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Spectroscopic Signature of Oxidized Oxygen States in Peroxides

Recent debates on the oxygen redox behaviors in battery electrodes have triggered a pressing demand for the reliable detection and understanding of non-divalent oxygen states beyond conventional absorption spectroscopy. Here, enabled by high-efficiency mapping of resonant inelastic X-ray scattering (mRIXS) coupled with first-principles calculations, we report distinct mRIXS features of the oxygen states in Li2O, Li2CO3, and especially, Li2O2, which are successfully reproduced and interpreted theoretically. mRIXS signals are dominated by valence-band decays in Li2O and Li2CO3. However, the oxidized oxygen in Li2O2 leads to partially unoccupied O-2p states that yield a specific intra-band excitonic feature in mRIXS. Such a feature displays a specific emission energy in mRIXS, which disentangles the oxidized oxygen states from the dominating transition-metal/oxygen hybridization features in absorption spectroscopy, thus providing critical hints for both detecting and understanding the oxygen redox reactions in transition-metal oxide based battery materials.

Lithium peroxide, Li2O2, has been an intriguing system for both structural and chemical properties related to its special oxygen states 1 . Technologically, Li2O2 is an important air purification agent in spacecraft because it is not hygroscopic as other peroxides and highly reactive with CO2. Recently, the non-divalent oxygen state has attracted increased attention in electrochemical energy storage systems including both alkali-ion batteries and Li-air batteries [2][3] . Li2O2 is one of the key reaction products in Li-air batteries 2 . Li2O2, together with Li2O and Li2CO3, also dominates the inorganic components of the critical solid-electrolyte-interphase layer formed on negative electrodes of Li-ion batteries [4][5][6] . More importantly, peroxides may be involved in redox reactions in transition-metal (TM) oxide based electrodes 3,7 . A view which is challenged by other models [8][9] .
The redox-active oxygen is a critical concept because conventional batteries rely on only TM redox reactions, and oxygen redox is potentially useful for improving the capacity and energy density of batteries [10][11] . Additionally, oxygen redox could also impact the conceptual developments of catalytic materials 10 . However, although it is widely believed now that oxygen in TM oxides based electrodes could be oxidized to non-divalent states during the electrochemical cycling, as indicated by various core-level X-ray spectroscopy and recent Compton scattering experiments [11][12] , the nature of such oxygen redox state has been under active debate [7][8][9] , and the oxidized non-divalent oxygen remains to be understood and reliably 4 characterized 11,13 . Therefore, a reliable and direct detection of the intrinsic oxygen state, as well as its theoretical understanding, has become crucial for both the fundamental understanding and practical developments of various electrochemical materials.
The challenge of detecting the unconventional oxygen states in TM oxides and the need for better characterizations stem from the fact that conventional O K-edge soft X-ray absorption spectroscopy (sXAS) involves entangled contributions through hybridizations between TMs and oxygen. To be more specific, O-K sXAS studies have shown that Li2O2 displays a characteristic broad feature around 530 eV to 532 eV in sXAS 14 . Unfortunately, this broad feature is located in the same energy range where TM contributes significantly to the O-K sXAS "pre-edge" signals through hybridizations, as identified in the seminal work by de Groot et al. in 1989 15 .
Moreover, the overall broadening of the XAS lineshape, due to the presence of a strong core hole created via absorption, often masks low-energy features that are relevant for understanding oxygen redox, complicating a simple interpretation.
Indeed, we have recently clarified that most of the claims and conclusions on oxygen redox states based on sXAS experiments merely represent the change of TM states upon electrochemical cycling 13 . An advanced characterization beyond conventional O-K sXAS with better elemental and chemical-bond sensitivity, as well as deeper probe depth, is urgently needed in order to detect and understand the intrinsic nature of oxygen states.
We have recently shown that high-efficiency full energy range mapping of resonant X-ray inelastic scattering (mRIXS) can successfully decipher the entangled O-K signals through the new dimension of information of emission photon energies 13 .
By covering the full excitation energy range of O-K sXAS, mRIXS detects the energy distribution curves of the fluorescence photons that is only counted as a single number in sXAS, i.e., mRIXS further resolves the emitted photons along the new dimension of emission energy at each absorption energy. Moreover, mRIXS does not suffer from core-hole broadening as in sXAS because the core-hole is filled in the final state of the RIXS process. mRIXS thus becomes a perfect tool-of-choice for reliable and conclusive studies of novel chemical states that cannot be resolved in sXAS 13,[16][17][18] .
Strikingly, O-K mRIXS has revealed a sharp feature of the oxygen redox state in battery electrodes that has been buried in conventional sXAS data, with 531 eV excitation energy and 523 eV to 524 eV emission energy, clearly separated from the TM-O hybridization features at 525 eV emission energy 13, 17-18 . However, while mRIXS has been established as a reliable probe of the critical oxygen states involved in the battery electrodes with oxygen redox activities, the interpretation of specific O-K mRIXS features has not yet been achieved. The experimental results of mRIXS involve complex processes that are related to electron 6 state configurations, electron correlations, and excitations, which are challenging topics in both fundamental physics and spectroscopic simulations. In general, signals in mRIXS could be categorized into three different types of contributions, the elastic line, non-resonant emission signals from the decays of the occupied valence band electrons to the core holes ("emission lines"), and low-energy excitations 13 . While model compounds may not represent directly the same mechanism as in the complex TM oxide systems, a benchmark study with combined experimental and theoretical results becomes crucial for a general identification of the mRIXS observations, which will shed light on the understanding of the unusual oxygen states involved in the intense debates on TM oxide based energy materials.
In this work, we provide a combined experimental and theoretical mRIXS study of Li2O2, Li2O, and Li2CO3. Our central goal is to detect and identify the nature of the aforementioned critical O-K mRIXS feature in Lithium peroxide, thus providing benchmarks and guidelines for understanding the O-K mRIXS findings in energy materials. We note that collecting reliable mRIXS data from Li2O2 is a nontrivial issue due to the typical low count rates of RIXS experiments and the radiation sensitivity of the material 14,19 . These technical challenges have now been solved through our recently commissioned RIXS system with ultra-high detection  Compared with Li2O, Li2CO3 is a more complex system and can be considered as a molecular solid with independent carbonate (CO3 2-) ions surrounded by Li + ions.
The mRIXS map Li2CO3 displays two main emission-line (without strong excitation energy dependence) features with several intensity packets in Figure 2(a), centered at 521 eV (low intensity) and 526 eV (high intensity). Again, the main emission lines correspond to decays of VB electrons to the core holes, indicating there are obvious splitting of valence states in Li2CO3. The well separated islands of mRIXS intensity at 533.7 eV excitation energy are again from sXAS-process, which is directly evidenced by the sXAS peak at the same excitation energy ( Figure S2) and is known from the C=O bond of carbonates [4][5] . The shift of the weak signals below 532 eV excitation energy in mRIXS is a typical Raman-like shift when excitation energy approaches the absorption edge 36 . The assignments and origins of the observed mRIXS features are further interpreted by mRIXS simulations (Figure 2(b)) and the density of states (Figure 2(c) (Figure 2(c)). The upper and lower VBs lead to two separated emission lines in the calculated mRIXS, centered respectively around 526 eV and 521 eV with the former being more intense than the latter. The split features at different emission energies are also reproduced (Figure 2(b)), consistent with experimental results. However, there is quantitative discrepancy between the experimental results and theoretical calculations on the energy values of the emission lines, especially in the lower excitation energy range. This is traced to the choice of 13 the U value in our DFT+U calculations. As shown in supplementary information ( Figure S4), although U = 6 eV is the optimal value for describing hole-polaron behavior in previous publications [33][34] , decreasing the U value from 6 eV to 3 eV leads to a better quantitative agreement with experiments. In this context, GW 37 quasiparticle corrections to DFT or DFT+U single-particle energies could be relevant to improving the predictive accuracy of first-principles BSE RIXS 28 approach. We also note that other theoretical method should be further explored for RIXS calculations, for example, a very recent theoretical work based on Wannier orbital method could reproduce the experimental results of Li2CO3. 38 Therefore, all the mRIXS observations in Li2O and Li2CO3 could be simulated and assigned to emission lines corresponding to the decay of VB electrons to the core holes generated during the sXAS process. The mRIXS contrast between the two systems is mainly due to the different VB configurations.   between the πu and πg* states (Figure 3(c)). Therefore, two mRIXS emission-line features arise from the decay of electrons in the (σg, πu) and πg* states to the core holes, leading to the two vertical mRIXS features at 525 and 528 eV emission energies (Figure 3(a)). Calculations based on VB decay again reproduce these emission-line features (Figure 3(b)). The feature at 525 eV emission energy is attributed to decays from the lower energy πu states, while the 528 eV feature is attributed to decays from the πg* states. The excitation energy dependence of the mRIXS features are again consistent with the sXAS results (Figure S3), where broad features at 529 eV to 533.5 eV, 533 eV to 536eV, and above 538 eV are observed.
The low excitation energy 529 eV to 533.5 eV sXAS feature corresponds to the special O-O bonding in Li2O2 13 , i.e., the σu* states from unoccupied pz orbitals as explained above. Features above 538 eV excitation energy are from sXAS process to the high-energy Li-O hybridization states (Figure 3(c)). However, the broad feature in the intermediate excitation energies, 533 eV to 536 eV, has no corresponding pDOS, thus cannot be reproduced from theoretical calculations, but it matches almost exactly the strong feature of Li2O (Figure 1). Our previous study has shown that Li2O2 could be degraded into Li2O under soft X-ray exposure 14 . We therefore assign the signals at 533 eV to 536 eV excitation energies to Li2O from irradiation effect and/or impurity, even with our controlled and fast experimental scans.
The most striking finding of Li2O2 mRIXS is the intense feature near the 529 eV to 533.5 eV excitation and 523.7 eV emission energies, which appears as the strongest mRIXS feature in theoretical calculations (Figure 3(b)). As mentioned above, the sXAS signals at this energy range corresponds to the unoccupied σu* states  direction and the outgoing polarization to be perpendicular to it, along px. Based on the incoming and outgoing photon energies, this mRIXS feature is reproduced successfully through a specific excitonic state, where the electron and hole has σu* and πu characters, respectively. As directly shown in Figure 4, the electron part of the excitonic wavefunction is composed of orbitals oriented along the peroxo bond axis, reflecting its pz derived antibonding σ* character. The hole density is formed predominantly from orbitals oriented along px orbitals with π bonding character. Therefore, the critical mRIXS feature at 523.7 eV emission and 529 eV to 533.5 eV excitation energy is an O-2p intra-band excitation between the occupied π bonding states and the unoccupied σ* antibonding states (Figure 3c). The mismatch between the energy difference of the excitonic states (Figure 3c) and experimental energy loss is mostly due to the core hole effect, which is accounted for in theoretical calculations that show consistent results to experiments (Figure 3b). We note that the mRIXS feature of Li2O2 is broader than the calculation results, and the O-K sXAS also shows a relatively broader peak compared with hard X-ray results ( Figure S3) 30 , therefore surface degradation/contamination of the Li2O2 at least partially contribute to the broadening of this particular mRIXS feature. Dynamic disorders due to finite temperature may also contribute to the experimental broadening. It is important to note that, compared with the mRIXS feature of Li2O2, the much sharper feature around the same emission energy in TM oxide based battery electrodes does imply 19 differences in excitations and/or associated electron states, a topic that deserves further studies to clarify. Samples are cooled by Liquid N2 and remain itinerant during the experiments to reduce radiation damage effects. Radiation damage has been carefully monitored before and after RIXS experiments. We note that radiation damage effect cannot be completely ruled out, however, as elaborated in the manuscript, based on our previous studies of irradiation effects of the same materials, which shows the same final formation of Li2O after extended soft X-ray exposure on one sample spot, the distinct RIXS maps that we focus on in this work directly show they are intrinsic material features.

Theoretical Calculations
First-principles simulations of the RIXS spectra of Li2O, Li2O2 and Li2CO3 were carried out using the OCEAN package [7][8] 19 . We note in this context that the RIXS simulations are sensitive to the choice of the U parameter employed. Particularly in Li2CO3, the choice of U=6 eV which is in the optimal range for describing hole-polaron behavior in oxides produces some additional shifts in the RIXS emission features relative to experiment (see Figure 2 of main text). A smaller value of U=3 eV for the O-2p and C-2p states in Li2CO3 yields RIXS maps in better agreement with experiment (see figure S4). Kohn-Sham wavefunctions and eigenvalues obtained through this procedure were used in the subsequent BSE calculations. An O K-edge core-hole lifetime parameter of 0.14 eV was used in the simulations. In simulating RIXS spectra incoming and outgoing polarizations were considered to be orthogonal to confirm with the experimental geometry and the spectra were averaged over polarizations along the three Cartesian axes.
In order to facilitate comparison with experiment, the incoming photon energy axis was calibrated by matching the calculated X-ray absorption spectrum onset in each case to experiment. Furthermore, an additional Gaussian broadening of 0.8 eV was applied to the simulated RIXS and XAS along the incoming photon energy axis.