Diagnostic Features of EPR Spectra of Superoxide Intermediates on Catalytic Surfaces and Molecular Interpretation of Their g and A Tensors

Abstract

The use of electron paramagnetic resonance spectroscopy to study the superoxide intermediates, generated by end-on and side-on adsorption of the naturally abundant and ¹⁷O-enriched dioxygen on catalytic surfaces is discussed. Basic mechanisms of O₂ ⁻ radical formation via a cationic redox mechanism, an anionic redox mechanism, and an electroprotic mechanism are illustrated with selected oxide-based systems of catalytic relevance. Representative experimental spectra of various complexities are analyzed and their diagnostic features have been identified and interpreted. The molecular nature of the g and A tensors of the electrostatic and covalent superoxide adducts is discussed in detail within the classic and density functional theory based approaches.

1 Introduction

Activation of molecular dioxygen is one of the central problems of oxidative chemistry with long record of extensive experimental and theoretical investigations [1]. The peculiar electronic and magnetic structure of O₂ is related to its triplet ³Σ ⁻_g ground state with two orthogonal π_g*(2p) singly-occupied molecular orbitals (α-SOMO). Despite its open-shell nature, dioxygen exhibits relatively low reactivity. This feature is related to the triplet-singlet spin barrier [2], which can be circumvented upon O₂ activation on catalytic surfaces via complex networks of redox processes until the terminal O²⁻ ion is formed [1, 3]. It involves a sequence of gradual reduction and dissociation steps including O_2(g) → O_2(surf) → O ⁻_2(surf)  → O ⁻_(surf)  → O ²⁻_2(surf)  → O ²⁻_(lattice) , where various surface reactive oxygen species (ROS), from electron-poor (electrophilic) to electron-rich (nucleophilic), of distinctly different reactivity and proton affinity, may appear. All of them can be directly involved in heterogeneous oxidation of exogenous organic reactants depending on process conditions [1]. Thus, the catalytic role of the surface active sites is to provide oxygen in a specific activated state, which then permits preferable reaction pathways of lower activation energy to take place. In the particular case of the transition-metal oxide or metallozeolite catalysts, the variety of shapes and favorable orientations of the energetically accessible 3d orbitals together with the multiplicity of valence and spin states of surface transition-metal ions allow them to react with dioxygen effectively, without violating symmetry and spin conservation rules [4, 5]. Paramagnetic oxygen species can be located on the surface or within the bulk of the catalyst when zeolites or mesoporous materials are involved. Electron paramagnetic resonance (EPR) alone, or more frequently combined with other techniques, has been successfully used to study their location, structure, and catalytic reactivity [1, 6–8]. In the case of well resolved spectra, the high information content as compared to that obtained from other spectroscopies used in catalytic research helps to identify the active centers or intermediates and their structure and spatial arrangement. However, since most of the catalytic materials are polycrystalline and exhibit high surface area, the use of powders may generate some difficulties for EPR studies connected with overlapping signals and decreased spectral resolution.

Extensive experimental and theoretical studies have been performed to elucidate the heterogeneous activation process of dioxygen, starting from early stages of O₂ ^– formation until final incorporation of the resultant O²⁻ ions into the oxide lattice [1]. Unlike diamagnetic O₂ ²⁻ and O²⁻ anions, the O⁻ and O₂ ⁻ oxygen species are paramagnetic and may be observed directly by means of EPR spectroscopy [9–11]. These radicals, especially when isotopically enriched ¹⁷O₂ is used, exhibit characteristic spectra of high information content, which allows one to characterize their molecular structure, formation, thermal stability, and reactivity.

The superoxide anion, O₂ ⁻, is a particularly important intermediate of the one-electron reduction of dioxygen, which occurs widely in nature [12, 13] and in homo/heterogeneous catalytic processes [14–16]. The first step in activation of a dioxygen molecule consists of electron transfer (ET) from metal to ligand (MLET) to form a metal-superoxo adducts. It is feasible owing to the low-lying β-LUMO states, which can accommodate additional electron (and spin) density due to high electronegativity of oxygen. Both side-on (η²) and end-on (η¹) modes of O₂ coordination were observed. Further electron density transfer may be followed by O–O bond cleavage, leading eventually to the formation of high-valent metal-oxo cores (4e⁻ reduction), exemplified by, e.g., intrazeolite {FeO}⁺ dispersed in ZSM-5 [17].

Another catalytically important way of facile generation of the superoxide radicals involves hydrogen peroxide catalytic chemistry [18–21]. Specific electroprotic interaction of H₂O₂ with the catalyst surface determines the nature of the resultant ROS, among them O₂ ⁻ and OH^• radicals and peroxo O₂ ²⁻ species can be easily generated by controlling pH of the solution along with the redox properties, crystallinity, and surface acidity of the catalyst [21]. Apart from heterogeneous activation of dioxygen in the context of catalytic reactions, a number of important pathways to formation of O₂ ⁻ radicals have been recognized [22], where the mentioned elementary steps (ET, electroprotic interactions) are involved. They include for instance O₂ reduction by photo-excited conduction band electrons in semiconductors [23], enzymatic processes involving for instance NADH oxidase and cytochrome bc ₁ complex [24], reactions in liquid phase between selected ROS (for instance ^•OH radicals with H₂O₂) during Fenton-type processes [25] or reductive activation of O₂ in bioinorganic complexes [26].

The adsorbed superoxide anion is usually identified on the basis of its g and ^O A tensors. Nonetheless, unambiguous proof for its formation at the surface of a catalyst can be obtained by analysis of the hyperfine pattern from the EPR spectra obtained with ¹⁷O-enriched oxygen since the natural abundance of this isotope, having a nuclear spin of I = 5/2, is very low (0.038 %). Complete resolution of the hyperfine structure is necessary in order to calculate the distribution of the electron spin density within the adsorbed superoxide species. This is important from the viewpoint of the surface chemistry since the total spin density on O₂ ⁻ reflects the degree of electron transfer from the surface center to the adsorbed molecule.

In this paper we describe typical features of the EPR spectra of the superoxide ¹⁶O₂ ⁻ and ¹⁷O₂ ⁻ radicals stabilized on various catalytic surfaces, provide simple guidelines for their straightforward analysis and molecular interpretation of the extracted parameters. The classic semiempirical approaches are supplemented by density functional theory (DFT) calculations. A concise and non-technical sketch of the EPR spectra analysis of the surface superoxide species presented in this paper may be helpful for a broader audience interested in the practical aspects of EPR spectroscopy in this field, and discussion of the surveyed case studies.

2 Experimental Part

Selected examples of surface superoxide intermediates discussed in this paper include the following catalytic materials: 12CaO·7Al₂O₃ calcium aluminate (mayenite), amorphous Nb₂O₅ and ZrO₂ oxides, transition-metal ion (TMI) exchanged ZSM-5 and dealuminated SiBEA zeolites, and TMI supported on SiO₂. The polycrystalline mayenite samples were obtained by conventional high temperature solid-state reaction between analytical grade CaCO₃ (Aldrich) and γ-Al₂O₃ (Aldrich) as described elsewhere [27, 28]. Amorphous Nb₂O₅ and ZrO₂ oxides were prepared by hydrolysis of the metal precursors (Nb(C₂H₅O)₄ and ZrOCl₂) in diluted aqueous ammonia solution. The samples were treated with 5–35 % hydrogen peroxide (Merck) in the pH range 2–4 at room temperature to generate ROS, and dried at room temperature in air prior EPR measurements. Nickel-exchanged ZSM-5 zeolite (Si/Al = 15, Zeolyst, Inc.) was obtained by ion exchange in aqueous Ni(NO₃)₂ solution, as explained elsewhere [29]. Chemical analysis by means of AAS method revealed the Ni/Al exchange degrees of 54 % (1.10 Ni wt%). Prior to adsorption of O₂ and CW-EPR measurements, the samples were activated in vacuum of 10⁻⁵ mbar at 773 K for 2 h, followed by reduction with CO (Aldrich, 99.95 %) at 673 K for 30 min [30]. Dealuminated zeolite SiBEA (Si/Al = 1000) was obtained from zeolite BEA (Si/Al = 11, RIPP China) by treating with 13 M HNO₃ solution (4 h, 353 K). The resulting sample was then contacted with a dilute aqueous solution of NH₄VO₃ (10⁻³ M, pH 2.4) at room temperature [31]. In such conditions, the prevailing VO₂ ⁺ cations react with the silanol groups of the dealuminated SiBEA. Chemical analysis of the sample revealed a vanadium loading of 0.9 wt%. As shown in our previous paper, vacuum treatment of such a sample at 773 K resulted in formation of paramagnetic VO₂ molecules that are clathrated in the zeolite channels [32].

EPR spectra were recorded at 77 K with an X-band Bruker ELEXSYS-580 spectrometer, using a rectangular TE₁₀₂ cavity and 100 kHz field modulation. The spectra processing was performed with the software provided by Bruker, whereas for the computer simulations the EPRsim32 program was used [33]. It calculates exact solutions for the spin-Hamiltonian by full matrix diagonalization. A hybrid search procedure combining genetic algorithm and Powell refinement was applied for optimization of the simulated spectra.

In the case of mayenite, Nb₂O₅, and ZrO₂, prior to the measurements the samples were sealed in quartz tubes and outgassed in a vacuum line of p < 10⁻³ mbar for 2 h at room temperature. Whereas for the zeolite samples, the superoxide radicals were generated by exposure of the thermally activated samples to 1–2 Torr of the naturally abundant (Aldrich, 99.95 %) or the ¹⁷O-enriched dioxygen (Icon Service Inc., New Jersey, USA).

DFT calculations of g tensors components and molecular diagrams of the magnetic-field induced couplings that show molecular orbital contributions to the g _ii elements (g _ii = g _e + Δg _ii) were performed for electrostatic, q–O₂ ⁻ (q = +1e, +2e, +3e, +4e), and covalent [Ni–O₂]⁺ adducts. For this purpose the one-component approach of Schreckenbach and Ziegler based on Pauli Hamiltonian [34] implemented in the ADF software [35] was utilized. The g tensor values were also calculated within the mean-field approximation for the spin–orbit coupling (SOMF) implemented in the ORCA software [36]. More computational details can be found elsewhere [37].

3 Results and Discussion

3.1 EPR Spectroscopy of Surface Superoxide Species

The EPR spectra of the rigid superoxide species enriched in ¹⁷O (I = 5/2) and trapped on the surface can be described in terms of the following spin-Hamiltonian:

$$\varvec{H}_S = \hbar^{ - 1} \mu_{\text{B}} \varvec{B}^{T} \cdot g \cdot \varvec{S} + h^{ - 2} \varvec{S} \cdot\,^{\text{O}} \varvec{A} \cdot \varvec{I}_{\text{O}} + \hbar^{ - 2} \varvec{S} \cdot\,^{\text{M}}\varvec{A} \cdot \varvec{I}_{\text{M}}$$

(1)

where the g tensor gauges the electronic Zeeman interaction, whereas the ^O A tensor corresponds to the oxygen-17 hyperfine, and the ^M A tensor to the possible metal superhyperfine interactions between the corresponding nuclear spin I and the electron spin S. For the powder samples characteristic features in the EPR spectra appear when ∂B/∂θ = 0 and ∂B/∂ϕ = 0, where B is the resonant magnetic field B(θ,ϕ) = hv/g(θ,ϕ)μ_B (when I = 0), v is the microwave frequency, and θ and ϕ represent angles of polar coordinates showing orientation of principal g tensor axes with respect to external magnetic field B [38].

The three possible solutions, θ = 0 (B _z), θ = π/2 and ϕ = 0 (B _x), θ = π/2 and ϕ = π/2 (B _y), correspond to the usual principal g _zz, g _xx and g _yy components of the g tensor of the ¹⁶O₂ ⁻ species, respectively (Fig. 1a). For each of these principal directions, the EPR signal is additionally split into 2I + 1 = 6 lines in the case of the ¹⁶O¹⁷O⁻ isotopomer (Fig. 1b), and into 2nI + 1 = 11 lines (with the intensity distribution 1:2:3:4:5:6:5:4:3:2:1) for the ¹⁷O¹⁷O⁻ isotopomer with equivalent nuclei (Fig. 1c). It is characteristic of the η² side-on binding of the superoxide moiety (Fig. 2a). For double labeled ¹⁷O¹⁷O⁻ species with nonequivalent oxygen atoms, the number of hyperfine features increase to (2I + 1) × (2I + 1) = 36 lines of equal intensity (apart from the case of overlapping lines) at each direction (Fig. 1d). Such a splitting scheme is characteristic of the η¹ end-on superoxide adducts (Fig. 2b).

Fig. 1

Simulated CW-EPR powder spectra of superoxide species for: a ¹⁶O₂ isotopomer in rhombic environment b ¹⁶O–¹⁷O isotopomer, c ¹⁷O–¹⁷O isotopomer with equivalent nuclei, d ¹⁷O–¹⁷O isotopomer with nonequivalent nuclei, e weighted sum of ¹⁶O–¹⁶O, ¹⁶O–¹⁷O, and ¹⁷O–¹⁷O for enrichment level p = 0.5, and f ¹⁶O–¹⁷O for rhombic symmetry with extra features indicated with dots that appear upon an increase of the g tenor anisotropy

Fig. 2

Structural models of surface superoxide species of a C_2v (η²) and b C_s (η¹) local symmetry trapped at the metal site M with I ≠ 0. Whereas O–O moiety possessing two perpendicular planes exhibits a local C_2v point symmetry, only the vertical plane is shared with the M center, lowering the overall symmetry of the whole M–O₂ ⁻ magnetophore to C_s. As a result it is expected that the g and ¹⁷O hyperfine tenors are coincident, but the metal superhyperfine tensor ^M A is not. c Calculated spin density contour for surface Ca²⁺–O₂ ⁻ magnetophore

Because the nuclear magnetic moment of the ¹⁷O nucleus is negative (g _O = −0.75752), the successive hyperfine lines appearing with the increasing magnetic field are transitions from m _I = 5/2 to m _I = −5/2, for singly-labeled species, and from m _I = 5 to m _I = −5 for doubly-labeled species, respectively, where m _I is the nuclear magnetic spin number. For the doubly labeled (¹⁷O–¹⁷O)⁻ species, it is sensible to define a total nuclear spin number I = I ₁ + I ₂ = 5 as a convenient label for the hyperfine transitions. As a result, beside the sextet with equally intense lines due to the ¹⁶O¹⁷O molecules, there is a structure of 11 lines due to the ¹⁷O¹⁷O molecules (Fig. 1b, c). Because of the simultaneous appearance of all isotopomers, there are in principle 51 hyperfine lines in total to be expected for all g tensor components, which often due to line crowding and overlapping may not all be resolved (Fig. 1e).

The intensity of these lines and their detectability can be controlled with the degree of the O-17 isotopic enrichment level p. The relative abundances (P ^nm) of the ¹⁶O₂, ¹⁷O¹⁶O, and ¹⁷O₂ isotopomers in the gas mixture are given by: P ^16–16 = (1 − p)², P ^16–17 = 2p(1 − p), and P ^17–17 = p ². At low enrichment levels (20–30 %), the signal due to the singly labeled molecules is dominant, while for mixtures with 60–70 % enrichment, the hyperfine patterns from both, singly and doubly labeled superoxide radicals, can be simultaneously observed giving rise to a complex EPR spectrum. It becomes dominated by the ¹⁷O₂ isotopomer for p above 80 %. Thus, for distinguishing between η² (side-on) and η¹ (end-on) coordination, higher O-17 enrichment levels with a dominant contribution from the double-labeled ¹⁷O–¹⁷O are required. The analysis of the experimental spectrum should be carried out by adding the component signals of the three isotopomers (¹⁶O–¹⁶O)⁻, (¹⁷O–¹⁶O)⁻, and (¹⁷O–¹⁷O)⁻ sharing the same g and A tensors, but weighted by their relative abundance P in the gas mixture (Fig. 1e).

This relatively simple situation becomes complicated in the powder samples when there is a large anisotropy of the g and ¹⁷O A tensors. In conjunction with the high nuclear spin quantum number I = 5/2, this situation favors the appearance of the extra lines in the powder spectrum (Fig. 1f), when the following inequalities are satisfied [39]:

$$2A_{i}^{2} {-}{\text{ h}}vA_{i} /m_{I} < \, {{\left( {g_{i}^{2} A_{i}^{2} {-}g_{j}^{2} A_{j}^{2} } \right)} \mathord{\left/ {\vphantom {{\left( {g_{i}^{2} A_{i}^{2} {-}g_{j}^{2} A_{j}^{2} } \right)} {\left( {g_{i}^{2} {-}g_{j}^{2} } \right)}}} \right. \kern-0pt} {\left( {g_{i}^{2} {-}g_{j}^{2} } \right)}} < 2A_{j}^{2} {-}{\text{h}}vA_{j} /m_{I}$$

(2)

These extra features correspond to additional solutions for ∂B/∂θ = 0 and ∂B/∂ϕ = 0 in the ij plane, and appearance of extra lines in the EPR spectrum that can exhibit quite significant intensity in comparison to the “normal” hyperfine pattern (vide infra).

Apart from the extra line effects, another conceivable complication of the powder EPR spectra of surface superoxide species stems from possible non-coincidence of the g and A tensors (low-symmetry features). This can be expected for superhyperfine coupling with magnetic metal centers M (I ≠ 0) constituting the adsorption site, when the unpaired electron is mainly confined to the end-on η¹ superoxide ligand, or in the case of the hyperfine structure coming from ¹⁷O₂ ⁻, when the unpaired electron is delocalized predominantly on the metal center M and, thus, defines the g tensor nature. For the analysis of such a metal superhyperfine coupling only those symmetry elements (Fig. 2a, b), which are shared between the corresponding magnetic nucleus and the magnetophore (the part of the superoxide adduct on which the spin density is delocalized, Fig. 2c) determining the g tenor, are decisive [40].

For axial (one C _n /D _n axis with n ≥ 3, D_2d) or orthorhombic (C_2v, D_2h) symmetries both g and A tensors share the same principal axes, while in monoclinic (C₂, C_s, C_2h) or triclinic (C₁, C_i) symmetries the orientation of g and A axes may be different. However, for powder EPR spectra the relative orientations of the principal axes of the g and A tensors can only be determined for the monoclinic case, provided that I > 1 and both tensors exhibit large anisotropies. Then, taking as an example a hypothetical low-spin Co(III)–O₂ ⁻ adduct with I = 7/2, for small |m _I| values (±1/2), the magnetic field extrema (∂B/∂θ = 0 and ∂B/∂ϕ = 0), associated with the characteristic features in the powder spectra, occur at the angles close to the principal axes of the g tensor, whereas for large |m _I| values (±7/2), they appear at the angles close to the hyperfine principal axes. The result of such competition is the presence of hyperfine lines with strong variation in spacing with m _I (Fig. 3). Another simple criterion of non-coincident axes is the presence of lines which are unaccounted for, lack of lines at positions anticipated from simple extrapolation starting from either side of the spectrum or failure to simulate spectra with correct line positions and intensities [41].

Fig. 3

Simulated CW-EPR powder spectra of hypothetical ¹⁶O₂ ⁻ superoxide bound to a metal center of I = 7/2 nuclear spin. The symmetry assumed for simulation is rhombic or monoclinic with noncoincidence angle α = 40° in xy plane

Even if in favorable situations it is possible to observe CW-EPR features smaller than 0.1 mT for the surface paramagnets [42], usually resolution is a crucial problem, particularly for the catalytic materials of high surface area. Often not all of the theoretically possible hyperfine lines may actually be resolved. By reading out the positions of characteristic spectral features, fairly accurate (within the first order) values of the EPR parameters can be extracted only in simple cases, when signals are not too complex, satisfactorily well resolved, and the axes are coincident [43]. For more complicated powder EPR spectra of surface superoxide species the line positions generally are not strictly linear in any of the magnetic parameters. Then computer simulation is the only way of reliable analysis of such spectra. For this purpose computer programs of various sophistication level, such as EPRsim32 [33] or EasySpin [44], are available.

3.2 Principal Mechanisms of O₂ ⁻ Formation and Varieties of Superoxide EPR Spectra

The shapes of the EPR spectra of the surface superoxide species depend on the chemical nature and the nuclear spin of the atoms that are in the intimate contact, as well as on the symmetry of the nearest surroundings [10]. As mentioned above, two generic forms include the η¹ end-on and the η² side-on geometries of the superoxide moieties that can be attached to the surface active center(s) via electrostatic or covalent bonds. When magnetic nuclei are present, the EPR spectrum is additionally featured by the hyperfine (O-17 labelled dioxygen) or the superhyperfine structure (metal centers with I ≠ 0). Depending on the local symmetry of the resultant magnetophore the experimental EPR spectra may be categorized into axial, rhombic, mono-, and triclinic symmetry. In the latter two cases, the principal axes of the g and A tensors are not coincident, which may give rise to complicated features in the EPR spectrum that can properly be analyzed by computer simulation only. Axial symmetry of the EPR signal (g _zz = g _|| and g _xx = g _yy = g _⊥) of the superoxide species is rather uncommon, and frequently results from unresolved g _xx and g _yy components due to line broadening or their dynamic averaging by rapidly tumbling O₂ ⁻ species on the surface [41].

Typical powder X-band EPR spectra of selected superoxide species trapped on various catalytic surfaces are shown in Fig. 4. The collected examples include the O₂ ⁻ radicals (i) stabilized within the nano-cavities of highly ionic nature [Ca₂₄Al₂₈O₆₄]⁴⁺(2O²⁻) (mayenite), (ii) exhibiting weak covalent interactions with the transition-metal ions (amorphous ZrO₂ and Nb₂O₅), (iii) species with significant covalent bonding interaction with the adsorption center (Ni(I)/ZSM-5), (iv) charge-transfer complexes VO₂/SiBEA, Mo(V)/SiO₂, Co(II)/MgO). They cover either the side-on (Ni(I)/ZSM-5, MgO, [Ca₂₄Al₂₈O₆₄]⁴⁺(2O²⁻)) and end-on structures (Co(II)/MgO, Mo(V)/SiO₂). Their spin-Hamiltonian parameters (g and hyperfine A tensors) are listed in Table 1.

Fig. 4

EPR spectra (77 K) of superoxide species supported on catalytic materials. a Mayenite (calcium aluminate 12CaO·7Al₂O₃), b amorphous ZrO₂, c MoO_x/SiO₂, d NiZSM-5 zeolite, e amorphous Nb₂O₅, (f) VO₂/SiBEA zeolite, and g Co/MgO. Experimental spectra—black lines, simulated spectra—gray lines. All spectra are presented with a common g-value scale. Spectra adapted from [27] (a), [49] (c), [30] (d), [21] (e), [53] (g)

Table 1 Spin-Hamiltonian parameters for superoxide species adsorbed on surfaces of selected catalytic materials

The powder EPR spectrum of the mayenite sample (Fig. 4a) shows an orthorhombic signal characteristic of O₂ ⁻ trapped on the Ca²⁺ cations in the η² side-on fashion within the nanocavities [45, 46]. Its analysis via computer simulation allowed extraction of the g tensor components (g _zz = 2.078, g _yy = 2.012, and g _xx = 2.005), which are in a nice accordance with predictions of the Känzig–Cohen model (vide infra). The O₂ ⁻ species are formed during the calcination as charge balancing anions (together with O₂ ²⁻, O₂ ⁻ or OH⁻) according to the anionic redox processes such as

$$2 {\text{O}}_{{ 2({\text{g}})}} + {\text{ 2O}}_{{({\text{cage}})}}^{ 2- } \to {\text{ O}}_{{2({\text{cage}})}}^{{ 2{-}}} + {\text{ 2O}}_{{2({\text{cage}})}}^{-} ,$$

(3)

and are encaged in the mayenite nanocavities, since its framework is positively charged, in contrast to the akin zeolites [45].

The superoxide radicals stabilized on amorphous ZrO₂ and Nb₂O₅ oxides (Fig. 4b, e, respectively) were generated by contacting the oxide samples with aqueous H₂O₂ solutions. The efficiency of O₂ ⁻ formation depends on pH of the reacting mixture, and the highest concentration of the O₂ ⁻ species was obtained for pH in the vicinity of the isoelectric point (IEP) of the oxide [21]. Based on the concerted in situ and spin trapping EPR measurements we proposed that O₂ ⁻ species are generated via electroprotic reaction

$${\text{H}}_{ 2} {\text{O}}_{{ 2({\text{aq}})}} + {\text{ HO}}_{{ 2({\text{aq}})}}^{-} = {^\cdot}{\text{OH}}_{{({\text{aq}})}} + {\text{ O}}_{{ 2({\text{aq}})}}^{-\cdot} + {\text{ H}}_{ 2} {\text{O}}_{{({\text{aq}})}} ,$$

(4)

followed by trapping of superoxide species at the oxide surface

$${\text{O}}_{{ 2({\text{aq}})}}^{-\cdot} + {\text{ M}}_{{({\text{surface}})}} = {\text{ M}}{-}{\text{O}}_{{ 2({\text{surface}})}}^{-\cdot} ,$$

(5)

where M = Zr or Nb. The superoxide and hydroxyl radicals generated in the liquid phase were simultaneously detected by EPR with the aid of a DMPO spin trap. The EPR spectrum of O₂ ⁻ stabilized on ZrO₂ (Fig. 4b) exhibits a rhombic signal with the g tensor anisotropy (Table 1) characteristic of high oxidation state of the Zr⁴⁺ center inferred from the position of the g _zz component [18], as explained below in more detail. In the case of amorphous Nb₂O₅ (see Fig. 4e), an additional clearly resolved superhyperfine structure due to ⁹³Nb (I = 9/2, 100 %,) is observed only in one of the principal A tensor directions (|A _yy| = 1 mT, with A _xx and A _zz remaining unresolved), proving definitely that the superoxide species is attached directly to the Nb(V) center. The spin-Hamiltonian parameters of this adduct are intermediate between those expected for electrostatically [10, 45, 47] and covalently [26, 30] bound O₂ ⁻ species. Yet, they clearly indicate formation of the surface superoxide Zr(IV)–O₂ ⁻ and Nb(V)–O₂ ⁻ adducts. Analogous reactivity toward H₂O₂ was recently described for TiAlPO-5 molecular sieves showing formation of Ti⁴⁺–O₂ ⁻ species with g _zz = 2.0212, g _yy = 2.0098, and g _xx = 2.0033 [48].

Paramagnetic superoxide intermediates are often encountered when catalytic surface reactions are initiated by an interfacial electron transfer from the metal center M to the ligated dioxygen (MLET) [49]

$${\text{O}}_{{ 2({\text{g}})}} + {\text{ M}}_{{({\text{surface}})}}^{z + } \to {{{\text{O}}_{2}^{ - } } {-} {{\text{M}}_{{({\text{surface}})}}^{{\left( {z + 1} \right) + }} }}.$$

(6)

Such cationic redox mechanism is often observed in the case of dioxygen contacted with transition-metal ions dispersed on oxides or molecular sieves [8, 15, 30, 49]. Quite often MLET is followed by spillover of the resulting superoxide species onto the support, favored by configurational entropy increase, especially upon temperature enhancement. Examples are provided by the variable temperature interaction of dioxygen with the surface of MoO_x/SiO₂ (Fig. 4c), VO₂BEA (Fig. 4d), NiZSM-5 (Fig. 4e) or CoO-MgO (Fig. 4f) catalysts.

Isolated Mo(V) centers of various coordination environment grafted on amorphous SiO₂ surface are capable of reductive ET activation of dioxygen [49]. The EPR signal of the corresponding O₂ ^– species is shown in Fig. 4c. Stabilization of superoxide on molybdenum centers and formation of an end-on charge-transfer η¹ O₂ ⁻–Mo(VI) complex was definitely resolved by using ⁹⁵Mo (I = 5/2) and ¹⁷O isotopic labeling [49].

Metallozeolites that accommodate 3d ions act as efficient cationic redox centers for O₂ activation, and their three-dimensional channel structure makes the cage metal centers easily accessible for gaseous dioxygen [29, 30, 50]. In particular, intrazeolite nickel(I) sites generated in situ via reduction of oxo-nickel species with CO (Ni²⁺–O–Ni²⁺ + CO = 2Ni⁺ + CO₂), exhibit high affinity toward dioxygen capture. Adsorption of 2 Torr of ¹⁶O₂ at 298 K on such samples leads to development of a well resolved orthorhombic EPR signal (Fig. 4d) with distinctly different g values (g _xx = 2.0635, g _yy = 2.0884, and g _zz = 2.1675) as compared with other O₂ ⁻ anionoradicals (Table 1). It can be assigned to a covalently bound superoxide species, produced following the MLET route O_2(g) + Ni(I)/ZSM-5 → O₂ ⁻–Ni(II)/ZSM-5 [9]. As it was deduced from the changes in the EPR signal intensity with time, the superoxide radical is quite stable at ambient conditions, even upon subsequent evacuation. The η² side-on attachment of the O₂ ⁻ moiety to the nickel center was inferred from the parallel ¹⁷O₂ adsorption experiments (see below). It is worth noting here, that the O₂ ⁻–Ni(II)/ZSM-5 adduct exhibits a reversed g tensor (g _e < g _yy, g _xx < g _zz) and ^O A _yy ≫ ^O A _xx, ^O A _zz, which is distinctly different from previously observed values for its close bioinorganic analogues (g _xx, g _yy > g _zz, A _ii unresolved). They also deviate dramatically from those of the side-on O₂ ⁻ electrostatic complexes, typified by the classic O₂ ⁻/MgO adduct with g _e ≈ g _xx, g _yy < g _zz, and A _xx ≫ A _yy, A _zz [51] (Table 1). This discrepancy results from the combined effects of the η² attachment and pronounced covalency of the nickel–oxygen bonding, giving rise to unusual redistribution of the spin density within the Ni(II)–O₂ ⁻ moiety [30].

Notable intrazeolite superoxide adducts (Fig. 4f) were also observed by contacting O₂ with an intrazeolite VO₂ molecule of unique high electron and oxygen donor properties, generated in situ during thermal reduction of VO₂ ⁺ exchanged into dealuminated BEA zeolite [32]. The clear hyperfine structure (Table 1) proves direct bonding of the O₂ ⁻ moiety to the vanadium (^V I = 7/2) core, revealing formation of a charge transfer VO₂ ⁺–O₂ ^– complex, stabilized by silanol nests of the dealuminated BEA. Successful computer simulation of the corresponding EPR spectrum could only be accomplished by assuming a local monoclinic C_s symmetry, with the non-coincidence angle (α = 16°) between the g and ^V A axes in the yz plane.

Another example of the low symmetry spectra of the covalently bound superoxide is provided by the variable temperature interaction of dioxygen with the surface of CoO–MgO, which acts as a heterogeneous oxygen carrier binding dioxygen reversibly [52]. At low temperatures (T < 100 K) surface electron transfer leads to reversible formation of the end-on η¹ O₂ ⁻–Co(III) adduct (g _zz = 2.141, g _xx = 1.983, g _yy = 2.033, A _zz = 3.1 mT, A _xx = 1.5 mT, A _yy = 0.7 mT), see Fig. 4g. Yet, upon raising the temperature to 290 K, the superoxide spills over onto MgO matrix, forming a side-on electrostatic η² O₂ ⁻–Mg²⁺ complex with g _zz = 2.077, g _yy = 2.008, g _xx = 2.002 [53]. The latter species, when O-17 dioxygen enriched at various levels is used, exhibit complex EPR spectra (Fig. 5a) due to the presence of extra hyperfine lines. Their appearance may be better understood by plotting the angular dependence of the resonant field B versus θ angle for the ¹⁷O–¹⁶O and ¹⁷O–¹⁷O isotopomers (Fig. 5a, bottom) [51]. The obtained “road maps” indicate that apart from the usual field extrema along the principal directions along the principal axes (corresponding to θ = 0° and 90°), in the zx plane there are additional local off-axes turning points (θ = 22.7°, 28.8°, 38.3°, 51.6°, 72.5°), which gives rise to five extra absorption lines (indicated with dots). They are even more intense than the regular ones (see Fig. 5b). More detailed analysis of the unusual EPR spectral features can be found in recent review [54].

Fig. 5

a CW-EPR spectra of O-17 enriched superoxide radical stabilized on MgO surface and its relation with angular dependence of the resonance field B in the zx plane (ϕ = 0°), b dependence of the EPR spectra on the O-17 enrichment level (adapted from Ref. [51])

The overlapping extra and regular hyperfine lines make the superoxide EPR spectra complicated for analysis. Figure 5b illustrates clear advantage of using different isotopic enrichment to make the interpretation easier. The enrichment of p = 28 % results in a dominant singly-labelled ¹⁶O¹⁷O species (6-line hyperfine pattern), while for p = 63 % EPR signal due to the double-labelled ¹⁷O¹⁷O (11 lines) predominates. The number of the hyperfine lines appearing simultaneously can be then largely suppressed. However, despite these changes, the magnitude of their splitting (the ^O A tenor) remains constant, helping in proper assignment of the hyperfine constants.

3.3 Electronic Nature of the Superoxide g Tensor: Electrostatic Adducts

The electronic nature of the experimental g tensor of the electrostatic superoxo complexes may be analyzed using the classic Känzig and Cohen model [55], at least as a first approximation. For the unbound O₂ ⁻ (σ ²_g π ⁴_u π* ³_g ) radical, the unpaired electron occupies two degenerate antibonding π*_g(2p) orbitals giving rise to the ²Π_3/2 ground state. In such a case the g tensor is extremely anisotropic with g _|| = 2〈+1, +1/2|L _z  + 2S _z | +1, +1/2〉 = 4 and g _⊥ = 〈+1, –1/2|L _x  + 2S _x | –1, +1/2〉 = 0. As a result, the corresponding EPR signal of the randomly oriented free superoxide radicals will extend over a wide magnetic field, being too weak to be detected, unless the orbital momentum is partially quenched due to the interaction with the nearest chemical environment. The resultant bonding interaction localizes the odd electron on one of the π_(x,y)*_g orbitals, while the crystal field distortion Δ gives rise to two states with the energies equal to ±½λ_O[1 + (Δ/λ_Ο)²]^1/2, where λ_Ο is a free oxygen spin–orbit coupling.

This simple case can be exemplified by the O₂ ⁻ species stabilized on ionic surfaces such as MgO, where the local C_2v crystal field gives rise to an orthorhombic g tensor with g _zz ≫ g _yy > g _xx ≈ g _e, which is described by the following equations

$$\begin{aligned} g_{{{\text{xx}}}} = & \, g_{e} {\text{cos2}}\alpha - {\mkern 1mu} (\lambda /E)\left( {1 - {\text{ sin2}}\alpha - {\text{ cos2}}\alpha } \right), \\ g_{{{\text{yy}}}} = & \, g_{e} {\text{cos2}}\alpha - {\mkern 1mu} (\lambda /E)({\text{sin2}}\alpha - {\text{ cos2}}\alpha - 1), \\ g_{{{\text{zz}}}} = & \, g_{e} + 2l{\text{sin2}}\alpha , \\ \end{aligned}$$

(7)

where tan2α = λ/Δ, l = i〈π_y*|L _z |π_x*〉, g _e = 2.0023, and λ is the spin–orbit coupling constant, Δ is the splitting of both π_g*(2p _x ) and π_g*(2p _y ) levels, while E is the separation between the π_g*(2p _x ) and σ_g(2p _z ) orbitals.

From the experimental g tensor values the molecular λ, Δ, and E parameters can then be derived. For instance, using the data from Table 1 for EPR spectrum of O₂ ⁻ encaged in the mayenite (Fig. 4a), the values of Δ = 0.44 eV and E = 3.04 eV were calculated, which are typical for the superoxide radicals adsorbed on divalent cation centers [56]. This indicates that superoxide species are trapped on the Ca²⁺ and not on the Al³⁺ sites. The value of λ = 0.0168 eV, very close to the pure atomic one (λ_O = 0.0167 eV) implies that the O₂ ⁻ radical is essentially stabilized via through-space electrostatic interactions.

Much more detailed insight into the molecular nature of the g tensor can be obtained from relativistic theoretical calculations based on the ZORA, SOMF or Pauli Hamiltonian, reviewed by us recently [37]. ZORA–SOMF hybrid method reproduces the g and A tensor parameters with higher accuracy, however calculations based on the scalar Pauli Hamiltonian are particularly useful for their chemical interpretation. In this approach the calculated g _ii components may be partitioned in the following way: $\Delta g_{\text{ij}} = \Delta g_{\text{ij}}^{\text{rel}} + \Delta g_{\text{ij}}^{\text{d}} + \Delta g_{\text{ij}}^{\text{p}}$, where Δg ^rel_ij combines scalar relativistic corrections, whereas the terms Δg ^d_ij and Δg ^p_ij stand for dia- and paramagnetic contributions to Δg _ij, respectively. The paramagnetic term (Δg ^p_ij ) dominates the g tensor values [57, 58], therefore, while analyzing the molecular nature of their anisotropy it is enough to restrict the discussion to this overwhelming term only. The main contributions to Δg ^p_ij are defined, in turn, by the magnetic field-induced couplings between the occupied and virtual magnetic orbitals (Δg ^p,occ-virt_ij ), accounting for more than 90 % of the total Δg shift. This may be deduced from the non-vanishing elements of the following integrals [57]:

$$\Delta g_{ij}^{p,m - n} \propto \frac{1}{{2c\left( {\varepsilon_{n}^{\sigma } - \varepsilon_{m}^{\sigma } } \right)}}\left\langle {\Psi_{m}^{\sigma } } \right|iL_{i = x,y,z} \left| {\Psi_{n}^{\sigma } } \right\rangle$$

(8)

where Ψ _m and Ψ _n are the unperturbed Kohn–Sham orbitals, ε are the magnetic MO energies, L _i=x,y,z is the orbital momentum operator, whereas σ stands for α or β spin. To simplify construction of the MO coupling diagrams that are used to interpret the g tensor anisotropy (Figs. 6, 7), only the most important contributions (exceeding 10 % of the total Δg _ij ) were taken into account.

Fig. 6

Magnetic field-induced molecular orbital diagram for the most important paramagnetic contributions to the g tensor components of a η²-{O₂ ⁻–q} and b η¹-{O₂ ⁻–q} electrostatic adducts (q = +2e), in spin-restricted scalar relativistic Pauli Hamiltonian calculations. The molecular orbital couplings are indicated with arrows, and the corresponding contributions are given in ppm

Fig. 7

Magnetic field-induced molecular orbital diagram for the most important paramagnetic contributions to the g tensor components of η²-{O₂ ⁻–Ni(II)} magnetophore, within the spin-restricted scalar relativistic Pauli Hamiltonian calculations. The couplings are indicated with arrows and the corresponding contributions are given in ppm

The purely electrostatic interaction of the superoxide species with the adsorption sites can be modeled with the simplest discrete η²-{O₂ ⁻–q} and η¹-{O₂ ⁻–q} side-on and end-on reference adducts, respectively, for q = +1, +2, etc. In such a case the DFT calculations can be compared directly with the popular Känzig and Cohen semi-empirical treatment of the g tensor of the bound O₂ ⁻ (²Π_3/2) species (vide supra).

As shown by the spin-restricted Pauli calculations, even for the simplest electrostatic η²-{O₂ ⁻–q ²⁺} epitome of the C_2v point symmetry (Fig. 6a), the obtained results (g _xx = 2.002, g _yy = 2.012, g _zz = 2.079) are in a surprisingly good agreement with the experimental data observed for the real η²-{O₂ ⁻–Ca²⁺}/mayenite or η²-{O₂ ⁻–Mg²⁺}/MgO highly ionic systems (Table 1). The g _xx value remains intact (g _xx ≅ g_e), since in the C_2v point group the spin–orbit coupling of the SOMO with the 9 b ₁ (π_x*) and 6 a ₁ (σ_2p) states is forbidden for L _x operator by symmetry. The g _yy component is featured by one relatively small coupling between the occupied 6 a ₁ (σ_2p) and the semi-occupied 9 b ₁ (π_x*) orbitals only, and it may be identified with the E parameter in the Känzig–Cohen approach. The shift of the most sensitive g _zz component arises from the strong coupling between the 8 b ₂ (π _y *) and 9 b ₁ (π _x *) orbitals, which corresponds to the Δ parameter. The coupling scheme in Fig. 6a accounts well for the g _zz ≫ g _yy > g _xx ≈ g _e sequence (predicted adequately already by the Känzig and Cohen treatment), and experimentally observed for most of the electrostatically bound superoxo species on ionic surfaces, where the simple crystal field account is valid [9].

A similar coupling scheme is observed for the end-on η¹-{O₂ ⁻–q ²⁺} epitome of C_s point symmetry (Fig. 6b). A distinct difference between the η² and η¹ binding schemes is a larger splitting between the involved magnetic orbitals for η¹, resulting in smaller anisotropy of the g tensor (in accordance with Eq. 8). This phenomenon affects mostly the g _zz component (g _zz = 2.077 for η² and 2.053 for η¹ binding mode), decreasing also the g _xx  − g _yy anisotropy. As a result, the EPR spectra of the end-on adducts show a tendency toward more apparent axial shape.

3.4 Electronic Nature of the Superoxide g Tensor: Covalent Adducts

A more involved situation with respect to the ionic environments can be anticipated for the more covalent O₂ ⁻–Ni(II)/ZSM-5 adduct, as it may be deduced already from its pronounced g tensor anisotropy (cf. the EPR spectra in Fig. 4). In comparison to the electrostatically attached O₂ ⁻, all the g tensor components of this adduct are substantially shifted toward higher g values. This is a consequence of direct involvement of the nickel-based states into the magnetic couplings, but for the most part, also due to the appearance of new magnetic transitions. They are shown in the molecular diagram for the discrete η²-{O₂ ⁻–Ni(II)} unit (Fig. 7). The g _xx component (equal to g _e in the electrostatic model) is now affected by two couplings 17 b ₂(d _xz  + π*) ↔ 22 a ₂($d_{{x^{2} - y^{2} }}$ − π*) and 22 a ₂($d_{{x^{2} - y^{2} }}$ – π*) ↔ 23 b(d _xz  − π*), whereas the Δg _yy shift is dominated by the 20 b ₁(d _yz  − π*) ↔ 22 a ₂($d_{{x^{2} - y^{2} }}$ − π*) transition. The contributions to the g _zz value include two strong 21 a ₁($d_{z^{2}}$ − π*) ↔ 22 a ₂($d_{{x^{2} - y^{2} }}$ − π*) and 18 a ₁($d_{z^{2}}$ − σ) ↔ 22 a ₂($d_{{x^{2} - y^{2} }}$ – π*) magnetic transitions. As a result, all the g _ii components acquire a pronounced mixed metal–ligand nature involving mostly the coupling of the SOMO with the relevant occupied states. This picture explains quantitatively large positive shifts of all g tensor components for the η²-{Ni(II)–O₂ ⁻} adduct (actually observed experimentally), and their distinctly different molecular character featured by g _zz > g _xx > g _yy > g _e, in comparison to the electrostatic η²-{q ²⁺–O₂ ⁻} analogue. The observed peculiarities arise mainly from the δ-type overlap of the out of plane π*_⊥ orbital of dioxygen moiety with the d(x ² − y ²) orbital of the nickel center, allowed in the η² geometry.

Apart from the bonding geometry, also the charge of the adsorption site strongly influences the EPR g tensor anisotropy of the bound O₂ ⁻. The calculated (SOMF-B3LYP) g _ii elements for η¹-{O₂ ⁻–q} with the increasing charge q (Fig. 8a) show a systematic decrease of g _zz value up to q = +3e. Such an effect was also observed experimentally for a series of superoxide adducts with Na⁺, Mg²⁺, and Sc³⁺ cations in a frozen MeCN solution [59]. The SOMF (Fig. 8a) and Pauli (Fig. 6b) calculations shows that the most sensitive g _zz value decreases systematically with charge from 2.115 (q = +1e) to 2.077 (q = +2e) and 2.023 (q = +3e). It is nicely accompanied by experimental values of 2.1106 (NaO₂ trapped in rare-gas matrix) [60], 2.24 (NaO₂/MgO) [61], and 2.1197 (CsO₂/MgO) [62] for the q = +1e case; 2.0451, 2.0499, 2.0558, and 2.0587 (Mg²⁺O₂ ⁻, Ca²⁺O₂ ⁻, Sr²⁺O₂ ⁻, and Ba²⁺O₂ ⁻, respectively, in MeCN) [59] for the q = +2e case; and 2.0304 (Sc³⁺O₂ ⁻ in MeCN) [59]. Although for the highest charge, q = + 4e, a reversed g tensor is predicted (g _zz, g _yy > g _xx), such situation is chemically unlikely. Indeed, for VO₂ or MoO_x species, where the metals are formally tetra- and pentavalent, the experimental g _ii parameters (Table 1) resemble those of q = +3e, implying that the effective charge is actually lower due to strong covalency of the vanadyl/molybdenyl bonds, in accordance with the chemical intuition. With an increase of the charge, the orientation selectivity for the g _zz component (the value of the resonant field B(θ, ϕ)) is partially lost, while in the xy plane almost all orientations of the paramagnets participate in resonance simultaneously.

Fig. 8

a Dependence of the g tensor components of η¹-{O₂ ⁻–q} species on the point charge value for q = +1e, +2e, +3e, and +4e, calculated with B3LYP-SOMF method along with the corresponding simulated powder EPR spectra. The unit spheres show orientation selectivity of particular magnetic field positions. b Sequence of EPR spectra (77 K) that illustrates spillover of O₂ ⁻ radicals from the activation Mo centers toward silica matrix. c EPR spectrum of ¹⁶O₂ ⁻ radicals on MgO showing how topographic speciation of superoxide species among adsorption sites of various coordination (O_3c, O_4c, O_5c) is revealed by the multiple g _zz component. Experimental spectra adapted from [49] (b) and [63] (c)

The effect of charge of the adsorption site can be used, e.g., to follow spillover of the O₂ ⁻ species in the case of supported systems (such as Mo^(VI)O_x/SiO₂) or dilute solid solutions (CoO–MgO). Time evolution of the superoxide species in Mo^(VI)O_x/SiO₂ at 294 K (Fig. 8b) shows that O₂ ⁻ initially bound to Mo sites diffuses onto the SiO₂ support, which is indicated by the appearance of a new g _zz component at lower magnetic field. After 55 min at room temperature all the generated superoxide species are stabilized on the silica matrix.

In the case of polycrystalline samples, site sensitivity of the superoxide radical reflects the heterogeneity of the stabilization centers. This is probably best illustrated with O₂ ⁻ stabilized on powder MgO sample. The appearance of several lines in the g _zz region can be explained by the presence of the topologically distinct adsorption sites, localized on planes (O_5c), corners (O_3c) or edges (O_4c) of the MgO nanocrystals (Fig. 8c). Such sites exhibit slightly different effective charges, therefore also different values of the Δ splitting, which is nicely reflected in the multiplication of the g _zz component.

3.5 Analysis of Superoxide ¹⁷O Hyperfine Tensor

As already discussed distinction between the η¹ and η² binding mode of the superoxide species can be at best resolved using the isotopically enriched dioxygen. Two examples that are invoked to illustrate this point include η²-{¹⁷O₂ ⁻–Ni(II)} adduct in ZSM-5 zeolite [30] and η¹-{¹⁷O₂ ⁻–Mo(VI)} adduct supported on SiO₂ [49] (Fig. 9). The EPR spectrum and its simulation of the ¹⁷O-enriched superoxo complex formed by reaction with Ni(I)/ZSM-5 centers is shown in Fig. 9a. The dioxygen bonding type is proved by the presence of the characteristic 11-line pattern in the g _yy direction, discernible better after magnification of the low- and high-field wings of the spectrum. Simulation of the ¹⁷O–¹⁷O component with two equivalent nuclei is shown in Fig. 9b. Although only the diagnostic A _yy splitting is well resolved, the values of the remaining A _xx and A _zz splittings are assessed with acceptable accuracy by computer simulation. These results confirm the η²-{O₂ ⁻–Ni(II)} structure of the observed paramagnetic adduct.

Fig. 9

EPR spectra (77 K) of a O-17 enriched superoxide adducts obtained after adsorption of ¹⁷O₂ (1 Torr) on Ni(I)/ZSM-5 zeolite. b Simulated ¹⁷O–¹⁷O component of EPR signal of isotopically enriched superoxide adduct. c O-16 and d O-17 enriched superoxide adducts with Mo(VI)/SiO₂ surface centers. Experimental spectra—black lines, simulated spectra—gray lines. Spectra adapted from [30] (a) and [49] (c, d)

From the unstructured rhombic EPR signal of the O₂ ⁻ species observed after adsorption of dioxygen on the MoO_x/SiO₂ surface (Fig. 9c), the oxygen binding mode cannot be safely deduced. Yet, the analysis of the hyperfine structure of the isotopically enriched oxygen (Fig. 9d) revealed the presence of two ¹⁶O–¹⁷O and ¹⁷O–¹⁶O isotopomers due to the linkage isomerism (¹⁶O¹⁷O⁻–Mo and ¹⁷O¹⁶O⁻–Mo) implying an end-on η¹ geometry [9]. It was further confirmed by the ¹⁷O–¹⁷O isotopomer with two nonequivalent nuclei that give rise to the complex hyperfine structure comprising of 36 lines.

Once the ^O A tensor components are determined, redistribution of the spin density within superoxo moiety can be obtained by means of standard treatment using the simple formula ρ ⁱ = B _i/B ₀. In this equation B ₀ = –336.8 MHz is the tabulated atomic value for the dipolar ¹⁷O hyperfine constant [64], whereas B _i should be determined from the dipolar part of ^O A hyperfine tensor. Thus, such analysis requires decomposition of the experimental ^O A tensor into the isotropic (a _iso) and dipolar (T) terms,

$$^{O} A = {\text{ a}}_{\text{iso}} + \varvec{T} = a_{\text{iso}} + \varvec{B}_{\varvec{y}} + \varvec{B}_{\varvec{x}} ,$$

(9)

where the second and the third matrix is related to the dipolar contributions along y (B _y ) and x (B _x ) axis, respectively.

Using the ^O A tensor values obtained by spectra simulation for the η²-{O₂ ⁻–Ni(II)} adduct (Table 1), such decomposition leads to: ^O A/MHz = [+28.88; –165.70; +39.44] = –32.46 + [+68.38; –136.80; +68.38] + [–7.04; +3.52; +3.52]. The obtained value of a _iso = −32.46 MHz is in line with its dominant spin polarization origin, found earlier for the ionic O₂ ⁻ radicals trapped on MgO surfaces (a _iso = −60.7 MHz) [51]. In comparison to the ionic adducts, reduction of its magnitude, may be associated with a sizable shift of the spin density from the superoxo moiety to the nickel core (Fig. 7). The obtained B _x = −7.04 MHz and B _y = −136.8 MHz values corresponds to ρ ^x_π  = 0.02 and ρ ^y_π  = 0.40 spin densities. As a result, the dioxygen moiety in the η²-{O₂ ⁻–Ni(II)} adduct bears 0.84 of the total spin density, confirming definitely its essentially superoxide nature. The remaining part of the spin density is redistributed on the nickel orbitals, giving rise to fairly even distribution of the spin density O(0.42)–O(0.42)–Ni(0.16) within the magnetophore unit. It confirms also substantial covalency of the nickel–dioxygen bond reflected in the unusual g tensor parameters of the η²-{Ni(II)–O₂ ⁻} adduct, as compared with other superoxide complexes discussed in this paper. Analogous calculations for O₂ ⁻ stabilized on MgO (η²-O₂ ⁻/MgO) adduct with hyperfine tensor ^O A/MHz = [–213.93; +20.19; +23.98] gives a _iso = –60.7 MHz and T/MHz = [–153.23; +80.89; +84.68] [51]. The resultant spin density on superoxide moiety equals 0.99 in accordance with nearly pure electrostatic nature of the surface adduct.

4 Conclusions

EPR spectroscopy combined with isotopic labelling is a powerful and very sensitive technique, which can be applied successfully to analysis of the superoxide intermediates in catalysis. It may resolve many problems related with definite identification of O₂ ⁻ species, establishment of the end-on versus side-on attachment mode, and provide an insight into the intimate nature of the dioxygen-surface site bond via molecular interpretation of g and O-17 hyperfine tensors. Interpretation of EPR spectra based on the diagnostic features of the bound superoxide species was described. The typical semi-empirical method and DFT-based analysis of the corresponding parameters were also discussed. The formation of O₂ ⁻ species on heterogeneous surfaces was categorized into cationic and anionic redox mechanisms as well as electroprotic processes in the case of H₂O₂ as a reactant. The experimentally observed variety of superoxide EPR signals and the molecular nature of their parameters were accounted for by the electrostatic (magnitude of the charge, O₂ binding mode) and covalent effects.