**3. Revision of basis sets and theoretical methods used to study the piezoelectric effect in perovskites**

The literature reports different methods and basis sets built by GCHF method for investigation of perovskites' piezoelectric effects. The RHF (Restricted Hartree-Fock) method together with the 17s11p7d/11s6p6d/5s3p1d GTOs basis was used for investigation of perovskites' piezo‐ electricity of lanthanum manganite [38]. Besides, the ROHF (Restricted Open-shell Hartree-Fock) method and the 14s7p7d/11s7p7d/9s7p1d GTOs basis set allowed the calculations of electronic structure of yttrium manganite [39]. After, studies of piezoelectric effects were done in praseodymium manganite using ROHF method and 18s12p5d3f/9s6p4d/9s5p1d GTOs basis set [40], in BaTiO3 using HF/16s9p5d/10s5p4d/6s4p1d GTOs method/basis set [41], as well as in lanthanum ferrite using HF/19s14p8d/14s9p7d/7s6p1d GTOs approximation/basis set [33]. Calculations for theoretical investigation of piezoelectric effect in samarium titanate and in yttrium ferrite were developed using DKH level (Douglas-Kroll-Hess second-order scalar relativistic) with 17s12p8d4f/10s6p3d/5s4p1d GTOs [42] and 14s9p8d/14s8p6d/6s4p1d [37] basis sets, respectively. On the other hand, quantum chemical studies for piezoelectricity of yttrium titanate and gadolinium niquelate using DKH approximation were been reported in literature. For the yttrium titanate, the 16s10p7d/11s6p5d/6s5p1d GTOs basis set was used [43], while, for gadolinium niquelate, the used basis set was 20s14p10d6f/13s8p7d/6s4p1d GTOs [44].

In the developed studies for piezoelectricity investigation, standard basis sets from literature mostly showed inefficient for theoretical description of studied perovskites, and, therefore, the electronic structure description of these materials is inadequate for a satisfactory interpretation of this effect. For this reason, we recommend the use of GCHF method strategy; even standard basis sets are inappropriate to describe the geometric parameters of studied perovskites under the piezoelectric effect perspective. Furthermore, using GCHF method basis sets allows choosing the ideal basis set to better describe the studied polyatomic environment.
