Transition metal migration and O2 formation underpin voltage hysteresis in oxygen-redox disordered rocksalt cathodes

Lithium-rich disordered rocksalt cathodes display high capacities arising from redox chemistry on both transition-metal ions (TM-redox) and oxygen ions (O-redox), making them promising candidates for next-generation lithium-ion batteries. However, the atomic-scale mechanisms governing O-redox behaviour in disordered structures are not fully understood. Here we show that, at high states of charge in the disordered rocksalt Li2MnO2F, transition metal migration is necessary for the formation of molecular O2 trapped in the bulk. Density functional theory calculations reveal that O2 is thermodynamically favoured over other oxidised O species, which is confirmed by resonant inelastic X-ray scattering data showing only O2 forms. When O-redox involves irreversible Mn migration, this mechanism results in a path-dependent voltage hysteresis between charge and discharge, commensurate with the hysteresis observed electrochemically. The implications are that irreversible transition metal migration should be suppressed to reduce the voltage hysteresis that afflicts O-redox disordered rocksalt cathodes.


GGA+U DFT calculations: pristine Li 2 MnO 2 F
First-principles density functional theory (DFT) geometry relaxations, using the DFT+U approach, were performed to parameterise the cluster-expansion model. All DFT+U calculations were performed using the plane-wave DFT Vienna Ab Initio Simulation Package (VASP) code. 1,2 Valence electrons were described by a plane-wave basis set with a cutoff of 550 eV. Interactions between core and valence electrons were described using the projector-augmented wave (PAW) method. 3,4 Electronic exchange and correlation were approximated using the semi-local Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional, 5 with a rotationally averaged Hubbard U correction 6 of 3.9 eV applied to the Mn 3d orbitals to correct the self-interaction error (SIE). 7 Reciprocal space was sampled with a discretization of 25 k -points Å −1 , and the electronic and ionic loops were converged with tolerances of 10 −6 eV and 0.02 eV Å −1 for the total energy and interatomic forces respectively. All calculations were initialised with Mn ions in a ferromagnetic configuration. Dispersion forces were included using Grimme's semiclassical D3 correction. 8 Calculations to parameterise the Li 2 MnO 2 F cluster expansion used a range of supercell sizes from (2×2×2) to (4×4×4) expansions of the two-atom primitive rocksalt unit cell.

Cluster expansion
The structures and energies from DFT+U calculations were used to fit a cluster-expansion model using the ICET code. 9 Relaxed structures from the DFT+U calculations were mapped back onto the rocksalt lattice using the map_structure_to_reference tool in ICET. Alloy cluster-expansions decompose the energy of a crystal structure into effective cluster interactions (ECIs), arising from individual local environments, based on the linear combination of energetic terms associated with many-body relationships between atoms. Once determined, the ECIs enable the efficient calculation of the large numbers of structure energies needed to obtain finite-temperature properties in disordered systems. 150 DFT calculations were used to fit a cluster expansion for cation and anion occupancy in the fully-lithiated (Li 2 MnO 2 F) rocksalt structure, consisting of pair interactions up to 7.5 Å, triplet interactions up to 4.5 Å, and quadruplet interactions up to 4.5 Å with the sum truncated at this point. The ECIs were obtained using a least absolute shrinkage and selection operator (LASSO) regression analysis, with a recursive feature elimination (RFE) approach, in which minimally contributing parameters are removed recursively, and a cross-validation score calculated, repeated until the cross-validation score no longer improves. The LASSO + RFE approach resulted in a fit with 19 non-zero ECIs. The cluster expansion was fit with a k-fold cross-validation root-mean-squared error (RMSE) obtained by the LASSO + RFE approach of of 8.5 meV atom −1 .

Monte Carlo simulations
From the parameterised cluster-expansion, the internal energy of disordered Li 2 MnO 2 F was calculated as a function of temperature from a set of canonical ensemble Monte Carlo (MC) simulations using the Metropolis-Hastings algorithm in a (6×6×6) supercell (432 atoms) expansion of the primitive rocksalt unit cell. Simulations were performed using the mchammer module within ICET. 9 The simulations were run for two million MC steps, with the first million used for thermal equilibration, and the second million for data production. From the second million steps, 700 structures were sampled at random, and the coordination environments around O-and F-ions were analysed using the polyhedral_analysis code. 10 To check for size-consistency, and ensure that larger cells do not display local clustering of species that could indicate phase-segregation, we performed additional MC simulations on supercells of 9×9×9 (1,458 atoms) and 18×18×18 (11,664 atoms). We analysed the cells, firstly by characterising the distribution of O environments, in the same manner as the analysis in Figure 1, Main Text. Secondly, we assessed the possibility of lithium clustering (i.e., phase-segregation-type behaviour) by calculating the number of Li-centered octahedra that edge-share with other Li octahedra. A large increase in Li-Li edge sharing octahedra relative to the 6×6×6 cell would indicate significant Li clustering and phasesegregation in the larger cells. The O-environment frequencies ( Figure S2) show a maximum difference of 5% and the Li-Li edge sharing octahedra ( Figure S3) have a maximum difference of <2%, indicating that the results do not change significantly in the larger cells.

SCAN metaGGA calculations of delithiated Li 2-x MnO 2 F
DFT calculations for the delithiated structures (Li 0.67 MnO 2 F) for the 'constrained-Mn' model and the 'Mn-rearrangement' model, and for the calculation of the delithiation convex hull were performed using the metaGGA functional SCAN, 11 using the VASP code. The SCAN functional was chosen since it gives relatively low errors for the energies of oxidised O chemical environments; i.e., peroxide, superoxide, and molecular O−O bonds. 12 Furthermore, SCAN give low errors for highly oxidised Mn chemical environemnts (Mn 5+ and Mn 7+ oxidation states) compared to DFT+U calculations (with +3.9 eV applied to the Mn 3d orbitals) and hybrid functionals. 13,14 For the SCAN calculations, valence electrons were described by a plane-wave basis set with a cutoff of 650 eV. Reciprocal space was sampled with a discretization of 25 k -points Å −1 , and the electronic and ionic loops were converged with tolerances of 10 −6 eV and 0.02 eV Å −1 for the total energy and interatomic forces respectively. All calculations were initialised with Mn ions in a ferromagnetic configuration. Dispersion corrections were not included for the SCAN calculations, because the standard parameterisation of the SCAN functional achieves an effective description of intermediate-range van der Waals forces. 12

Hybrid-exchange DFT calculations
Hybrid-exchange DFT calculations were performed to obtain high-accuracy energies for selected structures along the AIMD trajectory, presented in Figure 4 (Main Text). Hybrid DFT calculations were performed using the local basis set CRYSTAL17 code. 15 Electronic exchange and correlation were approximated using the screened hybrid-exchange functional HSE06, 16,17 with dispersion forces included using Grimme's semiclassical D3 correction. 8 All-electron atom-centred Gaussian basis sets were used for all atoms, available from the CRYSTAL online database (www.crystal.unito.it), with the online labels: Li (Li_5-11(1d)G_baranek_2013_LiNbO3), Mn (Mn_86-411d41G_towler_1992), O (O_8-411d1_cora_2005) and F (F_7-311G_nada_1993). The Coulomb and exchange series were truncated with thresholds of 10 -7 , 10 -7 , 10 -7 , 10 -7 and 10 -14 , as described in the CRYS-TAL manual. Reciprocal space was sampled using a single Γ-centered k -point. The self-consistent field (SCF) procedure was performed up to a convergence threshold of ∆E =10 -7 Hartree per unit cell. Calculations were initialised with Mn ions a ferromagnetic ordering and converged in the absence of spin constraints. Full geometry optimizations (lattice parameters and atomic positions) were performed using the default convergence criteria in CRYSTAL17.

Ab inito molecular dynamics (AIMD)
The ab inito molecular dynamics (AIMD) simulations were run with the VASP code 18,19 with exchange and correlation approximated using the same PBE+U approach (U = 3.9 eV on the Mn 3d orbitals) as discussed above for the DFT+U calculations. Dispersion corrections were included using Grimme's D3 correction. The AIMD calculations used a plane-wave cutoff of 400 eV and only the Γ-point for k -space sampling. All simulations were performed at 500 K, and used a time-step of 2 fs. For each system, the lattice parameters were kept fixed to the zero-pressure 0% optimized values. For each MD simulation, two equilibration stages were performed, first using a 2 ps NVE run by ramping the temperature up from 50 K to 500 K with temperature rescaling every 50 steps, followed by a 2 ps NVT run at 500 K.
The AIMD simulations were run on nine models of highly delithiated Li 0.67 MnO 2 F. Nine structures were randomly selected from a Monte Carlo simulation of Li 2 MnO 2 F trajectory at 2000 K.
In each cell, we obtained an approximate low-energy distribution of Li at this level of delithitation using the following approach. First, we identified all the tetrahedral sites in the structure that do not face-share with any Mn ions (denoted '0-TM' sites) 20 and occupied them with Li-ions, based upon the observation that lithium ions tend to occupy tetrahedral 0-TM sites at high levels of delithiation more frequently than octahedral sites. 21 Next, we removed all octahedral Li ions that face-shared with tetrahedral Li-ions in the 0-TM sites. Finally, we removed the correct number of remaining octahedral Li to obtain the composition, by iteratively selecting and removing the least-stable octahedral Li ion, based on their electrostatic site energy (calculated using a Ewald summation). The resulting structure was fully relaxed with DFT at the PBE + U level, and the relaxed structure was used in the AIMD equilibration step.

Analysis of computational results and figure generation
Analysis and figure generation used the Python packages pymatgen, 22 numpy, 23 polyhedral_analysis, 10 ASE 24 and matplotlib. 25 In particular, polyhedral_analysis was used as a general tool for analysis of polyhedra, such as to obtain distributions of octahedral environments for Figure 1b, Main Text and Figure S1, and O coordination environments in Figure S18. Structural figures were generating using the VESTA software. 26

Galvanostatic Intermittent Titration Technique (GITT)
Li 2 MnO 2 F samples were prepared by mechanochemical ball-milling under conditions described previously. 27,28 Free-standing electrodes were prepared by mixing 80 wt% active material, 10 wt% Carbon Super P conductive additive and 10 wt% polytetrafluoroethylene (PTFE) binder in a mortar and pestle and then calendared between rollers to a thickness of ∼0.15mm and cut into squares approximately 25-50 mm 2 in area. Sample loadings were typically 5-10 mg cm -2 . Electrochemical testing was performed in 2032 coin cells using a Li-metal disk as a negative electrode and glass microfibre separators (Whatman) soaked in LP30 electrolyte (Merck, 1M LiPF6 in 1:1 of EC:DMC).
All electrode processing was carried out under inert Ar atmosphere. GITT measurements were performed at room temperature, at a rate of 10 mA g -1 by applying successive steps of 2-hour constant current charges followed by 5-hour relaxations.

Resonant inelastic X-ray scattering (RIXS)
Resonant inelastic X-ray scattering data were obtained at the I21 beamline, Diamond Light Source.
Samples were transferred to the spectrometer using a vacuum transfer suitcase to avoid air exposure and were pumped down to UHV and left to fully degas overnight. The RIXS map was collected at 0.2 eV intervals in excitation energy. The measurements were performed at 20 K to minimise any possible beam damage.

Choice of temperature to model pristine material from Monte Carlo simulations
To simulate the disordered structure of pristine Li 2 MnO 2 F, we ran lattice Monte Carlo simulations using a cluster expansion Hamiltonian parametrised from first-principles density functional theory (DFT) calculations (as described in the Methods Section 1.2). This allows us to obtain thermally weighted configurations of ions. Li 2 MnO 2 F is prepared by high-energy ball-milling, and 27,28 therefore the choice of temperature for the Monte Carlo simulations to model the structure of the as-prepared material is not straightforward. This is due to the unclear and multifaceted relationship between the experimentally used high-energy ball-milling conditions and a thermodynamic "synthetic temperature". For instance, it has been hypothesised that ball-milling results in local heating or shear-induced reactions. 29,30 At present there is no direct method to predict the struc-  Figure S1.
The strong favourability for Mn-O and Li-F bonding in Figure 5 is consistent with previous studies of disordered rocksalt cathodes. 21,[32][33][34] The chemical short-range order described here and in previous results [35][36][37][38][39] means that disordered rocksalt cathode cannot be described as completely random distributions of cations and anions on their respective lattices. Experimental and computational studies that use random models of disordered rocksalt cathodes 40,41 will not give an accurate description of the frequency of different chemical environments.

Structures for the 'constrained-Mn' and 'Mn-rearrangement' models of Li 0.67 MnO 2 F
Structures for the 'constrained-Mn' model were generated from Monte Carlo (MC) simulations at 2000 K within a (3×3×3) expansion of the primitive rocksalt unit cell. We first selected 75 structures at random from the production run, and delithiated them to the composition of Li 0.67 MnO 2 F by randomly selecting 12 Li to remove from each unit cell. A second set of 75 structures were sampled at random from the MC trajectory, and these were delithiated using the same strategy as reported for approximating the low-energy distribution of Li ions in the large AIMD cell (Section S1.6). These two sets of structures are compared in Figure S5, and the dataset is combined to make Figure  The energies of the structures were calculated relative to the most-stable structure from the entire search.

Calculating the convex hull and voltage curve
The calculated convex hull for delithiation of Li 2-x MnO 2 F was obtained via a multistep process.
We first obtained a series of five structures from the cluster-expansion at 2000 K in a (3×3×3) unit cell, calculated their energies, and chose the most stable structure as a representation of the topotactic cathode framework (i.e., a Mn-framework connectivity that remains the same as in the pristine structure). To delithiate the structure, we performed stepwise calculations. Starting where E(Li

Obtaining discharged structures
To generate the discharged structures, we used structure mapping using the map_structure_to_reference   Figure 6, Main Text, is derived from this plot. The structure at the top of charge for the blue hull was obtained by taking the most-stable structure with the Mn ordering preserved, establishing the minimum number of Mn migration steps that would allow an O 2 molecule to form, performing these Mn migration steps, and relaxing the structure. This structure is most likely to represent a configuration formed under kinetic conditions during the first cycle. The gold points indicate structures from the 'Mn rearrangement' model, which searches all chemical space with no constraints on the possible positions that Mn can adopt. The 'Mn rearrangement' structures are therefore more representative of the products after multiple cycles (i.e., closer to a thermodynamic ground state). Figure 19: Room-temperature electrochemical galvanostatic intermittent titration technique (GITT) measurements of Li 2-x MnO 2 F, at a rate of 10 mA g -1 by applying successive steps of 2-hour constant current charges followed by 5-hour relaxations. Figure 20: Mid-point potential rest experiment. Voltage versus capacity plot for Li 2 MnO 2 F cycled at a rate of 10 mA g −1 . Charge in red, discharge in blue. The difference in equilibrium potential at this point is 0.16 V.