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Unified picture of anionic redox in Li/Na-ion batteriesMouna Ben Yahia, Jean Vergnet, Matthieu Saubanère, Marie-Liesse Doublet

To cite this version:Mouna Ben Yahia, Jean Vergnet, Matthieu Saubanère, Marie-Liesse Doublet. Unified picture ofanionic redox in Li/Na-ion batteries. Nature Materials, Nature Publishing Group, 2019, 18 (5),pp.496-502. �10.1038/s41563-019-0318-3�. �hal-02128369�

Unified Picture of Anionic Redox in Li/Na-ion Batteries

Mouna Ben Yahia1,2, Jean Vergnet2,3, Matthieu Saubanere1,2,∗, and Marie-Liesse Doublet1,2∗1Institut Charles Gerhardt, CNRS - Universite de Montpellier,

Place Eugene Bataillon, 34 095 Montpellier, France2Reseau Francais sur le Stockage Electrochimique de l’Energie (RS2E), FR5439, Amiens, France and

3College de France, Chimie du Solide et de l’Energie, UMR CNRS 8260, Paris, France.

Anionic redox in Li-rich and Na-rich Transition Metal Oxides (Arich-TMOs) has emerged asa new paradigm to increase the energy density of rechargeable batteries. Ever since, numerouselectrodes delivering anionic extra-capacity beyond the theoretical cationic capacity were reported.Unfortunately, most often the anionic capacity achieved in charge is partly irreversible in discharge.A unified picture of anionic redox in Arich-TMOs is here designed to identify the electronic originof this irreversibility and to propose new directions to improve the cycling performance of theelectrodes. The electron localization function (ELF) is introduced as a holistic tool to unambiguouslylocate the oxygen lone-pairs in the structure and follow their participation in the redox activityof Arich-TMOs. The charge-transfer gap of transition metal oxides is proposed as the pertinentobservable to quantify the amount of extra-capacity achievable in charge and its reversibility indischarge, irrespectively of the material chemical composition. From this generalized approach, weconclude that the reversibility of the anionic capacity is limited to a critical number of O-hole peroxygen, hO ≤ 1/3.

GENERAL CONTEXT

Increasing the energy density of cathode materials isa central goal of ongoing research in Li/Na-ion batter-ies. This implies improving simultaneously the mate-rial potential and capacity. Whereas potential can beeasily tuned through an appropriate choice of the re-dox centre of the electrochemical reaction, [1, 2] capacityis more challenging to increase without penalizing thematerial structure. Thanks to the cumulative cationicand anionic activity recorded in Li/Na-rich transitionmetal oxides (Arich-TMOs), [3–9] anionic redox emergedas a new paradigm to increase energy density. How-ever, extra-capacities due to anions generally lead tostructural instabilities resulting in significant irreversibil-ity in the first cycle, [10] capacity and potential fadingupon cycling, [11] cationic migrations [12, 13] and oxy-gen loss. [6, 12, 14–16] This yields continuous decom-position of the electrode upon cycling which constitutesa major drawback for practical applications. The op-portunity to play with M/M’ chemical substitutions [7],structural dimensionality [9] or cation-disorder [17] hasraised hopes that a winning combination can suppressthese irreversibilities, hence enabling long-term cyclingfor high-energy-density electrodes. Recent examples sup-porting this line were reported by different groups andsummarized in several reviews. [18–20] Among them,the tri-dimensional β-Li2IrO3 model electrode [9] com-bines improved cycling performance and a record ca-pacity of 2.5 Li/Ir; the lighter Li1.3Nb0.3Mn0.4O2 elec-trode [7] displays the highest first-charge capacity (> 300mAh/g) ever reported and the Na2/3[Mn0.72Mg0.28]O2

∗ matthieu.saubanere@umontpellier.frmarie-liesse.doublet@umontpellier.fr

electrode [21, 22] shows reversible anionic redox with-out Na-excess, cationic disorder or O2 release. [22] Overthe past 5 years experimental and theoretical studieshave contributed to figure out the origin of anionic re-dox as arising from oxygen lone-pair states in the ma-terial electronic structure. [16, 20, 23–25] However, de-bates and controversial interpretations persist in the lit-erature on the reversibility of the anionic process uponcharge/discharge. Yet, these questions are paramount todecide whether the objective of high-energy-density bat-teries can be achieved with Arich-TMOs materials.

This paper proposes a unified picture of anionic redoxin Arich-TMOs, irrespectively of their structural-typeand electronic structure. Based on rigorous concepts ofelectronic (band) structure theory, we investigate theimpact of the material electronic ground state, A-excess,M/M’ chemical substitution and cationic order/disorderon the electrochemical activity of the O-network. Thisconceptual approach is validated by first-principlescalculations through the computation of the ElectronLocalization Function (ELF). [57] ELF is a topologicaltool of the electron density that probes the regionsof space where paired-electrons are confined, and isused, for the first time in Arich-TMOs, to demonstratethe participation of oxygen lone-pairs in the redoxactivity of these electrodes. Within this framework, weidentify the charge-transfer gap of TMOs (∆CT ) andthe number of O-holes per oxygen (hO) as pertinentdescriptors to quantify the anionic capacity achievablein charge and its reversibility in discharge. This providesexperimentalists with measurable quantities to infer theoverall electrochemical performance of their materials,and new rational recipes to exit the maze of anionicredox.

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I. Oxygen Lone-Pairs in A-Rich TMOs

The participation of oxygens in the electrochemicalactivity of Arich-TMOs is now widely accepted as arisingfrom O(2p) lone-pairs, [16, 20, 23–25] hereafter denoted|O2p. How many oxygen lone-pairs occur in these mate-rials can be straightforwardly deduced from the universaloctet rule, which states that oxygen needs four electronpairs in its valence shell to be stable (see SupplementaryInformation S1). In layered or rocksalt Arich-TMOs, ofgeneral formulation A[AxM1−x]O2, the average numberof |O2p per oxygen, n, is directly linked to the x stoi-chiometry, which also sets the cationic order/disorderin the structure. Accordingly, LiMO2, Li2MO3 andLi5MO6 are cation-ordered phases, as n is an integer forx = 0, 1/3 and 2/3 (see Fig. 1). For x 6= 0, 1/3, 2/3, nis fractional and cationic disorder [23, 27] or crystal sitediscrimination [25, 28] is required to split the O-networkinto different O-sublattices, each of them recoveringan integer but different n. Finally, x > 2/3 impliesunconventional n > 2 number and TM oxidation stateswhich may lead to unfavorable situations where the TMcations become more electronegative than the anions,therefore preventing the formation of the oxide phase.This analysis already surmises that any anionic oxida-tion inevitably violates the octet rule, so that cationicmigrations and/or O-O pairing will be neccessary tocompensate for the oxygen destabilization.

Cationic M/M’ substitutions are levers to increasethe number of |O2p lone-pairs. As a robust criteria, weconsider that all metals forming peroxide phases (e.g.alkali, alkali-earth or divalent d10 TMs) have strongenough reducing powers to prevent M’-O bonding,therefore increasing n. Such substitutions might beseen as A/A’ rather than M/M’ as they lower thematerial total capacity when A 6= A’. Cationic vacanciesalso increase n. This explains why anionic redox canbe activated in materials showing no A-excess, asexemplified by the Na2/3[Mn0.72Mg0.28]O2 [21, 22] andNa4/7[�1/7Mn6/7]O2 electrodes [28] (see Fig. 2). For M’

being a dm<10 transition metal or a post-transitionalmetal, n is set by the (M+M’) stoichiometry andis invariant with the substitution ratio. In Li-richNMC [19, 29–33] or Li2[SnyM1−y]O3 (M = Ru, Ir)electrodes, [4, 8] the anionic capacity increases with ydue to the electrochemically inactive M’ and not to theincrease of n.

II. Anionic Activity in A-Rich TMOs

From now on, we will term ”anionic activity” anoxidation process involving the |O2p lone-pair states.Whether these states participate in the electrochem-ical activity of Arich-TMOs depends on the materialelectronic ground-state. According to the Zaanen-Sawatzky-Allen classification, [34] TMOs are describedin a Mott-Hubbard (U < ∆) or charge-transfer regime

FIG. 1. Oxygen Lone-Pair Count: Schematic electronicstructures for LiMO2 (x = 0), Li2MO3 (x = 1/3) and Li5MO6

(x = 2/3) where the |O2s and |O2p lone-pair states are high-lighted by red bands. In these structures, the average numberof TM around each oxygen is 3, 2 and 1, respectively, thusleaving n = 0, 1 and 2 |O2p lone-pairs per oxygen in eachstructure. For all x, the oxygen 2s-orbital makes negligiblesymmetry-allowed interactions with the metal d-orbitals andforms low-lying nearly non-bonding states. This leads to one|O2s lone-pair per oxygen which is too deep in energy to par-ticipate in the electrochemical reaction. Electron Localizationfunction (ELF) computed within the DFT+U framework forLiCoO2, Li2RuO3 and Li5OsO6 phases confirm the number of|O2s and |O2p lone-pairs per oxygen expected from the octetrule (see Section Methods).

(U > ∆) depending on the amplitude of the M-O chargetransfer (∆) with respect to the coulombic interactionsin the d-shell (U). The electronic regime of Arich-TMOsthus defines the amount of capacity available for theanionic process and is the first important criterionto consider when investigating the electrochemicalproperties of these electrodes. In the following, theanionic activity will be discussed separately for the tworegimes, in the specific case of single-TM oxides. Theconcepts and rules established in this framework willthen be extended to the general case of disordered andsubstituted TMOs, in order to build a unified picture ofanionic redox.

Mott-Hubbard Systems

Mott-Hubbard systems are described by a partially-filled metallic band, splitted by the U coulombic termand lying above the fully-filled anionic band. As shownin Fig. 3, the extraction of e− and Li+ from the struc-ture leads to an electrostatic stabilization of the (M-O)∗

states and a concomitant electrostatic destabilization ofthe |O2p states for the oxygens lying in the vicinity ofthe A+ vacancy. As long as the metallic states remainabove the anionic states, the oxidation corresponds to acationic process which is generally fully reversible.

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FIG. 2. Electron Localization Function computed fromfirst-principles DFT+U calculations (isovalues of 0.7) forLi[Li1/3M2/3]O2 (M = Mn, Ru, Sn) showing an equiva-lent number of oxygen lone-pairs per oxygen (one |O2s andone |O2p), irrespectively of the M-O bond covalency. ForNa2/3[Mg1/3Mn2/3]O2, the apparent Mn/Mg substitution in

fact corresponds to a Na/Mg substitution (Mg2+ acting as2Na+ in the charge compensation) so that the material stoi-chiometry is x = 1/3 (”A2MO3”). For Na4/7[�1/7Mn6/7]O2,one and two oxygen lone-pairs per oxygen occur in the Mn-rich (orange) and Mn-poor (red) O-environments, respec-tively.

When the two states get close in energy, the electronicground-state of the material is (quasi)degenerate which isunstable towards any structural distortion that removesthe degeneracy. The distortion must lower the crystalsymmetry to allow efficient interactions between (M-O)∗

and |O2p, both states having different symmetries inthe undistorted structure. It corresponds to the for-mation of a three-centered M-(O-O) species, through aso-called Reductive Coupling Mechanism (RCM) [4, 24]which opens a gap in the material electronic structure.Interestingly, the transition metal initially oxidized isbeing reduced when the structural reorganization takesplace, due to a redistribution of the |O2p electronsinto the new M-(O–O) bonding states (highlighted inorange in Fig. 3). The participation of the anions in theelectrochemical activity of Arich-TMOs is then activatedthrough the dynamic of the cationic process (O to Mcharge transfer). As a proof of concept, we computedthe ELF isovalue for a typical Mott-Hubbard system,namely the β-Li2−zIrO3 model electrode. [9] As shownin Fig. 3, one |O2p per oxygen is lost in the delithiatedstructure, concomitantly with the appearence of weakO-O bonds (see Supplementary Information S2 fordetails).

Charge Transfer Systems

Charge-transfer systems are described by an empty

FIG. 3. Dynamics of A-removal in Mott-Hubbard Sys-tems. Qualitative electronic structure of Arich-TMOs dis-playing a Mott-Hubbard electronic ground state (left). Theelectrostatic stabilization (resp. destabilization) of the (M-O)∗ antibonding states (resp. |O2p states) upon e− (resp.Li+) removal is shown by the dashed lines. The reductive cou-pling mechanism (grey inset) lifts the electronic degeneracyinto M-(O-O) bonding and antibonding bands represented inorange, which induces a |O2p to (M-O)∗ charge transfer. Indischarge, the re-insertion of Li should involve the (M-(O–O))∗ states hence allowing the system the return back to theundistorted structure through a perfectly reversible mecha-nism. Note that if all M(d) states are not involved in theRCM, a fraction of M(d)-states (dotted blue band) may re-main in the RCM-gap, therefore leading to some irreversibilityin discharge. The participation of the |O2p states in the oxida-tion process is illustrated for the β-Li2−zIrO3 electrode whichwas recently reported as exhibiting a mixed cationic-anionicredox activity. The ELF value computed for the lithiated(z = 0) and delithiated (z = 2) phases clearly shows the lossof one oxygen lone-pair per oxygen upon oxidation.

metallic band lying above the fully-filled anionic band(here the |O2p band) and separated in energy by thecharge-transfer gap ∆CT (see Fig. 4). The removal ofelectrons from the |O2p localized states generates un-stable oxygens that must recombine to recover a stableelectronic configuration (octet rule). As a result of O-Opairing, the narrow |O2p band splits into σ, π, π∗ andσ∗ discrete bands with an amplitude as large as the O-Odistance is short, i.e. as the (O-O)n− species are oxi-dized (red and yellow triangles in Fig. 4). As a robustcriteria, a given (O-O)n− dimer is stable as long as itshighest occupied states lie below the lowest unoccupiedmetallic band. Accordingly, the amplitude of ∆CT withrespect to O2−/(O2)2−, O2−/(O2)− or O2−/O2 redox en-ergies is the pertinent descriptor to predict the amountof extra-capacity achievable in charge and its reversibityin discharge.

Following the horizontal blue line of Fig. 4, (O-O)n−

species are stable as long as ∆CT > ∆σO−O (before (1)).

As for the reductive coupling mechanism discussed above,

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the anionic oxidation is fully reversible in discharge, sincethe electronic states involved in oxidation and reductionare similar. From (1) to (2) the metallic band lies be-tween the π∗ and σ∗ bands, so that (O2)2− peroxidescan form. As a result of the σ∗/M(d) band inversion, acationic reduction is expected in the first-step discharge,leading to voltage hysteresis. The peroxide reduction ina second-step discharge obviously depends on the capac-ity used for the cationic process. Above (2) the metal-lic band lies below the π∗-states of the oxidized species(∆π

O−O > ∆CT ). This results in the release of O2 gasconcomitantly with a cationic reduction, through a mech-anism known as a reductive elimination. [35]

Remarkably, the weak occurrence of transition metalperoxides reported in the literature [36, 37] suggeststhat most TMOs display ∆CT band gaps lower thanthe O2−/(O2)2− redox energy (below (1)). In contrast,alkali or alkali-earth oxides display much larger ∆CT

and are known to form peroxides. This strongly suggeststhat (O2)2− peroxides in charged Arich-TMOs shouldonly occur in M(d)-free/A(s, p)-rich O-environments, asexemplified in the Ba5Ru2O11 peroxide/oxide phase. [38]In this structure, the σ∗ states of peroxides (dO−O = 1.5A) are raised in energy far above the metallic band, thuspreventing their reduction in discharge.

III. The Unified Picture of Anionic Redox

All mechanisms described above can be put together tobuild a unified picture of anionic redox in Arich-TMOs.In this general framework, the number of holes per oxy-gen, hO, is shown to be the critical parameter governingthe reversibility of the anionic process.

In the most general case of Arich-TMOs combiningcationic disorder and chemical substitutions, the oxygennetwork consists in a statistical distribution of variousO-sublattices, each of them having a different number of|O2p lone-pairs due to different A/M/M’ local environ-ments. |O2p states being non-bonding, their energy isprimarily dictated by the electrostatic field exerted bythe surrounding cationic charges. The lower the cationiccharge around one oxygen, the smaller its Madelung po-tential and the higher in energy its |O2p states in theelectronic structure. How many holes are generated uponcharge on each O-sublattice thus depends (i) on the rela-tive energy of the electrochemically active O-sublattices,i.e. how homogeneous is the O-network, and (ii) on thematerial electronic ground-state, i.e. how much of thetotal theoretical capacity is available for the anionic pro-cess. Knowing this, the overall electrochemical behav-ior of Arich-TMOs can be deduced from the superimpo-sition of each O-sublattice individual activity, account-ing for their statistical weight in the pristine material,and following the mechanisms described above. This ap-proach is illustrated in Fig. 5 for a representative set ofA[AxM1−x]O2 showing different A/M/M’ compositionsand distributions and a theoretical capacity correspond-ing to (1+x) electrons. The important message of this

FIG. 4. Dynamics of the oxidation process in charge-transfer Arich-TMOs. Qualitative electronic structure ofArich-TMOs displaying a charge transfer electronic ground-state in the reduced phase (left). The splitting of the |O2p

narrow band into discrete σ, π, π∗ and σ∗ states is highlightedby the red (∆σ

O−O) and yellow (∆πO−O) triangles, as a func-

tion of the decreasing O-O distance (bottom horizontal axis)and the increasing oxidation state of the (O-O)n− species (tophorizontal axis). The different domains of anionic activity arerepresented by the intervals delimited by (1) and (2). The (1)to (2) narrow domain highlights the weak ability of transitionmetals to stabilize true peroxides in their structure (∆CT gen-erally smaller than the O2−/(O2)2− redox energy), in contrastto A(s, p) metals showing much larger ∆CT gaps in the oxidephases.

figure is that hO ≤ x is required for the anionic process tobe reversible. Above this critical value, the anionic oxida-tion in charge is partially irreversible in discharge, exceptfor O-sublattices having M(d)-free/A-rich local environ-ments for which a reversible O2−/(O2)2− redox pair canexist.

For homogeneous O-networks, hO ≤ x implies that atleast 1 − x electron of the total capacity is consumedby a preceding cationic process involving one or moreelectro-active metals (Fig. 5a). The voltage profile ofthese materials should display nicely reversible electro-chemical processes (see Fig.6a) and a potential drop be-tween the cationic and anionic reactions, as the signatureof two distinct Mn+/M(n+1)+ and O2−/(O-O)2(2−x)− re-dox pairs. The anionic process should be associatedwith a larger polarization than the cationic process, dueto the structural reorganization of the O-network. [39]This electrochemical behavior is exemplified by the tri-dimensional β-Li2IrO3 electrode [9] showing well-definedreversible plateaus upon charge/discharge, no voltagehysteresis and limited irreversible capacity. 3D structuresshould be favored over 2D structures in which cationicmigration is triggered by the interlayer electrostatic in-

5

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FIG. 5. Unified picture of anionic redox in Arich-TMOs. Cationic and anionic processes expected forA[AxM1−x]O2 (0 < x ≤ 1/3) showing different A/A’/M/M’compositions and distributions. The cationic and anionic pro-cesses are represented by blue and red rectangles, respectively,the area of which being correlated to reversible (dashed) andirreversible (plain) capacities. Mott-Hubbard and charge-transfer regimes are distinguished by a negative and positive∆CT , respectively. M’ refers to an electrochemically inactivemetal having no impact on the number of |O2p lone-pairs inthe structure (pink M’ = strongly correlated TM with half-filled d-band, post-transitional metal or d0 metal). A’ refersto an electrochemically inactive metal/vacancy increasing thenumber of |O2p lone-pairs in the structure (green A’ = A(s, p)mono- or divalent metal or metal vacancy). The number ofoxygen lone-pairs per oxygen is indicated in yellow and hO

is calculated for each system by substracting the cationic ca-pacity to the total capacity. For disordered materials, thestatistical weight of each O-sublattices is represented by theci coefficients. The total theoretical capacity is equivalentfor all examples (1 + x electrons) except for the last examplein which the A[AxM1−x]O2 general formulation is no longervalid due to the A/A’ substitution.

stability at low A-content. This phenomenon was shownto limit the reversible capacity of the layered α-Li2IrO3

electrode [8] compared to its 3D β-polymorph. [9] Favor-ing electronic delocalization in 2D structures through theincrease of bond covalency or with temperature shouldcontribute against this instability. This is supported bythe series of TM-chalcogenides (MX2 or MX3, X=S, Se,Te) [40, 41] showing stable layered structures and by thelayered Li2RuO3 electrode showing full reversible capac-ity when cycled at 50◦C. [42]

Any M/M’ chemical substitution for an electrochem-ically inactive M’ metal invariably leads to partialirreversibility of the anionic process due to the increaseof hO above the critical x value (Fig. 5b). Above x, thehighly oxidized O-network should disproportionate intohO-related fractions of O2−, (O2)2− and O2 sublatticeswith relative weights set by the chemical composition

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FIG. 6. Schematic galvanostatic curves of A-RichTMOs. Illustration of the cationic (blue) and anionic (red)processes in A-rich TMOs for the different scenarios given inFigs. 3 and 4. (a) Fully reversible cationic and anionic pro-cess with no O2 release and no cation migration in charge.(b)-(c)-(d) The first part of the discharge corresponds to acationic activity (blue) due to O2 release at high-charging.This leads to a hysteresis between charge/discharge (yellow).When O2 gas release occurs in first charge due to cationicmigration/disorder, the process is not reversible leading toa persistent hysteresis in further cycles and a S-shape curvedue to the multiplication of TM and (O-O) redox centers (b).The plateaus in charge are recovered if no O2 release occursat high charging and if cationic migrations are fully reversiblein discharge (c). The capacity loss in charge due to O2 gasrelease (red rectangle) is partially compensated in discharge(blue rectangle) by the activation of a novel TM redox couple(d).

of the pristine structure. Cationic migrations shouldtake place from the critical hO = x state-of-charge toassist the disproportionation. Oxygens having morecationic vacancies in their local environment will beprimarily oxidized, and prone to O2 gas release throughthe partial reduction of the surrounding transitionmetal. An hysteresis is expected in the voltage profile ofthe electrode and the total capacity achieved in chargecannot be fully recovered in discharge (see Fig.6b).Most Arich-TMOs reported in the literature belong tothis category. They correspond to the general formu-lation A[Ax(M1−yM’y)1−x]O2 with M’ = d0, half-filledd-band TM with large U splitting (e.g. Mn4+, Fe3+),or post-transitional (e.g. Sn4+, Te6+) metal. Theseelectrodes display large voltage hysteresis, cationicmigration and a capacity loss linearly correlated to y, asexemplified by the series of Li2[Ru1−yM’y]O2 (M’ = Sn,Ti, Mn) [4, 5, 43] and Li2[Ir1−ySny]O2. [8] Note that, inrare cases, the TM reduction induced by O2 release mayactivate a cationic redox-pair in discharge that was notaccessible in first charge. This could allow recovering,at least partially, the first-charge capacity in furthercycles (see Fig. 6c). Reaching the complete substitution

6

of M for an inactive M’ metal leads to charge-transfermaterials, such as Li2MnO3, [10, 44] in which thetheoretical capacity is fully supported by the anions,i.e. hO = (1 + x)/2. Unless x is decreased to activatea cationic redox-pair, [45, 46] charge-transfer TMOsshould display poor electrochemical performance [10]associated with a progressive decomposition of theelectrode upon cycling, persistent voltage hysteresisand capacity fade in the voltage profile (see Fig. 6d).Finally, chemical A/A’ substitutions with A’ beinghighly reducing metals (large ∆CT ) appears as theonly way to achieve a reversible anionic capacity withhO > x (see Fig. 5e) due to the possible stabilization ofperoxides (hO = 1) in M(d)-free/A’-rich environments.However, the statistical weight of this O-sublattice mustbe significant to benefit to the anionic capacity, whichimplies large A/A’ substitution ratio y, i.e. low capacityand poor electronic conductivity.

Noteworthy, any release of O2 gas in charge lowershO in further cycles. Consequently, Arich-TMOs candisplay nicely reversible electrochemical cycles after afirst charge that kills the activity of the most unstableO-sublattices. This is exemplified for instance by theLi1.2[Mn0.54Co0.13Ni0.13]O2 [3] and A1.3Nb0.3Mn0.4O2

(A = Li, Na) electrodes [47, 48] sustaining reversiblecapacity of ∼ 250 and ∼ 300 mAh/g, respectively.Interestingly, the lithiated Li1.3Nb0.3Fe0.4O2 electrodeshows significantly lower performance compared toits Mn-based homologue. While this behavior wasattributed by the authors to a Fe-O bond covalencylarger than Mn-O, [48] our unified picture shows it arisesfrom different hO. Alike Li2MnO3, Li1.3Nb0.3Fe0.4O2 isa charge-transfer insulator (inactive Fe3+ ions confirmedby DFT calculations in ref. [48]) for which the totaltheoretical capacity is fully supported by the anions(hO = (1 + x)/2). In the Mn-based system, 0.4 electronsare consumed by a preceding Mn3+/Mn4+ cationicprocess, leading to significantly lower hO and bettercycling performance, after the first cycle. The samecomparison can be made between the Li2MnO3 [10] andthe Mn-defective Na4/7[�1/7Mn6/7]O2 electrodes. [28]While the former displays no cationic redox and highlyirreversible anionic redox, the latter shows nicelyreversible cationic and anionic redox processes, verysimilar to the β-Li2IrO3 electrode [9] thanks to a limitedextra-capacity (hO < x). Finally, approaching thelimits of cationic and anionic electrochemical activitywith the Li-rich layered rocksalt Li3IrO4 (x = 1/2)electrode shows that the delithiated IrO4 electrodeconverts into IrO3 at the end of charge, which limits hO

to 1/3 in further cycles. [25] Overall, these examples

highlight the negligible role of M-O bond covalency inthe electrochemical behavior of Arich-TMOs and suggestthat hO = 1/3 is the upper limit for achieving reversibleanionic capacity in A[AxM1−x]O2 electrodes. Obviously,any chemical substitution lowering hO through theactivation of a cationic redox-pair, is a good strategyto favor structural stability and more reversible anionicelectro-activity, as nicely exemplified by transition metaloxyfluorides. [27, 49]

CONCLUSION

So far, most Arich-TMOs reported in the literatureas displaying high-energy-density due to anionic redox,are prone to structural instabilities that prevent theiruse in practical applications. Several alternatives havebeen proposed to limit or suppress these irreversibilities,among which the increase of M-O bond covalency, thechemical substitution of M for d0 metals or the useof cation-disordered rocksalt structures. The unifiedpicture developed in this paper contrasts with thesestatements in showing that the number of holes peroxygen (hO) is the critical parameter to sustain areversible anionic capacity. From a representative set ofmaterials reported in the literature, hO = 1/3 appearsas the critical value to avoid O2 release and achieve fullyreversible anionic redox. Measurable quantities suchas the TMO band gap (∆CT ) and the x stoichiometryare therefore sufficient to determine hO and to inferthe electrochemical behavior of A[AxM1−x]O2 electrodes.

Within this general framework, the best candidatesfor high-energy-density are those cumulating an opti-mal cationic capacity and an anionic capacity limited tohO ≤ 1/3. Tri-dimensional structures should be pre-ferred over layered structures to prevent structural in-stability at low A-content and take advantage of thefull theoretical capacity. Ordered structures should fa-vor homogeneous O-networks should avoid h Very fewTMOs should satisfy these requirements, in particularwhen they also have to meet industrial specificationssuch as cost, toxicity and natural abundance. Overall,strategies devoted to the activation of anionic redox as alever to improve the energy density of electrode materi-als are risky as they implicitly means that anions becomeless electronegative than cations at some point, thereforequestioning the structural stability of the materials. Thetriptych of high-potential, high-capacity and high struc-tural stability still appears out of our current reach andcalls for trade-offs.

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Methods

Spin-polarized calculations were performed usingthe VASP code [50, 51] within the density functionaltheory (DFT) framework. Perdew-Burke-Ernzerhof(PBE) functional [52] with a generalized gradient ap-proximation form (GGA-PBE) was adopted to treat theexchange correlation energy. The rotationally invariantDudarev method (DFT+U) [53] was applied to account

for strongly correlated d electrons with different Ueff

values. The range-separated hybrid functional [54](HSE06) was also used for a sake of comparison withDFT+U. To obtain a good numerical sampling of theelectron densities in Brillouin zone, the Monkhorst-Packtechnique [55] was used. Moreover, with the applicationof the projector augmented wave (PAW) technique, [56]the plane-wave energy cutoff was determined to be600 eV. For structural relaxations, all atomic coordi-nates and lattice parameters were fully relaxed untilthe force acting on each atom is less than 3.10−3 eV.A−1.

ELF: A pertinent tool to characterize and visualize |Olone-pairs in a material is known as the Electron Local-ization Function (ELF). To the best of our knowledge,this tool has never been used in A-rich TMOs, although|O lone-pairs are central in the rationalization of theirelectrochemical properties. It is a topological tool of theelectron density that pinpoints the regions of space wherepaired electrons are confined. Initially designed by Beckeand Edgecombe for atoms and molecules, [57] it was de-veloped in the Density Functional Theory framework bySavin [58] and is becoming popular in material sciencedue to its holistic approach to electronic structures. [59]ELF measures the Pauli repulsion through the proba-bility of finding an electron of spin σ in the vicinity ofanother electron of same spin. The explicit formulationis:

ELF =

[1 +

{K(r)

Kh[ρ(r)]

}2]−1

(1)

where K is the curvature of the electron-pair densityγ2(rσ1 , r

σ2 ), ρ(r) the electron density and Kh the value

of K for the homogeneous electron gas with dentity ρ.The ELF values were computed for the different mate-rials given as examples in the paper, at various Li/Na-contents. ELF values range from 0 (no paired electrons)to 1 (paired electrons) and are here plotted for 0.7 iso-values in Fig. 1, Fig. 2 and Supplementary InformationFig.S1, Fig.S2.

Data AvailabilityThe datasets generated during and/or analysed duringthe current study are available from the correspondingauthor on reasonable request.

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AcknowledgementsThe authors acknowledge the RS2E institution and theAgence Nationale pour la Recheche (ANR) - DeliRedoxn◦ ANR-14-CE05-0020 - for supporting this work.

Author ContributionsAll authors contributed equally to the DFT calculations& analyses. MS and MLD developed the theoreticalframework and wrote the paper.

Additional InformationSupplementary information is available in the online ver-sion of the paper. Reprints and permissions informationis available online at www.nature.com/reprints. Corre-spondence and requests for materials should be addressedto M.-L.D or M.S.

Competing financial interestsThe authors declare no competing financial interests.