Delocalized metal-oxygen π-redox is the origin of anomalous non-hysteretic capacity in Li-ion and Na-ion cathode materials
The anomalous capacity of Li-excess cathode materials has ignited a vigorous debate over the nature of the underlying redox mechanism, which promises to substantially increase the energy density of rechargeable batteries. Unfortunately, nearly all materials exhibiting this anomalous capacity suffer from irreversible structural changes and voltage hysteresis. Non-hysteretic excess capacity has been demonstrated in Na 2 Mn 3 O 7 and Li 2 IrO 3 , making these materials key to understanding the electronic, chemical and structural properties that are necessary to achieve reversible excess capacity. Here, we use high-fidelity random-phase-approximation (RPA) electronic structure calculations and group theory to derive the first fully consistent mechanism of non-hysteretic oxidation beyond the transition metal limit, explaining the electrochemical and structural evolution of the Na 2 Mn 3 O 7 and Li 2 IrO 3 model materials. We show that the source of anomalous non-hysteretic capacity is a network of π-bonded metal-d and O-p orbitals, whose activity is enabled by a unique resistance to transition metal migration. The π-network forms a collective, delocalized redox center. We show that the voltage, accessible capacity, and structural evolution upon oxidation are collective properties of 1 the π-network rather than that of any local bonding environment. Our results establish the first rigorous framework linking anomalous capacity to transition metal chemistry and long-range structure, laying the groundwork for engineering materials that exhibit truly reversible capacity exceeding that of transition metal redox.
Introduction<!>Methods<!>Results and Discussion<!>Electrochemical properties of π-redox dictated by network structure<!>Materials design rules for accessing non-hysteretic excess capacity using π-redox<!>Conclusion
<p>Electrochemical activity exceeding the limits of conventional transition metal oxidation, first observed in Li-excess materials, is one of the most actively researched routes for dramatically increasing the energy density of conventional Li-and Na-ion cathode materials. [1][2][3][4][5] Materials relying in part on this phenomenon avoid the composition and voltage limits of transition metal electrochemistry, 6,7 and achieve some of the highest energy densities reported to date. 4 Several redox mechanisms have been conceived to account for the anomalous capacity of Li-excess materials and related Na intercalation compounds. The anion redox hypothesis attributes the excess capacity to redox on O-p orbitals that are not σ-bonded to a transition metal. 8,9 Numerous proposals exist for how such oxygen-centric oxidation may proceed: formation of localized O-holes, O-O dimerization into peroxo-like structures or true peroxides, or the formation of trapped O 2 molecules or superoxide ions. 1,2,[10][11][12][13] Competing hypotheses argue that the excess capacity is coupled to structural changes of the electrode, such as metal migration due to the formation of highly-oxidized transition metal ions, 14 or O 2 evolution and densification. 15,16 Despite their tremendous promise, most electrode chemistries that exhibit an anomalous excess capacity suffer structural changes and irreversibilities due to the loss of O 2 and transition metal migration. Advancements in the suppression of metal migration, 3,15,17 surface protection, 5 and fluorination 18,19 have led to the development of cathodes that maintain an excess capacity over a large number of cycles. Nevertheless, these materials universally exhibit a large voltage hysteresis, signifying the existence of a thermodynamic asymmetry between their charge and discharge mechanisms that remains poorly understood and that continues to cloud efforts to identify the true origins of the anomalous capacity.</p><p>While the vast majority of electrode materials that boast an anomalous capacity are plagued by irreversibilities, there are two notable exceptions: Li 2 IrO 3 11, 20 and Na 2 Mn 3 O 7 . 21,22 Both compounds can access a capacity that exceeds that of conventional transition metal redox without voltage hysteresis, making them unique model systems to identify a redox mechanism that may dramatically increase the energy densities of rechargeable batteries.</p><p>Although localized and atom-centric theories have been invoked to account for the anomalous capacity in Li 2 IrO 3 and Na 2 Mn 3 O 7 , they are unable to explain important experimental observations and suffer from internal inconsistencies. For example, the structural evolution of Li 2 IrO 3 has been used to argue in favor of O-O dimerization, 11 but these distortions are not present in Na 2 Mn 3 O 7 . 23 The formation of isolated O-holes have been proposed as the oxidation mechanism in Na 2 Mn 3 O 7 , 21 but this mechanism does not explain the stepped voltage profile of the material, and is inconsistent with the distortions and electronic structure of Li 2 IrO 3 . 13 More generally, available theories fail to quantitatively explain the strong dependence of the redox process on transition metal chemistry and the long-range structure of the material. 1,2,12,24,25 Here, we resolve the oxidation mechanism of Na 2 Mn 3 O 7 and Li 2 IrO 3 . We first show that these two systems are uniquely resistant to transition metal migration as compared to materials known to exhibit hysteresis, suggesting that the oxidation of hysteretic systems is fundamentally tied to structural transformations. We then use high-accuracy GW and random-phase-approximation (RPA) calculations to show that the mechanism of nonhysteretic anomalous redox in Na 2 Mn 3 O 7 is the formation of delocalized π-states that hybridize a network of Mn-d and O-p orbitals, which we term π-redox. Molecular orbital group theory reveals that the π-bonded network forms a large bonding-antibonding gap, creating a high-energy antibonding state that acts as the redox center. The collective behavior of this network is responsible for the multi-step voltage profile observed in Na 2−x Mn 3 O 7 and the structural evolution observed in Li 2−x IrO 3 . Critically, we show that the oxidation potential, accessible capacity and structural evolution of such a π-bonded network are true collective properties arising from the size and connectivity of the network, rather than the aggregate behavior of local bonding environments. We conclude that in materials where transition metal migration can be suppressed, long-range structure compatible with the formation of large π-networks is the key materials design principle for realizing excess non-hysteretic electrochemistry.</p><!><p>Electronic structure calculations were performed using the Vienna Ab-Initio Simulation Package (VASP) 26 using the Projected-Augmented Wave (PAW) method. 27 All calculations was converged to 10 −6 eV in total energy and interatomic forces below 0.02 eV Å−1 . Structural optimization and broad comparison of π-delocalization to dimerization, metal migration, and O 2 evolution was performed using the SCAN exchange-correlation functional 28 as this method generally yields reliable structures by capturing both local and dispersion forces. 29 Critically, SCAN reliably captures the energetics of both O-O bond formation and the behavior of Mn in highly oxidizing environments. 30 An in-depth discussion of functional choice and the performance of SCAN in reproducing benchmark experimental data as compared to conventional PBE, PBE+U , and HSE methods can be found in Supplementary Discussion 2. All structural optimizations were performed with a reciprocal space discretization of 25 k-points per Å−1 without assuming any symmetry. RPA calculations were performed using the adiabatic connection fluctuation-dissipation theorem (ACFDT) 31,32 using 12 frequency points on a 2x2x2 Γ-centered k-point mesh, with respect to the unit cells provided in the Supplementary Information. GW 33 calculations were performed using a single-shot approach (G 0 W 0 ) due to computational limitations, using the same parameters but increasing the number of frequencies to 50. Structure and data processing relied on the pymatgen software package, 34 while the symmetry analysis of distortion modes was performed using the ISODISTORT tool. 35</p><!><p>Unique structural stability of Na with the caveat that we find the P3 stacking to be preferable to the commonly reported "as-synthesized" O3 structure even at x = 0. 21,23,36 There is evidence that oxidation into the x > 0 region is accompanied by the formation of the P3 phase, 23 so the discrepancy at x = 0 could arise due to small off-stoichiometry in the experimental sample or slight inaccuracies in our predictions of relative stability. We use the P3 structure at x = 0 for the remainder of our analysis but verify that the O3 structure leads to the same conclusions.</p><p>The Mn-O framework shown in Figure 1a is preserved on desodiation in the region of experimental interest (0 ≤ x ≤ 2) as all decomposition mechanisms are either thermodynamically or kinetically unfavorable. We consider all commonly proposed scenarios for structural evolution coupled to oxidation in this and similar systems: migration of Mn from the metal layer to the Na-layer, formation of peroxide O-O dimers, and O 2 evolution. The relative energies of these scenarios are shown in Figure 1b.</p><p>The equilibrium oxidation pathway is the release of O 2 gas accompanied by structural reorganization into MnO 2 . This conversion reaction is kinetically limited, with a lower bound on the activation energy given by the energy of local Mn migration. Mn migration typically proceeds through reduction to Mn 2+/3+ 37 or the formation of tetrahedral Mn 5+/6+/7+ as recently proposed in Li 2 MnO 3 . 14 However, the former mechanism requires an auxiliary source of charge balance, while the latter requires relatively small layer slab spacing so as to accommodate the short Mn-O bonds found in highly oxidized Mn environments. Correspondingly, we find that Mn migration into the Na layer is highly unfavorable at intermediate states of with respect to all local structural perturbations, rationalizing the exceptional structural stability observed experimentally in this system. 23 The structural stability of Na 4 Mn 6 O 14 at the top of charge, which we define as the resistance to transition metal migration, is similar to that of Li 2 IrO 3 , and much better than that of other well-studied hysteretic excess-capacity materials. We define two metrics to evaluate the likelihood of structural changes in the oxidized structure, shown schematically in Figure 1c. ∆E decomp defines the energy of decomposition by O 2 evolution and densification and thereby quantifies the average driving force acting on each transition metal M . ∆E * mig defines the activation energy for transition metal migration from an initial octahedral site to an adjacent tetrahedral site, providing a lower bound on the kinetic barrier to decomposition.</p><p>We compare these two metrics to the asymmetry in reported first-cycle voltage curves in Na 4 Mn 6 O 14 , 23  Oxidation via a delocalized π-bonded network of Mn-d and O-p orbitals</p><p>Having ruled out structure-altering redox mechanisms in Na 4 Mn 6 O 14 , we next explore structurepreserving oxidation, whereby the qualitative connectivity of transition metals and oxygens remains unchanged. We find that the mechanism of structure-preserving oxidation is the formation of an electrochemically active π-state, delocalized within the Mn 6 ring and with nearly equal contributions from Mn-d and O-p orbitals. To identify this state, we use a complimentary pair of techniques, GW and RPA. These methods provide highly reliable models of band structure and total energy by directly accounting for electronic correlation, [31][32][33] which is particularly important in systems exhibiting complex orbital hybridization. 40,41 While both methods are non-empirical, they rely on an initial set of orbitals obtained from a conventional density functional theory (DFT) functional. We use this fact to vary the electronic structure and compare scenarios with differing contributions of Mn and O to the redox-active state. For example, standard semi-local DFT yields orbitals for the hybridized scenario, while adding a fraction of exact-exchange generates orbitals consistent with Odominated redox. A full description of this procedure and the functionals used is available in Supplementary Data 2. We then obtain the band structure, total energy, and voltage profile of each scenario from GW and RPA.</p><p>We first show that the redox center must be a collective orbital of the Mn 6 ring. The electronic structure of the sodiated Na 4 Mn 6 O 14 endpoint is shown in Figure 2a as a plot of the density of states (DOS). A critical feature of this spectrum, independent of the choice of initial orbitals, is a narrow-energy state at the Fermi level, the highest occupied molecular orbital (HOMO). This state accounts for 4 electrons per Mn 6 and has the full symmetry of the 6-fold ring. The combination of 6-fold symmetry and 4-fold occupancy cannot be obtained from any combination of localized states, meaning that the HOMO must be a delocalized orbital.</p><p>We contributions, corresponding to the hybridized π[Mn-O] state. This mechanism suggests that oxidation beyond the transition metal limit involves a continuous rehybridization of metal and oxygen states, reminiscent of the behavior of conventional metal oxides. [42][43][44] The atomic orbitals which hybridize to form the π[Mn-O] state are shown in Figure 3a.  The redox-active HOMO is an antibonding orbital corresponding to the 2-fold degenerate e g irreducible representation of the D 3d point group. To derive the energy levels of the combined π system, we first determine the symmetrized orbitals of the ρ(Mn) and η(O)</p><p>subsystems and then form bonding and antibonding orbitals between states with matching irreducible representations, as described in Supplementary Methods 1 and shown in Figure 3b. By projecting the Na 4 Mn 6 O 14 DOS onto the ρ and η subsystems as shown in Figure 3c, we can isolate the predicted π-states from the t nb 2g (O h ) and e * g (O h ) states arising from octahedral MnO 6 environments. For the energetically-isolated antibonding e * g (D 3d ), a * 1g (D 3d ) and e * u (D 3d ) orbitals, the integral of the DOS matches the predicted degeneracy of these states. Independently, we confirm that these peaks in the DOS correspond to antibonding Mn-O interactions using crystal-orbital Hamiltonian population (COHP) analysis. 45 The molecular orbital diagram shown in Figure 3b reveals that the origin of excess capacity in Na 4 Mn 6 O 14 is a large bonding-antibonding gap within the delocalized π[Mn-O] system. This gap creates a high-energy antibonding state occupied by 4 electrons per Mn 6 ring environments where M is any 3d, 4d, or 5d transition metal with a known M 4+ oxidation state. Unlabeled points include all such metals M not explicitly marked in the other quadrants. Oxidation and reduction mechanisms are evaluated using the relative weight of the π-system in the projected DOS of, respectively, the HOMO and LUMO of hypothetical Na 4 M 4+</p><p>6 O 14 materials. The order parameters f M and f π quantify the degree of metal and total π-system contribution and are formally defined in Supplementary Data 2. b. Oxidation voltage of removing a single electron from Na 4 Mn 6−n Ti n O 14 , where n determines the extent of the π[Mn-O] redox center, shown for n = 1, 3, 5. Voltage is computed using RPA based on the calibration given in Figure 2d. A linear fit is shown to guide the eye. ring, which are accessible electrochemically. The practical capacity of the material is further limited to 2 electrons per Mn 6 ring by the fact that there are only 2 weakly-bound, face-sharing Na in the structure as shown in Figure 1a.</p><!><p>We next show that the π-redox oxidation potential is a true collective property of the πbonded network, rather than that of any specific bonding environment. To do so, we derive chemical rules dictating the formation of the π-network in a broad range of chemistries and study the effect of interrupting the network with inactive elements. The π-system is electrochemically relevant when the transition metal t nb 2g (O h ) orbitals are partially occupied, and is most prominent with d 3 and d 6 ions. To separate the impact of chemistry from bonding geometry, we repeat the DOS analysis for isostructural Na 4 M 4+ 6 O 14 materials, where M is any 3d, 4d, or 5d transition metal with a known M 4+ oxidation state. While these materials are hypothetical, their electronic structure is representative of the M 6 -ring environments ubiquitous in layered materials. The behavior of these systems is summarized in Figure 4a in terms of f M and f π , two order parameters quantifying the contribution of the transition metal and the π-system to the redox-active state (see Supplementary Data 2 for a formal definition). The π-system is active on oxidation when the transition metal has either a d 3 (Mn 4+ , Re A unique feature of π-redox is that the oxidation potential is not determined by any local bonding environment but rather by the total size the delocalized π-system, making voltage a collective property of the network. We probe the impact of π-delocalization by substituting Ti 4+ , a π-inactive ion, into the Mn 6 ring of Na 4 Mn 6 O 14 . As shown in Figure 4b, a Mn n Ti 6−n ring creates a π-system consisting of n Mn-d and O-p orbitals. The voltage required to remove 1 electron from this system is shown in Figure 4b, by analogy to the first voltage plateau of Na 4−x Mn 6 O 14 . Formation of a larger π-system lowers the oxidation voltage by increasing the bonding/antibonding gap within the π-orbitals and thus moving the antibonding HOMO to a higher energy. Extrapolating the trend in Figure 4b, it may even be the case that a larger π[Mn-O] system can be oxidized below the typical voltage of O 2 evolution, 3.4-3.8V, making the process thermodynamically favorable relative to O 2 loss.</p><p>The dramatic impact of π-network size on oxidation voltage proves that the electrochemical potential of π-redox is primarily a network effect, dictated by the number of building blocks in the network and not the properties of any local environment. This network prop- that break the various symmetries of the system. Across a wide range of oxidation and reduction, the only active distortion modes are the a 1g modes that preserve the symmetry of the ring. This highly symmetric evolution is consistent with the behavior of a delocalized π-redox center, meaning that the experimentally observed reduction in O-O distance is not due to an interaction between those oxygens, but rather due to an expansion of π-hybridized</p><p>Ir-O rings. The shortening of O-O bonds is a side effect of the geometry of the Ir ordering as shown in Figure 5a. Minor symmetry breaking observed at particular electron counts in Li-excess materials and related Na compounds arises from structural changes due to metaloxygen bond breaking, 2,13,15,25,47 which has been correlated with transition metal chemistry 48 and the fractional concentration of holes per oxygen. 12 We confirm that the likelihood of metal-oxygen bond breaking is critical to predicting voltage hysteresis and propose two thermochemical predictors of structural stability: the energy of decomposition and the barrier to transition metal migration (Figure 1c). These two thermochemical predictors reveal the existence of strong correlations between transition metal chemistry and the susceptibility of the electrode to structural degradation and voltage hysteresis (Figure 1d). Furthermore, they</p><p>show that in some cases, transition metal migration may even by triggered by the formation of highly-oxidized metal states such as Mn 7+ , Ir 7+ and Ru 7+ , revealing an alternative redox mechanism that has important and undesirable structural consequences. In cases where the structure is preserved, it has been argued that localized oxygen holes relax by forming peroxo-like O-O bonds or by partial charge transfer to adjacent transition metals.  rather than independent O-O interactions. This behavior contrasts with that of sulfides, 49,50 where we find that structure-preserving anion redox through S-S dimerization is favored over π[S]-redox, as described in Supplementary Discussion 1. Finally, the apparent charge redistribution between transition metals and oxygen reported in a number of systems 46,48 is an artefact of the projection of the delocalized π-state onto atomic orbitals. We have shown that the key properties of the π-redox center arise from its delocalized, network structure and cannot be explained by a locally projected bonding model.</p><!><p>The absence of voltage hysteresis in Na 4 Mn 6 O 14 and Li 2 IrO 3 is explained by the stability of the charged material to local structural perturbations. First, formation of the delocalized π-redox center stabilizes the charged state and reduces the driving force for decomposition.</p><p>Second, the large layer spacing and P3 stacking in Na 4 Mn 6 O 14 suppresses Mn migration into the Na layer. While strategies for controlling metal migration have been discussed elsewhere, 3,14,15,17 the π-redox mechanism leads to several new design rules for engineering materials capable of reversibly providing excess capacity.</p><p>The delocalization of Mn and O orbitals into increasingly large π-networks necessarily improves the reversibility of excess oxidation by lowering the oxidation potential and reducing the driving force for decomposition, as summarized schematically in Figure 6a. The presence of a large π-network lowers the average oxidation voltage and creates an initial low-voltage plateau, as compared to materials where such hybridization and delocalization is not possible ("no π-network"). Both effects lower the free energy of the charged state thereby decreasing the driving force for decomposition, as shown in the top panel of Figure 6a. The stabilized charged state in the π-network scenario can then be reduced with minimal voltage hysteresis.</p><p>In contrast, in materials where the choice of transition metal or crystal structure does not allow metal/O hybridization and π-delocalization ("no π-network" scenario), the unstable</p><!><p>We have shown that the origin of anomalous non-hysteretic capacity in Na</p>