Computational Screening of Oxide Perovskites as Insertion-Type Cathode Material

material are available. Ideally such a screening study should be done jointly with materials synthesis experts. [51] However, we view our screening study also as a motivation for our experimental colleagues to address the preparation of materials that have not been produced yet. In the present study the veri ﬁ ably existing niobate compounds LiNbO 3 , NaNbO 3 , and KNbO 3 have been discarded due to high volume change in the case of Li and high diffusion barriers in the case of Na and K. However, our calculations suggest that especially the Mg-intercalated NbO 6 framework could be an interesting research direction in the development of high-energy cathode materials for Mg-based batteries


Introduction
The electrification of transportation devices is widely regarded as crucial for the transition toward renewable energy systems [1][2][3] but, while electric vehicles (EV) based on hydrogen fuel cells continuously suffer from high fuel costs due to unfavorable round trip efficiencies, [4,5] the price for Li-ion batteries, scaled by their energy capacity, has been reduced by about 97% since market introduction in 1991, accompanied by significant performance gains. [6]Accordingly, the growth of the battery market for light-duty EVs exceeds all expectations [7][8][9] and batteries are at least considered as viable options for heavy-duty EVs [10] and short-to-medium distance shipping. [11][14] A circulatory material flow could offer remedy in the described scenario, but issues concerning sustainable manufacturing [15] and recycling [12,16] of currently used battery materials are not fully resolved yet.19] In order to suffice user demands on range and flexibility of mobile applications, one particular requirement on the energy storage is high energy density and/or high specific energy. [20]Concerning batteries, although substantial improvements on the engineering level have been made recently, on the materials' side, there are so far no post-Li alternatives reaching up to the performance of state-of-the-art technologies based on lithium-ion shuttles. [8,9]One research trend, therefore, aims at rendering Li-ion technology more sustainable.This can obviously be done by replacing critical materials with less critical ones, as is reflected in the trend toward Co-and Ni-free LFP cathodes [21] or in the substitution of natural graphite by the synthetic equivalent. [22]Also performance enhancement of current technology may decrease the materials exploitation, for example, by increasing the cycle life of the battery or by elevating the energy that can be stored in a certain amount of material.A completely different but recently strongly pronounced idea is the substitution of Li as the shuttle ion.Due to chemical similarity, the most obvious candidate is the Earth-abundant element Na.[25] This problem is even more pronounced for other considered shuttle ions such as K, Mg, Ca, Zn, and Al.As a result, a complete research field focusing on the development of corresponding materials has evolved during the last years. [26]Many reviews highlight the progress in the field, [27][28][29][30][31] but the ultimate chemistries are yet to be found and the corresponding materials have to be developed.
One in many regards particularly interesting class of materials are oxide perovskites, which are named after the Russian politician and leisure time mineralogist L. A. Perovski, who allegedly enabled the discovery of the prototype crystal CaTiO 3 with its typical corner-sharing oxygen octahedra. [32]The first application of this class of materials was BaTiO 3 , which has served as dielectric DOI: 10.1002/aesr.202300204 The electrification of the transportation sector exacerbates all issues concerning the use of critical materials in state-of-the-art batteries and, therefore, urges the development of new technologies based on potentially greener and more abundant materials.One research trend is the substitution of Li as shuttle ion with other elements such as Na, K, Mg, Ca, Zn, Al, that is, the so-called post-Li technology.Although significant progress has been achieved in this field recently, these novel battery chemistries are mostly not matured yet.In the present work, the development of new battery materials by screening the materials' class of oxide perovskites as high-energy insertion-type cathode material is addressed.Based on density functional theory calculations, the specific energy, the energy density, the volume change, and the energy above hull are derived for 280 compounds and appropriate screening criteria are employed.In a second step, the diffusion barriers are determined for the most suitable materials.Eventually, MgNbO 3 , ZnVO, and AlMoO 3 are suggested as candidate materials for post-Li batteries for further investigation with MgNbO 3 appearing particularly promising.medium in capacitors since the 50s of the last century. [33]esearch then became aware of the tunability of these materials' properties by substituting the cations on the A-and B-position in ABO 3 , which together with the oftentimes straightforward synthesizability led to a range of applications.Examples can be found in catalysis and electrocatalysis [34] but oxide perovskites are also used as ionic conductors in solid oxide fuel cells [35] or as supercapacitors. [36]espite their popularity, oxide perovskites have hardly been studied for their use in post-Li systems.Li x La 1Àx TiO 3 has been discussed as potential solid electrolyte material for Li-ion batteries but intercalation of Na and Mg was not feasible. [37,38]On the cathode side, CaMO 3 (M = Cr, Co, Fe, Mn, Ni, Mo) has been studied with first-principles methods but no electrochemical activity could be observed for the suggested material CaMoO 3 in a subsequent experiment. [39]On the other hand, Ca intercalation into CaMnO 3 has been reported, although the process was accompanied by partial degradation of the material. [40]To the best of our knowledge, a more comprehensive investigation of oxide perovskites with respect to battery materials particularly for post-Li technology is still lacking.
In order to fill this gap, we employed density functional theory (DFT) which is well suited to describe battery components on the atomic level [41] to systematically investigate the materials' class of oxide perovskites as potential high-energy cathode materials for the intercalation of the abovementioned shuttle ions.In total, we performed DFT calculations on 280 different compounds and we evaluated different properties such as theoretical specific energy, theoretical energy density, theoretical volume change, and chemical stability.For those candidate materials with promising properties, we additionally evaluated the diffusion barrier of the corresponding ion.Eventually, we were able to narrow down the initial material space to the three compounds MgNbO 3 , ZnVO 3 , and AlMoO 3 which we suggest for further investigation.MgNbO 3 seems to be the most promising candidate material among these three.

Calculational Details
Oxide perovskites have the general stoichiometry ABO 3 where the B-site cation is octahedrally coordinated with oxygen and the A-site cation resides in the interstitial voids of these cornersharing octahedra.The ideal cubic structure only contains five atoms per unit cell, but many real compounds are subject to distortions of this highly symmetric phase, leading to a wide range of geometries with lower symmetry, still fulfilling the above given structural definition.These distortions can be classified in three categories: 1) tilting of the octahedra as famously described by A. M. Glazer [42,43] ; 2) Jahn-Teller distortions of the octahedra; and 3) ferroelectrical displacement of the B-site cations within the octahedra. [44]It has been shown in a DFT analysis that the energy is lowered significantly (several 100 meV atom À1 ) by structural distortions so the highly symmetric cubic phase is not realized in many compounds. [45]On the other hand, combining only the distortions of type (1) and (3) gives rise to 61 symmetrically nonequivalent geometries, [44] a number which is far too large for the screening of several hundred compounds.Therefore, we decided to follow the rather pragmatic approach of Emery and Wolverton [46] and only evaluate the most common perovskite geometries, that is, the cubic phase (Pm3m), the rhombohedral phase (R3c), the tetrahedral phase (P4mm), and the orthorhombic phase (Pnma) for every input stoichiometry.
In this computational screening study, we consider the shuttle ions Li, Na, K, Mg, Ca, Zn, and Al.Thus the results of our materials screening are relevant both for Li-ion and for post-Li battery technologies.To study insertion-type cathode materials, the A-site has to be occupied by one of these shuttle ions Li, Na, K, Mg, Ca, Zn, Al, while the BO 6 octahedra serve as host structure for the topotactic intercalation reaction.The B-side can at least in principle be occupied by any other metal of the periodic table, [47] but for our screening we chose a rather practical approach and excluded all elements: 1) which are not stable (Tc, Pm, the elements beyond Bi); 2) which are too toxic for any real live technology (Be, As, Cd, Te, Hg, Tl, Pb); 3) which are too rare for any large-scale application (Ru, Rh, Pd, Re, Os, Ir, Pt, Au); and 4) although we allowed for stoichiometries with untypical oxidation states, we excluded alkali and alkaline earth metals due to their inertness to take up and release electrons.This gives us in in total 7 ⋅ 40 ¼ 280 different stoichiometries ABO 3 as input for the investigations.
Furthermore, we focus on high-energy materials, which enable the complete deinsertion of the A-site cations.Therefore, we modeled the cathode material in the low state of charge, that is, ABO 3 and in the high state of charge, that is, BO 3 , as depicted in Figure 1.Each structure was modeled in the four abovementioned geometries, and the lowest energy structure was used for the investigation of the battery properties.Topotacticity of the intercalation reaction is thus introduced by restricting both the low state of charge and the high state of charge to a perovskite geometry although exactly the same symmetry is not necessarily demanded.
The ground-state energy of every input structure was calculated using DFT employing the exchange-correlation functional suggested by Perdew, Burke, and Ernzerhof. [48][51] Hence we added an on-site interaction term U (PBE þ U) in the functional form suggested by Dudarev et al. [52] with values of U Co ¼ 3.32, 25, and U W ¼ 6.2 eV.Note that this is on par with the functional as applied by the Materials Project database, [53] rendering the calculations comparable.57] Electronic wave functions were expanded up to energies of 600 eV and it was made sure that total energies converged within a few meV atom À1 with respect to the number of k-points in the first Brillouin zone.All structures were optimized until the entries of the stress tensor and all forces were below 0.01 eV Å À1 without constraining any internal degree of freedom.The spin state of many perovskites is still subject to ongoing debate [58] and the difference in ferromagnetic and nonmagnetic states may easily result in energetic errors of more than 1 eV atom À1 .Furthermore, it is well known [59] and also confirmed by our experience that sometimes the correct nonmagnetic ground state is not found when the calculation is initialized ferromagnetically.Therefore, we explicitly searched for high-spin and low-spin states for all possibly magnetic elements, [59] while all other elements were initialized with low magnetic moment.No attempt was made to find antiferromagnetic states as this approximation typically results only in low energetic errors compared to ferromagnetic states [60] and the exact magnetic ordering is of no particular interest for the present study.
Theoretical specific energy ρ grav and theoretical energy density ρ vol , both evaluated with respect to metal anode, have been approximated by where E ABO 3 and E BO 3 are the DFT energies of the cathode materials in the corresponding state of charge and E A is the DFT energy of the metallic species A. M ABO 3 and V ABO 3 are the mass and the volume of the perovskite materials per formula unit.Zero-point energies and entropic contributions were neglected for all energetic considerations.The theoretical volume change was obtained by Chemical stability and synthesizability were addressed by comparing a compound's energy to all possible configurations with the same stiochiometry (allotropes and potential decomposition products) that are available in the Materials Project database. [53]he difference to the configuration with the lowest energy, commonly termed the energy above hull E hull , was then evaluated.To be specific, E hull is the difference to the energetically most favorable phases which are built of exactly the same elements.Therefore, it represents a metric for thermodynamic stability, which can be seen as an indicator for synthesizability. [61]till, we would like to stress that a compelling prediction of a materials' synthesizability is clearly not possible.Here, only a few remarks on the calculation procedure shall be given.As described above, we used the same functional form as the Materials Project database, rendering the calculations in principle comparable.Nevertheless, deviating input parameters with respect to the basis set and the particular choice of the pseudopotentials can lead to differences in the resulting total energies.In order to minimize these deviations, not total energies but formation energies were compared.Two other problems arise due to this necessary procedure.1) It is well-recognized that the O 2 molecule is overbound in the generalized gradient approximation calculations, leading to erroneous results for the formation energies of oxide species, and 2) some compounds were calculated with the PBE þ U functional, whereas, for the metallic elemental phases, the original functional was used, again resulting in poor estimations for the formation energies.In order to account for these errors, we adapted the empirical corrections described by Wang et al. [62] Note also that we allowed negative values of E hull which means that the considered compound is lower in energy than the convex hull spanned by the compounds of the database.Nudged elastic band (NEB) calculations [63] were employed to evaluate the diffusion barrier E diff of certain species.The A x BO 3 supercells were created with x ¼ 0.0555=0.0625 in the high vacancy limit and x ¼ 0.9445=0.9375 in the low vacancy limit, where the first number corresponds to cubic and tetragonal cells and the second one to rhombohedral and orthorhombic ones.We investigated all symmetrically nonequivalent diffusion paths, that is, one for cubic and rhombohedral cells, two for tetragonal, and three for orthorhombic ones.The calculations were performed with five images, only in some cases with convergence issues, the number was reduced to four or three.Optimized NEB algorithms [64] were used to optimize the ion positions until the forces on every ion were lower than 0.05 eV Å À1 .The climbing image method was used to ensure that the transition state was found. [65]Ab initio molecular dynamics simulations are another computational tool to study dynamical processes in batteries, [66] also in materials such as perovskites, [67] but their high numerical demand prohibits their use in computational screening studies.

Results
We will now describe our approach to screen the oxide perovskite materials.As described earlier, the full or empty electrode materials ABO 3 and BO 3 , respectively, were considered in four different symmetries each.The one lowest in energy was then used for all further investigations.It has already been mentioned that in a previous study, distorted perovskites deviated by several 100 meV atom À1 from the cubic structure. [45]Our investigation reveals that the difference may even be in the order of one eV atom À1 , as is deduced from the comparison of the total energies of the different polymorphs of VO 3 and AlVO 3 in Figure 2.While for some of the analyzed compounds as for instance VO 3 the energy difference between the polymorphs is only a few meV atom À1 and the lowest-energy geometry only slightly deviates from the cubic structure, the octahedra in other compounds as for instance AlVO 3 are considerably tilted and distorted, leading to significant deviations in energy.This confirms once more that the cubic structure is an invalid approximation in many cases and taking into account the less symmetric phases is clearly necessary.In general, of all 280 ABO 3 /BO 3 stoichiometries 206/161 attained the lowest energy in the orthorhombic phase, 52/77 in the rhombohedral phase, 17/42 in the tetrahedral phase, and 5/0 in the highly symmetric cubic phase.
The battery properties which are directly accessible from the calculations are depicted in Figure 3.In the energy-related plots, the rows for Mg, Ca, and Al nicely mirror the advantage of multivalent batteries, that is, high energy density with respect to both, weight and volume.Zn is an exception as it has the least negative standard electrode potential of the analyzed shuttle ions.In order to filter potential high-performance materials, we compared the obtained values to state-of-the-art electrode materials investigated on an equal level of theory.Commonly used cathode materials as LiCoO 2 (LCO), LiMn 2 O 4 (LMO), and LiFePO 4 (LFP) have for instance been investigated within the PBE þ U framework by Chevrier et al. [68] and the derived properties shown in Table 1 serve as reference for the screening in the present work.Although on the material's level, LCO outperforms LMO and LFP by far, the latter two materials suffice the performance criteria of EV batteries, [9] which means they can be considered high-energy cathode materials.Thus, we set our screening criteria accordingly.In absolute numbers: we demand a high-performance cathode to possess ρ grav > 500 Wh kg À1 and ρ vol > 2000 Wh dm À3 .
2. Total energy per atom for the different distortions of VO 3 and AlVO 3 as example.The lowest energy structures are depicted for both cases.The structure of VO 3 is almost cubic and the different modeled distortions hardly differ in energy, whereas in AlVO 3 the octahedra are severely tilted and distorted and the orthorhombic phase is more than 1 eV atom À1 lower in energy than the ideal cubic phase.The volume change of the electrode upon intercalation is another relevant quantity, as too high values may lead to stress and strain and eventually pulverization of the material.Visual inspection of Figure 3 shows that in contrary to the energyrelated properties, which are strongly dependent on the A-site cation, the volume change rather seems to be related to the element on the B-site, although this trend is not as clear.In general, many of the investigated materials, in particular most of the lanthanide-containing compounds, show a change in volume of over 20% abs which is the maximum of the color code in Figure 3. Again, we compared these values to the ones derived from Chevrier et al. [68] and set our screening criterion for volume change a bit more loosely to ΔV V < 10% abs .The use of E hull to estimate synthesizability is common practice as has been thoroughly discussed in a recent review. [61]In that regard, E hull ¼ 0 indicates that a certain material is positioned on the convex hull and, therefore, claimed to be thermodynamically stable.Nevertheless, due to imperfections of DFT, the negligence of kinetic effects, and unknown complications in the synthesis procedure, positive values for E hull may still correspond to synthesizable materials, and synthesis of materials with E hull ¼ 0 may fail. [61]Furthermore, one has to keep in mind that although at the time of writing this manuscript the Materials Project database contains over 150 000 crystal structures evaluated with DFT, there may be stable compounds missing in the database, so the convex hull which is spanned by the comprised materials and which our computation of E hull relies on may be incomplete.
Here, we aim at a criterion to discard all unsynthesizable materials, but the choice of the appropriate threshold value for E hull is a challenging task.Studies similar to the present one use values in the range of 50-100 meV atom À1 , [51,69] but also smaller thresholds can be found in literature. [47]On the other hand, the authors of the correction scheme we employed [62] report a root mean square error of 92 meV atom À1 in the prediction of formations energies for a dataset of 222 compounds, which means that outliers may have errors far beyond 100 meV atom À1 .Therefore, we decided to set the screening criterion to E hull < 200 meV.While this value potentially allows many unstable materials to pass the stability screening, it insures that the likelihood of discarding a stable material with potentially promising battery properties is very small.This approach is further justified by the comparison of our stability predictions to a recent study on the prediction of stable perovskites by a machine learning approach. [70]In this study, the authors designed the stability descriptor τ based on oxidation states and ionic radii, where τ < 4.18 indicates perovskite structure with an accuracy of 92% for oxides.We have evaluated τ for the perovskites of our own dataset where values for the ionic radii were available in the extended list of Ouyang. [71]Figure 4 shows that the descriptor-based method predicts stable perovskites up to roughly E hull ¼ 200 meV atom À1 , implying that lower threshold values for the screening would possibly lead to the rejection of stable compounds.As a result of the high threshold value, only few compounds ABO 3 are filtered out due to the stability criterion (see Figure 3).On the contrary, the deintercalated cathode host BO 3 is predicted to be unstable for many B-cations (Al, Si, Sc, Ti, Mn, Co, Ga, Zr, Sn, Sb, Hf, Bi, Ho, Er, Tm, Lu), rendering all corresponding materials as unsuitable for high-energy battery electrodes.
Among the 280 compounds, there are 30 which passed the presented screening process.Further, 17 were discarded since either for ABO 3 or BO 3 the perovskite structure collapsed during the DFT geometry optimization, leaving only 13 compounds for which we determined the energetic barrier for the solid-state diffusion of the A-cation.Commonly, 650 meV are assumed as maximum diffusion barrier, still allowing sufficient charge/ discharge rates in nanostructured materials. [27,72]As shown in Figure 5, none of the perovskite structures in the low vacancy limit and hardly any in the high vacancy limit fulfill this criterion, in contrast to, for example, spinel materials. [73,74]This observation is in line with previous studies on oxide perovskites. [39,75]otwithstanding, the screening reveals MgNbO 3 , ZnVO 3 , and AlMoO 3 as interesting materials, exhibiting sufficient mobility in the deintercalated state.Interestingly enough, the charge carriers for all these three materials are multivalent ions whose migration is usually hindered by high diffusion barriers. [76,77]owever, here these materials exhibit diffusion properties that are superior to those with monovalent ions among the considered favorable candidates.
Table 1.Battery properties of state-of-the-art cathode materials.The battery properties for LCO, LMO, and LFP were derived based on the DFT calculations of Chevrier et al. [68] as described in the Calculational details.The threshold criteria have been derived in order to screen the material properties of Figure 3.  [70] is compared with our screening criterion for E hull .The blue left-bottom quadrant contains the compounds which are predicted to be stable by the descriptor method (τ < 4.18).It is clear that a screening criterion for E hull lower than 200 meV atom À1 would result in discarding materials, which are predicted to be stable by the descriptor method.
Additionally, it is interesting that the value of E diff strongly differs depending on the exact path taken in the structure.In the case of AlMoO 3 for instance, the barrier varies by more than 2 eV within the three paths in the low vacancy limit and by more than 1 eV within the high vacancy limit.A comprehensive study taking all possible diffusion paths into account is thus necessary in the search for a channel for ionic diffusion.A further observation is the discrepancy of the barriers in the low vacancy limit and the high vacancy limit in many cases which amounts to roughly 2 eV as in the example of CaTaO 3 .Since any volume effect on E diff can be excluded due to the imposition of the strongly limiting screening criterion, the discussed discrepancy indicates that the interaction of the shuttle ions on the A-site within the BO 3 host structure may significantly affect their ionic mobility.
An overview of the properties of the candidate materials is given in Table 2.While MgNbO 3 attains the lowest energy in the rhombohedral symmetry (R3c), ZnVO 3 and AlMoO 3 are energetically more favorable in the orthorhomic structure (Pnma).For the materials in the high state of charge, the tetragonal structure (P4mm) is attained in all three cases.The specific energy of all three materials is roughly in the range of LMO and LFP or slightly above (compare to Table 1).At the same time, with respect to the energy density, the candidate materials outperform LMO and LFP by far.For instance, the energy density of MgNbO 3 is 50% higher than that of LFP.The energetic performance of LCO, on the other hand, could not even be approached.The values for the volume change are reasonably low for all three materials, which was ensured by the screening criterion.The values for E hull indicate that NbO 3 and MoO 3 are probably stable materials whereas VO 3 is right under the threshold criterion and therefore not very likely to be stable.The corresponding intercalated compounds MgNbO 3 , ZnVO 3 , and, AlMoO 3 are located in the intermediate range, that is, they are potentially, but not very likely, stable.
As discussed above, the diffusion barriers for MgNbO 3 , ZnVO 3 , and AlMoO 3 in the low vacancy limit are very high, whereas they show promising values in the deintercalated state.A closer look on the diffusion path for MgNbO 3 in Figure 6 reveals another interesting fact: The diffusion path in the intercalated material goes downhill.This indicates indeed that the initial and final configurations are not the energetically most favorable ones for the given stoichiometry, but the intermediate images seem to be more stable.We performed DFT geometry optimizations of the distinct images to confirm the outcome of the NEB calculations.The final structures of every image are visualized in the Supporting Information.They reveal that the perovskite-typical corner-sharing oxygen octahedra is retained in every image and the structure does not collapse.Hence, the intermediate images attaining lower energy are still perovskites.This may indicate that the true barrier for solid-state diffusion in the low vacancy limit is lower than the value given in Table 2.The barriers for ZnVO 3 and AlMoO 3 are very high, so electrochemical activity in these compounds is rather unlikely.The diffusion paths for all compounds in Figure 5 are provided in the Supporting Information.Note that also LiCrO 3 , MgMoO 3 , and AlVO 3 show downhill diffusion paths.   .Diffusion barriers of MgNbO 3 .In the high vacancy limit, MgNbO 3 exhibits low diffusion barriers.In the low vacancy limit, the diffusion path goes downhill, indicating that the initial and the final structure are energetically unfavorable for the given stoichiometry.A more detailed discussion can be found in the text.

Conclusion
In the present work, 280 different oxide perovskites have been investigated as potential high-energy insertion-type cathode materials for batteries.Based on DFT calculations, the specific energy, the energy density, the volume change, and the energy above hull were derived for all compounds.Appropriate screening criteria on these properties were applied to filter out all unsuitable materials.Additionally, it was ensured that the perovskite structure was retained during DFT geometry optimization.
For the 13 materials that passed the screening process, the diffusion barriers for the migration of the shuttle ions were derived.Again, a screening criterion ensuring sufficient ionic mobility was employed.None of the investigated compounds exhibited low diffusion barriers in the low vacancy limit and the compounds MgNbO 3 , ZnVO 3 , and AlMoO 3 only did in the high vacancy limit.After all, we were able to narrow down the initial 280 compounds to the three compounds MgNbO 3 , ZnVO 3 , and AlMoO 3 to be used in post-Li battery technologies with multivalent ions, which we suggest for further investigation.Of these materials, MgNbO 3 seems to be particularly promising, as there is reason to believe that the real diffusion barrier for MgNbO 3 in the low vacancy limit is considerably lower than suggested by our calculations.
To the best of our knowledge MgNbO 3 has never been synthesised, but similar niobate perovskites have been discussed in literature.For instance, ceramic materials within the solid-solution K x Na 1Àx NbO 3 (0 < x < 1) have been studied due to their promising piezoelectric properties, [78,79] and LiNbO 3 is known for its ferroelectricity and its optical properties. [80]Even more interesting, high ionic Li mobility was achieved in the defective perovskite material Li x La ð1ÀxÞ=3 NbO 3 , [81][82][83] but the research has not been extended to other shuttle ions.
We would still like to note that even if some material should be synthesizable according to our E hull criterion, it is not guaranteed that synthesis routes to prepare this particular material are available.Ideally such a screening study should be done jointly with materials synthesis experts. [51]However, we view our screening study also as a motivation for our experimental colleagues to address the preparation of materials that have not been produced yet.In the present study the verifiably existing niobate compounds LiNbO 3 , NaNbO 3 , and KNbO 3 have been discarded due to high volume change in the case of Li and high diffusion barriers in the case of Na and K.However, our calculations suggest that especially the Mg-intercalated NbO 6 framework could be an interesting research direction in the development of high-energy cathode materials for Mg-based batteries.

Figure 1 .
Figure 1.Battery cathode materials based on the perovskite structure considered in this study.The fully intercalated material ABO 3 represents the low state of charge while the fully deintercalated material BO 3 represents the high state of charge of the cathode material in the battery.All structures were restricted to the perovskite geometry.

Figure 3 .
Figure 3. Derived battery properties for 280 ABO 3 compounds.Green indicates preferable values for the given property whereas red means the opposite.This is why the color code goes from red (low values) to green (high values) in the case of the theoretical specific energy and the theoretical energy density, but from green (low values) to red (high values) in the case of the theoretical volume change and the energy above hull.

Figure 4 .
Figure 4. Comparison of stability predictions.The stability descriptor τ derived by Bartel et al.[70] is compared with our screening criterion for E hull .The blue left-bottom quadrant contains the compounds which are predicted to be stable by the descriptor method (τ < 4.18).It is clear that a screening criterion for E hull lower than 200 meV atom À1 would result in discarding materials, which are predicted to be stable by the descriptor method.

Figure 5 .
Figure 5. Diffusion barriers for the 13 compounds that have passed the previous screening procedure.All symmetrically nonequivalent diffusion paths are shown in the high vacancy limit and the low vacancy limit.The threshold of 650 meV is depicted as the criterion for sufficient ionic mobility.None of the compounds show barriers below the threshold in the low vacancy limit and MgNbO 3 , ZnVO 3 , and AlMoO 3 show sufficiently low values in the high vacancy limit.

Figure 6
Figure 6.Diffusion barriers of MgNbO 3 .In the high vacancy limit, MgNbO 3 exhibits low diffusion barriers.In the low vacancy limit, the diffusion path goes downhill, indicating that the initial and the final structure are energetically unfavorable for the given stoichiometry.A more detailed discussion can be found in the text.

Table 2 .
Summary of properties.The numerical values of the derived properties for MgNbO 3 , ZnVO 3 , and AlMoO 3 are shown.In case a compound had several inequivalent diffusion paths only the value for the lowest barrier is given.