# _Ab Initio_ Study of the Mechanism of Proton Migration in Perovskite LaScO\({}_{3}\)
## 5 Conclusions  
Although oxygen vacancies are currently playing a decisive role in characterizing devices based on ABO\({}_{3}\) perovskites, we investigated the proton conductivity in defect-freeperovskites based on metal oxides. Understanding the mechanism of proton conductivity in a defect-free material, which occupies at least 80% of even perovskite doped and enriched with oxygen vacancies, is important for the further improvement of environmentally friendly energy devices. We investigated the behavior of the proton in the perovskite LaSrO\({}_{3}\) crystal depending on its initial location and velocity, external electric field, and temperature. The discontinuous nature of proton diffusion in perovskite was established and four types of jumps determined by the structural features of the perovskite were identified. Average execution time for all types of proton jumps is between 32 and 47 fs. The activation diffusion energy varies in the range of \(0.95\leq E_{a}\leq 1.75\) eV. The difference in the frequencies of different types of jumps can be as high as 2.3. It is found that proton migration in solid defect-free perovskite LaScO\({}_{3}\) is characterized by the equation  
\[\ln D=10.11\text{-}15.37(1000/T),\]  
where the diffusion coefficient \(D\) is in cm\({}^{2}\)/s and the temperature \(T\) is in K.  
The scale of the proton's displacements in the presence of an electric field and without it was established by the visual observation on the proton trajectory and the partition of the space occupied by atoms, using Voronoi polyhedra. Regardless of the presence of an electric field in the entire temperature range under study, the angles formed by a proton with oxygen ions form a smaller number of peaks (from 4 to 5) than the angles created by a proton with lanthanum ions (5-6) or scandium ions (6-7). This is due to the stronger attraction of the proton to oxygen. The set of ab initio molecular dynamic tests is evidence in favor of the polaron character of proton migration in the LaSrO\({}_{3}\) perovskite. This is confirmed by the fact that the immediate environment of the proton and the temperature of the system determine the trajectory of its motion to a much greater extent than the external electric field. Further improvement of semiconductor electrolytes should be based on taking into account the mechanism of proton migration along a perfect perovskite crystal. This, along with investigating the effect of oxygen vacancies, could significantly improve the performance of the clean energy devices. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12115302/s1](https://www.mdpi.com/article/10.3390/app12115302/s1)]([https://www.mdpi.com/article/10.3390/app12115302/s1](https://www.mdpi.com/article/10.3390/app12115302/s1)). Conceptualization, A.Y.G. ; methodology, A.Y.G. and D.S.P. ; software, D.S.P. ; validation, A.Y.G. and D.S.P. ; formal analysis, A.Y.G. and D.S.P. ; investigation, A.Y.G. and D.S.P. ; resources, D.S.P. ; data curation, D.S.P. ; writing--original draft preparation, A.Y.G. ; writing--review and editing, A.Y.G. and O.R.R. ; visualization, D.S.P. ; supervision, A.Y.G. and Y.P.Z. ; project administration, Y.P.Z. and O.R.R. ; funding acquisition, Y.P.Z. and O.R.R. All authors have read and agreed to the published version of the manuscript. This work is partly supported by Government of Russian Federation, the State Assignment number FEUZ-2020-0037, registration number 075-03-2022-011; and is partly executed in the frame of the scientific theme of Institute of high-temperature electrochemistry UB RAS, number FUME-2022-0005, registration number 122020100205-5. Not applicable. All the details regarding the reported results can be obtained upon private request from the authors. These calculations were performed on a hybrid cluster type computer \"URAN\" at the N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences with a peak performance of 216 Tflop/s and 1864 CPU.