materials [3; 4; 5; 6]. The electrocatalytic mechanisms of OER and ORR in SOC involve processes of oxide ion diffusion and electronic transfer. Therefore, a high mixed ionic-electronic conductivity (MIEC) is decisive for good performance. Transition metal oxides with a perovskite-type structure are attractive materials since they may present both ionic and electronic conductivity; the ionic through oxygen ion vacancies and the electronic through the corner-sharing octahedra frameworks [7]. In addition, perovskite oxides are structurally stable, possess flexible structure-compositions for easy tuning, and are cost effective. A large number of perovskite materials are known to catalyze the ORR in SOFC [8], whereas examples of the less mature SOEC technology have emerged in the last few [6]. In addition to its MIEC properties, the ORR/OER catalyst must have chemical and mechanical stability and relatively low thermal expansion coefficients (TECs) that should be alike in the three cell components (electrolyte, anode, and cathode). Moreover, they should not react with each other at the working temperatures of the SOC. Fe-based perovskites are particularly appealing due to the high abundance of Fe oxides; their thermal expansion coefficient (TEC) values, which are closer to those of commonly used electrolytes; the energy of the Fe-O bonds in oxide-ion vacancy formation under the air and fuel operating conditions; and the remarkable variability of oxidations and spin states of Fe ions [9; 10; 11; 12; 13; 14]. The YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7+\delta}\) (\(0\leq\delta\leq 1\)) (YSCFO) system has recently been shown to display electrocatalytic activity and mixed ionic-electronic conductive (MIEC) properties, being therefore proposed as a potential air electrode for SOFCs [15]. According to the results obtained by [PERSON] et al. [15], the area specific resistance (ASR) values measured in YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7+\delta}\): CGO | CGO | YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7+\delta}\): CGO symmetrical cells are 0.20 and 0.08 \(\Omega\) cm\({}^{2}\) at 923 and 973 K, respectively; the activation energy is 1.40 \(\pm\) 0.02 eV. The YSCFO shows an incremental increase of the TEC value from 18.02 \(\times\) 10\({}^{-6}\) K\({}^{-1}\) in the RT-673 K range to 23.24 \(\times\) 10\({}^{-6}\) K\({}^{-1}\) for 673-1173 K, associated with the oxygen loss above 673 K. Moreover, experimental measurements of DC resistance for YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7/08}\) and YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7/85}\) have shown, respectively, semiconducting and metallic behavior. The optical band gap for the insulating phase was reported to be between 0.73 and 1.2 eV [16]. In addition, the YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7.56}\) phase has been described as a p-type semiconductor from the analysis of the temperature dependence of the DC conductivity [15]. Previous works have demonstrated that the DFT methodology is suitable for reproducing the electronic and magnetic properties of the system [16; 17]. The perovskite-related crystal structure of YSr\({}_{2}\)Cu\({}_{2}\)FeO\({}_{7+\delta}\) (Figure 1) presents an alternation of FeO\({}_{1+\delta}\)/SrO/CuO\({}_{2}\)/Y/CuO\({}_{2}\)/SrO layers along the \(c\)-axis [18; 19].