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Abstract We present theoretical justification for distorted Ruddlesden–Popper (RP) phases of the first-order by using hybrid density functional theory (DFT) calculations and group-theoretical analysis. We, thus, demonstrate the existence of the Jahn–Teller effect around an Fe $$^{4\texttt {+}}$$ 4 + ion in Sr $$_{2}$$ 2 FeO $$_{4}$$ 4 . On the calculation side, we have established a combination of Wu–Cohen (WC) exchange and Perdew-Wang (PW) correlation in a three-parameter functional WC3PW, giving the most accurate description of Sr $$_{2}$$ 2 FeO $$_{4}$$ 4 from the comparison of three hybrid DFT functionals. Self-consistently obtained Hartree–Fock exact exchange of 0.16 demonstrates consistent results with the experimental literature data. Importantly, we explain conditions for co-existing proper and pseudo-Jahn–Teller effects from the crystalline orbitals, symmetry-mode analysis and irreps products. Moreover, phonon frequency calculations support and confirm the results of symmetry-mode analysis. In particular, the symmetry-mode analysis identifies a dominating irreducible representation of the Jahn-Teller mode (X2+) and corresponding space group (SG) of ground state structure (SG Cmce model). Therefore, the usually suggested high-symmetry tetragonal crystal structure (SG I4/mmm model) is higher in energy by 121 meV/f.u. (equivalent to the Jahn-Teller stabilization energy) compared with the distorted low-symmetry structure (SG Cmce model). We also present diffraction patterns for the two crystal symmetries to discuss the differences. Therefore, our results shed light on the existence of low-symmetry RP phases and make possible direct comparisons with future experiments.

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Sr-doped lanthanum scandate La1−xSrxScO3−δ (LSS) is a promising perovskite-type material for electrochemical applications such as proton conductors. Oxygen vacancy is a common defect in ABO3-type perovskites. It controls ion transport as well as proton uptake. The energetic, structural, and electronic properties of oxygen vacancy in LSS are studied deploying the DFT method with meta-GGA functional. The vacancy formation energies in LSS were calculated for various Sr concentrations. Unlike other perovskites, in this material, the electrons are trapped at the oxygen vacancy site (the F-type centres, common in ionic oxides like MgO and Al2O3) rather than localised on the nearest to the vacancy B-cations. The process of oxygen vacancy formation is considered relative to Sr concentration x and oxygen nonstoichiometry factor δ. Three primary regimes are discussed: (I) localized at the vacancy electrons, x/δ < 2, (II) electron charge balanced system, x/δ = 2, and (III) delocalized electron holes, x/δ > 2. For x/δ ≥ 2 oxygen vacancy formation energy reaches the saturation level of ~3.5 eV, which is potentially beneficial for the proton uptake.