# _Ab Initio_ Study of the Mechanism of Proton Migration in Perovskite LaScO\({}_{3}\)
## 3 Results
The first peak in the \"proton-scandium\" distribution is not split and is well-resolved. The most probable distance from the proton to the Sc atom is 2.2 A. The next two most pronounced peaks of this distribution are at 4.5 A and 6 A. It is in the vicinity of these distances that the majority of the following Sc atoms adjacent to the proton are located. The \"proton-oxygen\" distribution has a clearly pronounced peak at 1.0 A, which shows that hydrogen forms a bond only with one oxygen atom, located in its field. In this case, the spectrum of distances between the proton and the rest of the oxygen atoms blurs as this distance increases. This feature of the \"oxygen\" spectrum is associated with a large number of O atoms in the system compared to other atoms and with their high mobility. Figure 12 indirectly reflects the location of the proton by the distribution of angles that a proton forms with a pair of any atoms of the same type (i.e., O, Sc, and La). The top row of figures shows the angular distributions obtained in the absence of the electric field, and the bottom row of figures shows the same distributions when the field strength \(E\) = 0.7 \(\times\) 10\({}^{10}\) V/m acts in the [10] direction in the systems under consideration. The temperature of the system in the absence and in the presence of an electric field is approximately the same (\(T\) = 683 \(\pm\) 2 K). It is seen that the corresponding angular distributions (when the angles are formed by atoms of the same type) are in good agreement with each other. The significant identity of the corresponding angular spectra indicates that the electric field has no significant effect on the proton movement in the LaScO\({}_{3}\) crystal. Figure 4:3 Distribution of distances between the proton and other atoms of the perovskite system: (**a**) lanthanum, (**b**) scandium, and (**c**) oxygen, obtained over a time interval of 1 ns in series 1. Due to the limited space for the proton to move along the LaScO\({}_{3}\) crystal, which is associated with the rigid structure of this compound, an increase in the angle, at the top of which the proton is located, when the sides pass through the centers of two atoms of the same type (O, Sc, and La), means an increase in the average distance between the proton and these atoms. Due to the high mobility of the proton, it more likely interacts with the closer atoms. Figure 12 shows that the smallest angular range is characterized by the interaction between the proton and oxygen atoms. It is this interaction that is decisive for the proton. However, the structural skeleton of a compound is not determined by oxygen, but by the metals forming this compound, i.e., Sc and La. The angular range of interaction of the proton with La is less than that with Sc. Therefore, it is easier to regulate the physical properties of the LaScO\({}_{3}\) compound by replacing La (rather than Sr) atoms with other atoms. As can be seen from Figure 13, the situation with the distribution of preferential interactions does not change, as the temperature of the system under consideration increases from 153 K to 1099 K. Even at the highest temperature, as before, the smallest angular range is observed for the proton interactions with oxygen atoms, and the largest one is for that with Sc. In all cases considered, the shape of the angular spectra does not undergo too large changes as the temperature of the system increases. Nevertheless, for the oxygen and lanthanum subsystems, the disappearance or the appearance of separate subpeaks in the angular distribution is observed at the temperature variation. Such changes are less pronounced for the scandium subsystem. Since the shape of the angular distribution characterizes indirectly the interaction between the proton and the atoms selected in the compound, the resulting response of the system to an increase in temperature means that the replacement of La by other atoms should create a corresponding effect at high temperatures.