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

Abstract

Dioxides (dioxygenyl (O₂⁺), dioxygen (O₂), superoxide (O₂˙⁻) and peroxide (O₂²⁻)) 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 (>200) 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.

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1. 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 (O₂), 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 O₂ 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 O₂ to survive. The gradual decay of these kinetic barriers to oxidation in the body is responsible for ageing. In humans, reactive oxide species (ROSs): O₂˙⁻, O₂²⁻, O²⁻, HO₂, H₂O₂ 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.^3–5

Metal–oxygen (M–O₂) 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’ (O₂^x, where x = −2, −1, 0 or +1) has warranted detailed scientific study in multiple fields.^1,2,6

O₂^x are homonuclear molecules that possess covalent O–O bonds and their characteristic symmetric stretching vibrations (ν_O–O) are visible spectroscopically. Examining the ν_O–O spectral band can provide valuable information about the chemical nature of the O₂^x. The oxidation state and reactivity of O₂^x, depends on the number of electrons occupying the highest occupied molecular orbital (HOMO), which are the π*(2p_xy) valence antibonding orbitals (Fig. 1), their spin state(s) and the O–O bond order (B_O, defined as the number of covalent bonds, see eqn (1)). O₂⁺ cations possess one electron in the π*(2p_x) antibonding orbital and have a B_O of 2.5. O–O bonding electrons in O₂⁺ cations experience high effective nuclear charge from the O nuclei, so have a short O–O bond length (B_L, 1.12 Å) and a high wavenumber ν_O–O (1876 cm⁻¹) value.^7,8 From O₂⁺ to O₂²⁻, the B_O decreases by 0.5 for each electron added into the π*(2p_xy) orbital. As an electron is added to the π*(2p_xy) orbital, increased antibonding and Coulombic repulsion between bonding electrons cause the O–O B_L to increase and the ν_O–O to red-shift. O₂²⁻ possesses a B_O of 1 and has the longest O–O bond (1.49 Å) of the homonuclear dioxides with the lowest ν_O–O value (∼743 cm⁻¹).⁹ In addition to O–O bond lengthening and the characteristic red shifts in ν_O–O spectra, each electron transferred to O₂^x causes a decrease in the bond force constant (B_k) and a drop in the bond dissociation enthalpy (B_H) of the O–O bond, discussed in more detail later.

where B_O = bond order, q = number of bonding electrons, q* = number of antibonding electrons.

Fig. 1 Molecular orbital diagram of O₂^x species based on filled π*(2p_xy) valence orbitals: O₂⁺ (black arrow only), high-energy singlet (¹Σ⁺_g) O₂ (black and orange arrows only), singlet (¹Δ_g) O₂ (black and green arrows only), triplet (³Σ⁻_g) O₂ (black and red arrows only), O₂˙⁻ (black, green, red arrows only) and O₂²⁻ (black, green, red, orange arrows).

Neutral O₂ contains two electrons in the π*(2p_xy) orbital(s) that can occupy three different spin states (Fig. 1); high-energy singlet (¹Σ⁺_g), singlet (¹Δ_g) and triplet (³Σ⁻_g). Unlike many common diatoms and organic molecules, which favour the ¹Δ_g state, the ³Σ⁻_g state is the lowest energy ground state of O₂ with two electrons in degenerate orbitals with the same spin. The ³Σ⁻_g O₂ orbital structure complicates coupling with other molecules in the ¹Δ_g state, which adds to the chemical stability of ³Σ⁻_g O₂. It is the: one-electron, two-electron or four-electron transition from ³Σ⁻_g O₂ to: O₂˙⁻, O₂²⁻ or O²⁻, respectively, and back again, that underpins the oxygen reduction and evolution reactions (ORR/OERs). For non-aqueous lithium oxygen (Li–O₂) batteries, in situ surface enhanced Raman spectroscopic (SERS) studies of ν_O–O have been instrumental in showing a O₂˙⁻ intermediary reaction mechanism and the existence of lithium peroxide (Li₂O₂) as the primary battery discharge product.^10–12

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 low-donor number solvents, such as acetonitrile, lead to a surface reaction resulting in thin, insulating Li₂O₂ film growth. In contrast, in high-donor number solvents, such dimethyl sulfoxide resulted in preferential Li₂O₂ particle growth in solution. High donor number solvents are thereby preferable in the context of Li–O₂ batteries as Li₂O₂ solution growth leads to higher capacities.

Creighton et al. first reported the ν_O–O stretch of O₂˙⁻ with Raman spectroscopy of KO₂ and contaminated Na₂O₂ in 1964.¹³ This was corroborated and expanded upon with other group-1 alkali-metal cation complexes ([M⁺⋯O₂˙⁻], where M = Li, Na, K, Rb or Cs) in the following decade at a variety of different temperatures.^14–21 Sawyer et al. synthesised and spectroscopically characterised the first O₂˙⁻ salt with an organic cation, in 1983, by substituting K⁺ with tetramethylammonium (TMA⁺).²² [TMA⁺⋯O₂˙⁻] had a spectrum analogous to KO₂, though slightly red shifted (∼22 cm⁻¹).²² Since then, the ν_O–O of many O₂˙⁻ complexes [C⁺⋯O₂˙⁻] have been detected in a variety of systems and phases. Such as: solid salts,^13,22 doped into other salts,²³ as an organometallic complex,⁶ dissolved in organic solvents²⁴ or generated electrochemically at a SERS active electrode–electrolyte interface.^10,11,25,26

Understanding the reactivity and bonding environment of the O₂˙⁻ intermediate is crucial in the development of more stable M–O₂ battery electrolytes and in particular, ambiguity around the existence and chemical character of the lithium superoxide (LiO₂) intermediary remains.^27,28 Thus, a detailed look at the ν_O–O spectra of species produced during ORR/OERs is warranted to better understand in the reaction mechanisms in non-aqueous electrolytes in order to assist in the fundamental understanding of lithium–oxygen and in more general other M–O₂ batteries.

2. Experimental

2.1. Calculation of ion properties

Ionic volumes, ionic surface area, charge distributions and electrostatic potential surface distributions for a number of molecular ions were determined using a simple density functional theory (DFT, B3LYP functional, 6-31G* basis set) in Spartan 16. Ionic volumes and surface areas for atomic cations were calculated using a simple pace-filling calotte (CPK) model.

3. Results and discussion

3.1. Meta-analysis of superoxide's Raman spectra

To investigate possible trends of O₂˙⁻ bonding, relevant literature reports of >50 species were collated and examined.^{10,11,13–18,25,26,29–60} See Table S1 (ESI†) for a catalogue of reported [C⁺⋯O₂˙⁻] complexes.

Raman spectral band positions reflect molecular energy levels in a vibrating bond and are well known to be influenced by (1) the mass of the atoms in the bond, (2) the bond force constant and (3) lattice/symmetry effects. For [C⁺⋯O₂˙⁻], counter cations (or strongly coordinating solvents) attract O–O bond electron density at different rates which also influences the force constant of the vibration, resulting in ν_O–O band shifts, explained further below.⁶¹

The molecular mass-to-charge ratio (M_rQ⁻¹, units: mol g⁻¹ C⁻¹) of an ion can dictate its Columbic attractive strength towards counter-ions. Generally, ions with low M_rQ⁻¹ values are stronger Coulombic attractors than ions with high values. In a [C⁺⋯O₂˙⁻] complex, where interactions between O₂˙⁻ and the counter-cation (C⁺) are weak: electron density is more concentrated on the O₂˙⁻ anion, the effective nuclear charge experienced by O–O valence bonding electrons is lower and the bond is longer than when O₂˙⁻ is strongly coordinated. This effect is visible spectroscopically, with weakly coordinated O₂˙⁻ complexes having lower wavenumber ν_O–O values (e.g. tetrabutylammonium [TBA⁺⋯O₂˙⁻]: <1115 cm⁻¹)^{10,11,25,26,60} and strongly coordinated O₂˙⁻ complexes having higher ν_O–O values (e.g. [Na⁺⋯O₂˙⁻]: ≥1155 cm⁻¹).^{15,17,47–52,62} The strength of the attraction between the coordinating cation and O₂˙⁻ effects valence bond electron density and the O–O bond force constant, causing the observed difference in ν_O–O wavenumbers.

For monovalent [C⁺⋯O₂˙⁻] complexes (independent of phase), plotting reported ν_O–O values against the M_rQ⁻¹ value of the coordinating cation (Fig. 2) shows an inverse trend (R² = 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⁻¹ C⁻¹) and Cs⁺ (132.9 mol g⁻¹ C⁻¹) have similar M_r values as TMA⁺ (74 mol g⁻¹ C⁻¹) and tetraethylammonium (TEA⁺) (130.0 mol g⁻¹ C⁻¹), respectively, but have higher wavenumber ν_O–O spectral bands (>15 cm⁻¹). This difference in the ν_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 O₂˙⁻ valence bond electron density than large molecular organic cations. Therefore, as a general rule: strong O₂˙⁻ coordination has a higher wavenumber ν_O–O spectral band.

Fig. 2 ν _O–O Raman bands for [C⁺⋯O₂˙⁻] complexes plotted against the M_rQ⁻¹ value of the coordinating cation (listed data in Table S1, ESI†). An inverse trend is visible with heavier coordinating cations having lower wavenumber ν_O–O bands indicating a less energetic O₂˙⁻ bond vibration and a ‘freer’ more Lewis basic species. A general fit produced R² 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 R² 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 LiO₂ related species. These do not match the expected trend for Li⁺, discussed later. Error bar refers to broad band between 1150–1200 cm⁻¹ reported as LiO₂ by Xia et al.³⁶

3.2. Ionic charge dispersion

The immediate coordinating environments ability to interact with O₂˙⁻ also provides interesting information about the reactivity and basicity of O₂˙⁻ in the complex which is reflected in the ν_O–O value. From Fig. 2, [C⁺⋯O₂˙⁻] containing high M_r cations (e.g. TBA⁺) have low ν_O–O values indicative of a more ionic ‘freer’ O₂˙⁻ species. In these complexes, O₂˙⁻ is a stronger Lewis base and can be expected to more readily donate electron density. Inversely, low M_r cation containing [C⁺⋯O₂˙⁻] complexes such as (H⁺) have stronger C⁺-to-O₂˙⁻ interactions with slight covalent character, resulting in higher wavenumber ν_O–O bands indicative of a weaker Lewis base O₂˙⁻ species. It was found that for cations coordinating O₂^x species, the: size, mass and charge influence the strength of coordination and in turn the O–O bond force constant which causes detectable changes in ν_O-O. Thus, the physical parameters of one ion can indirectly influence the bond force constant and wavenumber of bonds present in the counter-ion. These values for ions can be simply quantified in terms of the M_r, ionic volume (i_v) and the charge on the ion (z). In O₂^x complexes; changes in the M_r and i_v of the coordinating counter-ions were found to be inversely proportional to changes in ν_O–O whilst changes in the charge of the counter-ion were proportional quantified by the term. Considering the effect the size of the cation has on the ν_O–O of O₂˙⁻ complexes, this can be quantified by either the ionic volume (i_v) or the available ionic surface area (i_s.a.), measured in ų and Ų, respectively. i_v and i_s.a. values are known for most alkali-metal cations and can be calculated computationally using simple CPK or DFT models for larger molecular cations.

The ν_O–O of a [C⁺⋯O₂˙⁻] complex changes proportionally with the charge (q) on the cation and inversely proportionally with the molecular mass (M_r) and i_v (and i_s.a.) of the coordinating cation (eqn (2)). Assuming a uniform charge distribution over the ion: multiplying the M_rQ⁻¹ and a spatial component (i_v or i_s.a.) gives a parameter (eqn (3)), hereon named the ‘ionic charge dispersion’ (Ж).

where: ν_O–O = O₂˙⁻ stretch (cm⁻¹), M^C_r = molecular mass of coordinating cation, Q^C = charge on cation, i^C_v = ionic volume of cation (ų).

The Ж 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 (Ж) 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. Ж is an analogue of the charge density of an ion (M_rQ⁻¹i_v⁻¹). However, charge density does not account for the proportional relationship between: M_r, i_v and the Columbic attractive strength of the ion. Thus, Ж has been derived as a simple value to describe these ionic properties. Ж is a measure the ‘bulkiness’ of the counter-ion, where, the higher the Ж value the bulkier the ion is.

Excluding outliers, plotting the reported ν_O–O values of [C⁺⋯O₂˙⁻] complexes from Table 1 against the calculated (units: mol g⁻¹ ų C⁻¹) or (units: mol g⁻¹ Ų C⁻¹) of each coordinating cation shows a clear inverse exponential relationship (Fig. 3 and Fig. S1, respectively, ESI†). Ж 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 Ж 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 R² value of 0.952 (given the larger number of independent reports using different phases, systems and detection equipment spanning over >50 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 LiO₂ except for one³⁶ were excluded, this is discussed in Section 3.6.

Table 1 Table of calculated i^C_v, i^C_s.a., and values for some common cations and IL cations. Cations with smaller Ж values are expected to be stronger Lewis acids

Cation	M r (g mol^−1)	i ^Cv (Å^3)	i ^Cs.a. (Å^2)	Q (C)	(g mol^−1 Å^3 C^−1)	(g mol^−1 Å^2 C^−1)
H^+	1.0	7.2	18.1	1	7	18
Li^+	6.9	5.6	10.2	1	39	71
Na^+	23.0	10.1	19.3	1	233	443
Ca^2+	40.1	15.0	29.4	2	301	589
K^+	39.1	21.1	37.0	1	827	1446
Bi^3+	209.0	31.85	48.60	3	2219	3386
Rb^+	85.5	26.6	43.1	1	2272	3681
Cs^+	132.9	35.2	51.9	1	4678	6903
TMA^+	74.1	105.2	128.4	1	7799	9523
TMP^+	91.1	115.2	141.8	1	10 497	12 923
TES^+	119.3	148.5	109.8	1	17 704	13 093
TEA^+	130.3	195.4	177.5	1	25 451	23 115
Pyr14^+	142.3	183.2	129.4	1	26 060	18 408
TPA^+	186.4	250.4	273.8	1	46 662	51 030
Di-Im^2+	296.4	358.0	338.4	2	53 062	50 154
TBA^+	242.5	324.0	355.0	1	78 566	86 065
N1888^+	368.7	489.0	540.1	1	180 316	199 128

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Fig. 3 ν _O–O Raman band positions for [C⁺⋯O₂˙⁻] complexes plotted versus the calculated (see Table S1, ESI†) of the coordinating cation. Empirically derived equations for the lines of best fit and R² values for the fits are shown in bottom left-hand corner. Ж^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 reference³⁶ of LiO₂ (ν_O–O) has been considered due to the wide variation in wavenumber position reported, as discussed within the main text.

When detecting the ν_O–O of O₂˙⁻, 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 . With this knowledge, O₂˙⁻ 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 ν_O–O and 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 numbers⁶³ and the potential at an electrode surface, where O₂˙⁻ is generated electrochemically (to be discussed elsewhere).

Considering these findings, hydrogen superoxide (HO₂) has a high ν_O–O value (>1165 cm⁻¹)^26,29 and O₂˙⁻ can be considered to have some covalent character, sharing part of its valence bonding electron with the cation. Whereas, tetrabutylammonium superoxide (TBAO₂) has a low ν_O–O value and can be considered to contain dissociated ions. Fig. 4 depicts this relationship between the cation, O₂˙⁻ and ν_O–O schematically.

Fig. 4 Schematic depicting the strength of ion interactions in [C⁺⋯O₂˙⁻] complexes. The size of the white arrows indicates the strength of the interaction between O₂˙⁻ and the coordinate-cation. Small, light cations have concentrated charge with stronger electrostatic forces of attraction and may even be able to abstract O₂˙⁻ 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.

3.3. Ionic charge dispersion of other ions

The Ж 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). Ж is a simple value that can be calculated for any ion to approximate its coordination strength and/or propensity to interact with oppositely charged ions. Small Ж values indicate ions that are strong: coordinators or Lewis acid/bases, whilst large values represent weak: coordinators or Lewis acid/bases. This can be further explained in terms of hard–soft acid–base (HSAB) theory. Hard acids interact better with hard bases and soft acids with soft bases.⁶⁴ Ions with low Ж values can be consider hard Lewis acid/bases and ions with high Ж values can be considered soft Lewis acid/bases.

Tables 1 and 2 list calculated Ж values for some common cations and anions, respectively. The Ж value is a clear simplification of the charge on an ion, excluding many important contributions to inter-ion interactions such as: steric hindrance, charge density, the component molecules oxidation states and symmetry etc. However, as discussed, Ж values give a good approximation for the influence of the cation on the ν_O–O of O₂˙⁻ and are likely applicable to other systems too. Furthermore, additional quantifiable values for other ion properties (such as: symmetry etc.) could be added to refine the Ж parameter further in future. When selecting ions for their attractive strength Ж parameters (and possibly Ж^C : Ж^A ratios) could be used to quickly screen some of the near infinite number of ions and combinations that can be selected. Also, Ж parameters give a quick and cheap starting point when designing and tailoring novel IL electrolytes or salts. This is a good starting point compared with more precise computational or experimental techniques which are expensive, time consuming and would necessarily come later after first narrowing the field of search. Based on the value, the calculated Coulombic attractive strength of cations on anions is suggested to be similar for: Na⁺ and Ca²⁺ (233 and 301 g mol⁻¹ ų C⁻¹), Rb⁺ and Bi³⁺ (2272 and 2219 g mol⁻¹ ų C⁻¹) and TEA⁺ and Pyr₁₄⁺ (25 451 and 26 060 g mol⁻¹ ų C⁻¹, respectively).

Table 2 Table of calculated i^A_v, i^A_s.a., and values for common anions and IL anions. Anions with smaller values are expected to be stronger Lewis bases

Anion	M r (g mol^−1)	i v (Å^3)	i sa (Å^2)	Q (C)	(g mol^−1 Å^3 C^−1)	(g mol^−1 Å^3 C^−1)
O^2−	16.0	14.7	29.0	2	−118	−232
F^−	19.0	14.5	28.8	1	−276	−547
OH^−	17.0	17.1	32.8	1	−291	−558
O2^2−	32.0	25.1	44.1	2	−402	−705
O2˙^−	32.0	23.1	40.7	1	−738	−1302
Cl^−	35.5	23.7	39.9	1	−840	−1415
Br^−	79.9	28.0	44.7	1	−2239	−3569
NO3^−	62.0	41.2	61.6	1	−2552	−3817
SO4^2−	96.1	55.0	73.7	2	−2642	−3538
I^−	126.9	34.8	51.5	1	−4414	−6539
DiCN^−	66.0	65.0	88.7	1	−4295	−5859
ClO4^−	99.4	54.1	70.2	1	−5384	−6981
OTf^−	149.1	83.6	81.4	1	−12 455	−12 127
TFSI^−	280.1	153.5	115.2	1	−43 014	−32 262

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Similarly, for the of anions, the Coulombic attractive strength of anions on cations is suggested to be similar for: F⁻ and OH⁻ (−276 and −296 g mol⁻¹ ų, respectively), Cl⁻ and O₂˙⁻ (−840 and 738 g mol⁻¹ ų, respectively), whilst I⁻ is comparable with dicyanamide (DiCN⁻) and ClO₄⁻ (−4414, −4295 and −5384 g mol⁻¹ ų, respectively).

3.4. 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 O₂^x bond parameters such as the bond order (B_O), bond dissociation enthalpy (B_H), bond force constant (B_k) and bond length (B_L) require various experimental procedures to derive, like X-ray crystallography (XRC). Bond parameter values for most O₂^x species exist and can be correlated well with empirically measured ν_O–O values. Table 3 lists these bond parameters for different O₂^x species. Correlating these O–O bond parameters allows for variations in each bond parameter to be estimated by only measuring the ν_O–O of the O₂^x species.

Table 3 Bond parameters of various O₂^x species and their outer π*(2p_xy) valence orbital structures are listed. Raman spectral band ν_O–O^x/ν^peroxide_O–O ratios show good approximations with B_O indicating that energy changes in the bond vibration are directly proportional to the addition or removal of a valence electron. Correlating these values allows ν_O–O to be used to approximate the B_O and other bond parameters

O–O bond parameters	O2^2−	O2^•−	O2	O2^+	Ref.
Where: a = νO–O of (weakly coordinated) Cs2O2 salt, b = νO–O of TBAO2 generated in dimethyl sulfoxide (DMSO), c = νO–O of gaseous dioxides.
π*(2pxy) MO outer valence structure	↿⇂ ↿⇂	↿⇂ ↿	↿ ↿	↿	—
Bond length/BL (Å)	1.49	1.34	1.24	1.12	68
Bond enthalpy/BH (kJ mol^−1)	149	360	498	644	68
Bond force constant/Bk (mdyn Å^−1)	2.56	6.18	11.4	16.3	8, 13 and 69
ν O–O ^x	743^a	1108^b	1556^c	1876^c	9, 15, 53, 58 and 70–72
Bond order/BO	1	1.5	2	2.5	—
ν O–O ^x/ν^peroxideO–O	1	1.49	2.10	2.53	—

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Considering the relationship between ν_O–O and the coordinating cation discussed in the previous section: [C⁺⋯O₂˙⁻] complexes with strong coordinating cations can be considered to have partial-covalent character, i.e. the coordinating cation abstracts some amount of the O₂˙⁻ valence bond electron density. This bond electron density abstraction interaction between the dioxide ion and its coordinator is here on referred to as secondary covalency. For different O₂˙⁻ species, the amount of electron density abstracted by the cation can be estimated by considering the B_O of other O₂^x species. A change of 0.5 in the B_O corresponds to an electron being added or removed from the O–O bond. By assuming the B_O is variable, then a change of 0.25 indicates a valence bond electron being shared with the coordination environment, discussed later. A fully dissociated O₂²⁻ species has a B_O of 1 and there is an approximately linear relationship between the B_O and the bond force constant.^66,67 As the bond force constant dictates the wavenumber of the ν_O–O, therefore, calculating the ratio between the ν_O–O of various O₂^x species and the ν_O–O of O₂²⁻ (ν_O–O^x/ν^peroxide_O–O) generates values that match well with the actual O–O B_O (Table 3) as observed by Livneh et al.⁹

Due to their high values; Cs⁺ (4678 g mol⁻¹ ų C⁻¹) and TBA⁺ (78 656 g mol⁻¹ ų C⁻¹) are weak coordinating cations. Therefore, the B_O of Cs₂O₂^9,15,53 and [TBA⁺⋯O₂˙⁻]^25,26 can be assumed to be 1 and 1.5 and their Raman spectra used as ν_O–O values for dissociated O₂²⁻ and O₂˙⁻, respectively. In reality, both oxides will have some slight covalent character, however, even without considering this, and also the contributions from anharmonicity in the O–O bond vibration (which are relatively small and decrease in magnitude from O₂⁺ to O₂²⁻),⁹ we see good agreement between the B_O and ν_O–O^x/ν^peroxide_O–O ratios in Table 3. Fitting bond parameters in Fig. 5 with respect to known B_O values allows simple fits (eqn (6) and Table S2, ESI†) for estimating O₂^x bond parameters to be derived. The trends are approximately linear, however, more accurate cubic fits where used. Therefore, provided the ν_O–O of a O₂^x is know, it is suggested that all other bond parameters can be estimated.

y = Ax³ + Bx² + Cx + D (6)

where B_O = bond order, n = number of bonding electrons, n* = number of antibonding electrons.

Fig. 5 Fitted plots of O₂^x bond parameters from Table 3 against the B_O. Colour-coordinated axis labels are shown above the graph. Cubic lines of best fits are shown by dashed lines. Fit values shown in Table 4.

To further qualify that the relationship between the ν_O–O of O₂^x and its bond parameters are approximately linear/cubic: it would be expected that a O₂^x species with secondary covalency (i.e. a O₂^x species with the outer valence electron partially shared with its coordinating environment) would have a B_O between that of two fully dissociated O₂^x species. For example, a O₂^x species with a B_O between that of O₂²⁻ (B_O = 1) and O₂˙⁻ (B_O = 1.5) would be expected to have a B_O of ∼1.25, and would have a π*(2p) orbital structure between that of a O₂²⁻, [↿⇂ ↿⇂], and O₂˙⁻, [↿⇂ ↿], species. Thus, such a O₂^x species would have a detectable bond vibration and ν_O–O band somewhere between that of a strongly coordinated O₂²⁻ species (e.g. H₂O₂: 875 cm⁻¹) and a fully-dissociated O₂˙⁻ (e.g. a [TBA⁺⋯O₂˙⁻]: ∼1108 cm⁻¹) species.⁶⁷ Therefore, ν_O–O values between those of these two species can be considered to have secondary covalent character, with valence bond electron density being shared by the O₂^x anion with its coordinating environment. Such a O₂^x species would be expected to have a partial dipole moment induced by the coordination interaction and the ν_O–O band would be both Raman and IR active.⁷³ Searching the literature this was indeed found to be the case for the ν_O–O of organic peroxyls,^74,75 transition metal superoxo-complexes,^6,76,77 and metalloenzymes,⁷⁸ which all had Raman and/or IR values reported in the range between 875–1108 cm⁻¹. Also, this trend in ν_O–O would be expected to be the same for O₂^x species with superoxo-oxyl and oxo-dioxygenyl character which was also observed to be the case and is discussed in detail below. To clarify language, the O₂^x valence electron is assumed to be partially shared with the coordinating species and:

• Peroxo-superoxyl refers to a coordinated O₂^x species with a π*(2p) valence orbital structure between [↿⇂ ↿⇂]–[↿⇂ ↿], a B_O between 1–1.5 and a ν_O–O value between 875–1108 cm⁻¹.

• Superoxo-oxyl refers to a coordinated O₂^x species with a π*(2p) valence orbital structure between [↿⇂ ↿]–[↿ ↿], a B_O between 1.5–2 and a ν_O–O value between 1179–1552 cm⁻¹.

• Oxo-dioxygenyl refers to a coordinated O₂^x species with a π*(2p) valence orbital between [↿ ↿]–[↿], a B_O between 2–2.5 and a ν_O–O value between 1552–1825 cm⁻¹.

3.5. Secondary covalent bonding

All the above discussed ν_O–O spectral bands for various O₂^x species (>200) have had their estimated bond properties calculated (using eqn (6) and Table 4) and have been plotted against their calculated B_O (Fig. 6). O₂^x species with B_O values divisible by 0.5 can be considered ionic or neutral whilst those with B_O values in-between can be considered to have some amount of electron donation occurring between O₂^x and its coordinating environment, i.e. secondary covalent bonding. Therefore, the B_O is assumed to be on a spectrum and to vary depending on how strongly coordinated the O₂^x diatom is (and therefore, how much of its valence electron it shares).

Table 4 Cubic fit constants from Fig. 5 and eqn (6). In principle, all O₂^x parameters can be estimated by simply measuring ν_O–O

x	y	A	B	C	D
B O	ν O–O	592	−550	884	−184
B O	l	−0.0933	0.52	−1.157	2.22
B O	k	−2.607	15	−17.948	8.15
B O	H	108	−632	1489	−816

---

Fig. 6 Fitted plots of estimated bond parameters for various O₂^x species calculated from the ν_O–O values reported in the literature (see Table S2 for values, ESI†). Light green shaded regions signify O₂^x species that are ionic or neutral with valence bond electrons concentrated in the π_2px,y* orbitals. Light orange regions signify O₂^x species with secondary covalent interactions with the coordinate environment and where the outermost valence electron is shared with the coordinator. Colour coordinated axis labels are shown above the graph.

Experimental data on O–O bond parameters have been reported throughout the scientific literature for different O₂^x complexes. XRC or neutron diffraction techniques have been used to measure the B_L of many species, therefore, the estimated B_O and B_L values calculated from the ν_O–O value can be cross-compared with experimental results to gauge their accuracy. Where the information was available for some of these cross-comparisons are listed in Table S2 (ESI†) with the difference between the measured and calculated B_L values shown as a percentage (the literature is exhaustive and largely disorganised, i.e. individual bond parameters and ν_O–O values tend to be reported in different chemical, crystallographic, spectroscopic journals, and could warrant further compilation in future). Overall, the experimentally reported B_L and the estimated B_L values match well (generally <4% difference), supporting the correlation well. This relationship is useful for analysing O–O properties from experimental ν_O–O results.

where: B_O,c = calculated bond order, B_O,i = nearest B_O to the B_O,c devisable by 0.5 (if the nearest bond order is less than B_O,c then the species is covalent in the opposite direction). A change in bond order of 0.5 is equivalent to adding/removing an electron from O₂^x. A change in bond order of 0.25 is equivalent to adding/removing 1/2 an electron (i.e. secondary covalent bond). An electron donation value of 100% indicates half the O₂^x valence electron is being shared with the coordinate environment, i.e. a fully covalent interaction.

Considering the change in the estimated B_O value of O₂^x species (calculated using the measured ν_O–O values) between strong and weak coordination, the secondary covalent character (i.e. amount of electron donation/abstraction between O₂^x and its coordinating environment) can be roughly estimated (eqn (7)). This is another useful, low-cost, method for estimating the interaction between a O₂^x species and its environment based solely on its experimental ν_O–O bond vibration (see examples below). Thus, a value for the amount of electron donation/abstraction for a O₂^x can be teased out of the ν_O–O literature. One side note, these values are not suggested to be precise; as contributions from anharmonicity are excluded etc., rather they are useful tools for quickly calculating approximate values for O₂^x bond parameters, which confirm and enhance the understanding of its vibrational spectra. This is particularly useful for helping to understand dynamic systems that are in flux such as at an electrode surface where countless thermodynamic, kinetic and charge transfer processes are occurring simultaneously, allowing for a general understanding of reaction processes to be rationalised with respect to O₂^x in terms of its ν_O–O. This also enables O₂^x species to be used as diagnostic molecules to probe the coordination strength of its environment by measuring the generated ν_O–O band.

Some examples calculations are given: NaO₂ (1156 cm⁻¹), TBAO₂ (∼1108 cm⁻¹), Cu:O₂ complex A (1033 cm⁻¹),⁶ have calculated B_O values of 1.549, 1.5, and 1.409 and electron donation values of 19.5, 0 and −36.4%, respectively. Values greater than ±50% can be considered to have significant secondary covalent character. In NaO₂, Na⁺ can be thought of as abstracting ∼20% of an electron from the outer electron bond density of O₂˙⁻, which has slight oxygen character, relative to TBAO₂. While in Cu:O₂ complex A, the Cu-centred ligand can be thought of as donating ∼36% of an electron to O₂˙⁻ giving it slight peroxide character, relative to TBAO₂.

Therefore:

It should be emphasised this method is not meant to be precise, rather to be used as a tool for approximating O–O bond properties, at a glance, using empirically derived ν_O–O values for O₂^x species’ with complex structures or coordinate environments. This approach of deriving bond properties from spectral bond vibration values in different coordination environments could deliver comparable results for other homonuclear bonds and provide similar quick approximations, though this would require further work.

3.6. The trouble with lithium superoxide

Meta-analysis of reported Raman bands of LiO₂ 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 O₂˙⁻ region (1100–1200 cm⁻¹) have been reported as being either chemically stable LiO₂ or from polyvinylidene fluoride (PVDF) binder degradation during cycling of non-aqueous Li–O₂ cells (Fig. 7).^27,38,79 Fundamental in situ SERS studies also report the presence of LiO₂ as an intermediate produced during ORR at the roughened Au (rAu) electrode surface.^10,11,26 LiO₂ has long been believed to be both thermodynamically and kinetically unstable at temperatures above 25 K^{10,50,80–85} and it is still unclear whether this observed intermediary species is a pure LiO₂ phase or a partially electrolyte/electrode stabilised [Li⁺⋯O₂˙⁻] complex.^86,87 This has led to some uncertainty over whether LiO₂ can exist as a stable discharge product, reaction intermediate, or at all. In light of the trend in ν_O–O of O₂˙⁻ discussed previously, looking at the ν_O–O spectra of these reports can add to the debate.

Fig. 7 Plot of ν_O–O spectral bands attributed to LiO₂ in the non-aqueous Li–O₂ battery literature (see Table S1, ESI†). The expected ν_O–O for LiO₂ based on the meta-analysis would be 1167 ± 10 cm⁻¹, with this range highlighted by the red box.

Variation in reported bands comes down to the following: (1) O₂˙⁻ is reacting with PVDF abstracting a proton and forming an alkene bond that causes a concomitant shift in the G-band with a serendipitously similar bond vibration to O₂˙⁻ observed in situ. (2) δ⁺ proton sites in the structure of PVDF ([–CH₂–CF₂–]_n) binder are stabilising O₂˙⁻ and Li⁺ interactions allowing a stabilised [(Li⁺)_x⋯O₂˙⁻] complex to deposit and grow on the cathode/binder. This could explain the accompanying distorted carbon G-band (∼1505 cm⁻¹). (3) Due to similarities in the wavenumber of their spectral bands, A Li₂O₂·2H₂O species, similar to the Na₂O₂·2H₂O species (∼1135 cm⁻¹)⁴⁸ observed in non-aqueous Na–O₂ batteries, is being formed when H₂O is present in the electrolyte. (4) A thermodynamically irregular or amorphous LiO₂ phase or a weakly coordinated [Li⁺⋯O₂˙⁻] complex is formed. (5) A partially intercalated O₂˙⁻ species in the carbon cathode that allows Li⁺ to bind but inhibits disproportionation to Li₂O₂ is formed. The interaction between O₂˙⁻ and the graphitic layers could produce the observed G-band (∼1505 cm⁻¹) shift.

From the derived relationship, the expected ν_O–O for LiO₂ was estimated to be 1167 ± 10 cm⁻¹, with this range shown via a red box in Fig. 7. Region (A) ν_O–O values would fit with the expected value of a LiO₂ species. Only one value matched this and it was reported by Xia et al. who observed a broad ν_O–O band (1150–1200 cm⁻¹) after discharging a non-aqueous Li–O₂ battery.³⁶ Region (B) ν_O–O values would be expected to be partially stabilised [Li⁺⋯O₂˙⁻] species’ or incorrectly assigned bands. Other reports of ν_O–O in a variety of different systems (Table S1, ESI†) are likely surface/solution stabilised [Li⁺⋯O₂˙⁻] species or possibly PVDF degradation products.^27,42,88

In summary, it is suggested that many of the ν_O–O values reported as LiO₂ are too low and instead environmental influences (electrolyte and electrode) are helping to stabilise a [(Li⁺)_x⋯O₂˙⁻] complex (where x < 1). Current evidence suggests; that for species generated on cathodes with PVDF binder (1) is the most probable cause of these reported ‘ν_O–O’ spectral bands. However, (2) and (5) are other possibilities, but again are not a pure LiO₂ product. In addition, during in situ spectroelectrochemical investigations of the interface partially electrolyte stabilised [Li⁺⋯O₂˙⁻] complexes are being detected. Though, the report by Xia et al. suggests that it may still be feasible to produce a pure LiO₂ phase during discharge if the conditions are right though the presence of toroid discharge product morphologies (associated with water containing electrolytes)^89,90 may suggest HO₂ was being detected rather than LiO₂.

4. Conclusions

Superoxide (O₂˙⁻) vibrational spectral bands reported in the literature were collated (>50 species) and trends in their coordinating environment were observed and described. The Ж 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 Ж 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 O₂˙⁻ 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 (>200 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⁻ 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 LiO₂ was analysed and most reported bands were found to be too low to be a pure LiO₂ phase, suggesting that coordinate [Li⁺⋯O₂˙⁻] complexes or degradation products are the most likely cause of these spectral reports in the non-aqueous Li–O₂ battery literature.

Nomenclature

O2^+	Dioxygen cation
O2	Dioxygen
O2˙^−	Superoxide anion
O2^2−	Peroxide anion
ROS	Reactive oxide species
O2^x	Dioxide species, where x = −2, −1, 0, +1
ν O–O	O-O symmetric stretching vibration
[M^+⋯ O2˙^−]	Alkali-metal superoxide complex
[C^+⋯ O2˙^−]	Cation coordinated superoxide complex
C^+	Coordinate cation
M r Q ^−1	Molecular mass-to-charge ratio
M r	Relative molecular mass (mol g^−1)
[(Li^+)x⋯O2˙^−]	Superoxide rich lithium coordinate complex
XRC	X-ray crystallography
i v	Ionic volume
i s.a.	Ionic surface area
B O	Bond order
B L	Bond length
B k	Bond force constant
B H	Bond dissociation enthalpy
C	Cation
A	Anion
Ж	‘Ionic charge dispersion’
q	No. of bonding electrons
q*	No. of anti-bonding electrons
Q	Charge on an ion (C)

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We recognise funding from the joint Engineering and Physical Sciences Research Council (EPSRC) and Innovate UK grant PLAB (Practical Lithium-Air Batteries) EP/L505274/1 that enabled this work. Dr Peter Goodrich and Professor Christopher Hardacre at Queens University Belfast for the supply of ionic liquids, as well scientific discussions with Dr Sarah Ball, at Johnson Matthey, are gratefully acknowledged.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Tabulated data from meta-analysis. See DOI: 10.1039/c8cp04652b

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