Evaluating chemical bonding in dioxides for the development of metaloxygen batteries: vibrational spectroscopic trends of dioxygenyls, dioxygen, superoxides and peroxides

Dioxides (dioxygenyl (O2 ), dioxygen (O2), superoxide (O2 ) and peroxide (O2 2 )) are of immense biological, chemical and environmental importance. The ability to accurately detect and measure the changing strength of their chemical bonding and coordination in situ or operando is extremely beneficial in order to evaluate their chemical properties, this has been particularly important recently in the field of metal–oxygen batteries, where understanding the reactivity of the O2 intermediate is crucial in the development of more stable electrolytes. Meta-analysis of the collated vibrational Raman and IR spectral bands of numerous (4200) dioxygen species was used to interpret the effect that the immediate chemical environment has on the O–O bond. Subsequently, the dioxide vibrational spectral bands were empirically related directly with the bond electron density and other fundamental bond properties, with surprisingly high accuracy, allowing each property to be estimated, simply, from experimental spectroscopic observations. Important chemical information about the strength of secondary interactions between reduced oxygen species and its chemical environment can be also elucidated which provides a convenient method for determining the attractive strength an ion exerts over neighbouring counter ions.


Introduction
Oxygen (O) is a reactive and abundant element of immense chemical, biological, and environmental importance, warranting classification as a field of study in its own right similar to organic (carbon) and inorganic (transitional metal) chemistries. 1,2 Gaseous dioxygen (O 2 ), composed of two covalently bonded homonuclear atoms, constitutes 20.95% of Earth's atmosphere, providing an oxidising environment and thermodynamic driving force for many biological processes. Crucially, the controlled reaction of O 2 in the oxidation of glucose during aerobic respiration allows life on Earth to thrive. However, living organisms must also possess kinetic barriers to slow oxidation reactions with O 2 to survive. The gradual decay of these kinetic barriers to oxidation in the body is responsible for ageing. In humans, reactive oxide species (ROSs): O 2 À , O 2 2À , O 2À , HO 2 , H 2 O 2 and OH are produced as by-products of normal cell processes and are used in the immune response of white blood cells. However, excessive production of ROSs adds oxidative stress to cells causing cell and DNA damage (specifically mitochondrial DNA) which is linked to the formation of cancer cells. [3][4][5] Metal-oxygen (M-O 2 ) batteries have to deal with many of the same problems faced by biological systems, such as controlling the production and side reaction rate of ROSs. In addition, dioxide ligands are prevalent in organometallic and catalysis chemistry. Therefore, the chemistry of dioxide species' (O 2 x , where x = À2, À1, 0 or +1) has warranted detailed scientific study in multiple fields. 1,2, 6 O 2 (1) where B O = bond order, q = number of bonding electrons, q* = number of antibonding electrons. Neutral O 2 contains two electrons in the p*(2p xy ) orbital(s) that can occupy three different spin states (Fig. 1); high-energy singlet ( 1 S + g ), singlet ( 1 D g ) and triplet ( 3 S À g ). Unlike many common diatoms and organic molecules, which favour the 1 D g state, the 3 S À g state is the lowest energy ground state of O 2 with two electrons in degenerate orbitals with the same spin. The 3 S À g O 2 orbital structure complicates coupling with other molecules in the 1 D g state, which adds to the chemical stability of 3 S À g O 2 . It is the: one-electron, two-electron or four-electron transition from 3  intermediary reaction mechanism and the existence of lithium peroxide (Li 2 O 2 ) as the primary battery discharge product. [10][11][12] Johnson et al. 11 in particular highlighted the effect of solvent choice in the determination of the ORR pathway via either surface or solution route. Using SERS they showed that lowdonor number solvents, such as acetonitrile, lead to a surface reaction resulting in thin, insulating Li 2 O 2 film growth. In contrast, in high-donor number solvents, such dimethyl sulfoxide resulted in preferential Li 2 Fig. 2) shows an inverse trend (R 2 = 0.757). In Fig. 2, two further sub-trends are apparent for: (1) single atom cations (shown in blue) and (2) molecular cations (shown in red). Single atom cations such as Rb + (85.5 mol g À1 C À1 ) and Cs + (132.9 mol g À1 C À1 ) have similar M r values as TMA + (74 mol g À1 C À1 ) and tetraethylammonium (TEA + ) (130.0 mol g À1 C À1 ), respectively, but have higher wavenumber n O-O spectral bands (415 cm À1 ). This difference in the n O-O spectral bands can be accounted for by considering the size difference in these cations. Single atom alkali-metal cations are spatially smaller allowing them interact more closely with O 2 À valence bond electron density than large molecular organic cations. Therefore, as a general rule: strong O 2 À coordination has a higher wavenumber n O-O spectral band.

Ionic charge dispersion
The immediate coordinating environments ability to interact with O 2 À also provides interesting information about the reactivity and basicity of O 2 À in the complex which is reflected in the n O-O value. From Fig. 2 (2)). Assuming a uniform charge distribution over the ion: multiplying the M r Q À1 and a spatial component (i v or i s.a. ) gives a parameter (eqn (3)), hereon named the 'ionic charge dispersion' (\ ).
(2) ] complexes plotted against the M r Q À1 value of the coordinating cation (listed data in Table S1, ESI †). An inverse trend is visible with heavier coordinating cations having lower wavenumber n O-O bands indicating a less energetic O 2 À bond vibration and a 'freer' more Lewis basic species. A general fit produced R 2 values of 0.757 for the overall trend. Two sub-trends are apparent: (1) single atom and (2) molecular coordinating-cations. Lines of best fit for both trends (dashed lines) had R 2 values of 0.850 and 0.867 for single atom (blue) and molecular (red) coordinating cations, respectively. Circled bands (purple dashed line) are reports of LiO 2 related species. These do not match the expected trend for Li + , discussed later. Error bar refers to broad band between 1150-1200 cm À1 reported as LiO 2 by Xia et al. 36 where: n O-O = O 2 À stretch (cm À1 ), M C r = molecular mass of coordinating cation, Q C = charge on cation, i C v = ionic volume of cation (Å 3 ).
The \ value can be used to estimate the Coulombic attractive strength of an ion and the effect it will have on counter-ions. The Cyrillic symbol for Ž (\ ) is used for ionic charge dispersion, subscripts i v and i s.a. denote the use of ionic volume or ionic surface area, respectively, and superscripts A and C denote anion and cation, respectively. \ is an analogue of the charge density of an ion (M r Q À1 i v À1 ). However, charge density does not account for the proportional relationship between: M r , i v and the Columbic attractive strength of the ion. Thus, \ has been derived as a simple value to describe these ionic properties. \ is a measure the 'bulkiness' of the counterion, where, the higher the \ value the bulkier the ion is. Excluding outliers, plotting the reported Table 1 against the calculated \ C iv (units: mol g À1 Å 3 C À1 ) or \ C is:a: (units: mol g À1 Å 2 C À1 ) of each coordinating cation shows a clear inverse exponential relationship ( Fig. 3 and Fig. S1, respectively, ESI †). \ provides a much better fit than using the M C r or i C v of the coordinating cation alone. The spatial components i C v or i C s.a. are used to calculate \ but it appears to be unimportant which is used as they both change proportionally with one another between different cations. However, i C v gives a slightly better fit with a higher R 2 value of 0.952 (given the larger number of independent reports using different phases, systems and detection equipment spanning over 450 years this is a fairly good fit) compared with 0.942 using i C s.a. (Fig. S1, ESI †). Plotting on a logarithmic scale shows this correlation more clearly (Fig. 3). All reports of LiO 2 except for one 36 were excluded, this is discussed in Section 3.6.
When detecting the n O-O of O 2 À , the derived equation for the line of best-fit (eqn (5)) from Fig. 3 can be used to help estimate its ionic character and the coordination strength of the environment in terms of \ C iv . With this knowledge, O 2 À can be used as a diagnostic molecule to probe ion and even electrolyte interactions spectroscopically in environments where the coordination strength is unknown (e.g. novel electrolytes). This relationship between n O-O and \ C iv in Fig. 3 was found to hold in most cases. However, it can be manipulated by changing the symmetry, steric hindrance and charge of the coordinating cation, as well as the solvents Gutmann acceptor/donor numbers 63 and the potential at an electrode surface, where O 2 À is generated electrochemically (to be discussed elsewhere).
Considering these findings, hydrogen superoxide (HO 2 ) has a high n O-O value (41165 cm À1 ) 26,29 and O 2 À can be considered   ] complexes plotted versus the calculated log 10 \ C iv (see Table S1, ESI †) of the coordinating cation. Empirically derived equations for the lines of best fit and R 2 values for the fits are shown in bottom left-hand corner. \ C was calculated using i C v which provides a better fit than using i C s.a. . i C v and i C s.a. . Ionic volumes and surface areas were calculated in Spartan 15 using a CPK model for single atom cations (blue) and DFT (B3LYP, 6-31G*) for molecular cations (red). A single reference 36 of LiO 2 (n O-O ) has been considered due to the wide variation in wavenumber position reported, as discussed within the main text.
to have some covalent character, sharing part of its valence bonding electron with the cation. Whereas, tetrabutylammonium superoxide (TBAO 2 ) has a low n O-O value and can be considered to contain dissociated ions. Fig. 4 depicts this relationship between the cation, O 2 À and n O-O schematically.

Ionic charge dispersion of other ions
The \ value estimates the dispersion of a formal charge on an ion by assuming the charge is delocalised (i.e. dispersed uniformly across the volume and molecular mass of the ion Based on the \ C iv value, the calculated Coulombic attractive strength of cations on anions is suggested to be similar for: Na + and Ca 2+ (233 and 301 g mol À1 Å 3 C À1 ), Rb + and Bi 3+ (2272 and 2219 g mol À1 Å 3 C À1 ) and TEA + and Pyr 14 + (25 451 and 26 060 g mol À1 Å 3 C À1 , respectively). Similarly, for the \ A iv of anions, the Coulombic attractive strength of anions on cations is suggested to be similar for: F À and OH À (À276 and À296 g mol À1 Å 3 , respectively), Cl À and O 2 À (À840 and 738 g mol À1 Å 3 , respectively), whilst I À is comparable with dicyanamide (DiCN À ) and ClO 4 À (À4414, À4295 and À5384 g mol À1 Å 3 , respectively).

Dioxygen spectra and important bond parameters
It is of great practical value to relate physical bond parameters with spectral measurements so they can be derived with ease experimentally. To that end, several efforts have been made, however, these methods remain empirical. 65 Key O 2 x bond À and the coordinate-cation. Small, light cations have concentrated charge with stronger electrostatic forces of attraction and may even be able to abstract O 2 À electron density producing a covalent-like interaction, whilst the reverse is true for ions where the charge is dispersed over a large mass and area.   (Table 3) as observed by Livneh et al. 9 Due to their high \ C iv values; Cs + (4678 g mol À1 Å 3 C À1 ) and TBA + (78 656 g mol À1 Å 3 C À1 ) are weak coordinating cations.

Secondary covalent bonding
All the above discussed n O-O spectral bands for various O 2 x species (4200) have had their estimated bond properties calculated (using eqn (6) and Table 4) and have been plotted against their calculated B O (Fig. 6). coordinating environment) can be roughly estimated (eqn (7)). This is another useful, low-cost, method for estimating the

The trouble with lithium superoxide
Meta-analysis of reported Raman bands of LiO 2 shows that it sticks out like a sore-thumb in terms of both a wide range of reported values and that these values, are in the main, fall outside the trend of all other measured superoxide species (Fig. 2 and 3). 28 Raman spectral bands in the O 2 À region (1100-1200 cm À1 ) have been reported as being either chemically stable LiO 2 or from polyvinylidene fluoride (PVDF) binder degradation during cycling of non-aqueous Li-O 2 cells (Fig. 7). 27 Table S1, ESI †). The expected n O-O for LiO 2 based on the meta-analysis would be 1167 AE 10 cm À1 , with this range highlighted by the red box.

Conclusions
Superoxide (O 2 À ) vibrational spectral bands reported in the literature were collated (450 species) and trends in their coordinating environment were observed and described. The \ parameter based on the mass-to-charge ratio and ionic volume of the coordinating ion was derived, which gave an excellent approximation of the collated results. The \ parameter can be calculated with relative ease for most ions and is analogous to charge density and gives a simple low-cost method of quantifying an ions Coulombic attractive strength over oppositely charged species. It was determined that O 2 À can be used as a diagnostic molecule to probe the coordination strength of its immediate environment, by observing its vibrational spectrum. Furthermore, dioxygen vibrational spectral bands reported in the literature were collated (4200 species). The trends due to the changes in the coordinating environment were observed, where changes in the O-O vibrational spectral band were shown to be a result of electron abstraction/donation from/into the O-O bond via a 'secondary covalent' bonding interaction between the dioxygen species and its coordinating environment. A simple cubic approximation was drawn that enabled the bond order, bond dissociation enthalpy, bond length and bond force constants to be estimated solely using experimentally measured O-O spectral bond vibrations. For the bond length this approximation gave estimated values that matched extremely well with reported values (0.5-5%) measured experimentally using X-ray crystallography. It was shown by estimating the bond order allowed for the level of e À abstraction by the environment (i.e. the strength of the secondary covalent interaction) can also be estimated for any dioxygen species based solely on its vibrational spectra.
Raman spectrum of LiO 2 was analysed and most reported bands were found to be too low to be a pure LiO 2 phase, suggesting that coordinate [

Conflicts of interest
There are no conflicts to declare.