Spin‐Forbidden Branching in the Mechanism of the Intrinsic Haber–Weiss Reaction

Abstract

The mechanism of the O₂ ^⋅− and H₂O₂ reaction (Haber–Weiss) under solvent‐free conditions has been characterized at the DFT and CCSD(T) level of theory to account for the ease of this reaction in the gas phase and the formation of two different set of products (Blanksby et al., Angew. Chem. Int. Ed. 2007, 46, 4948). The reaction is shown to proceed through an electron‐transfer process from the superoxide anion to hydrogen peroxide, along two pathways. While the O₃ ^⋅− + H₂O products are formed from a spin‐allowed reaction (on the doublet surface), the preferred products, O^⋅−(H₂O)+³O₂, are formed through a spin‐forbidden reaction as a result of a favorable crossing point between the doublet and quartet surface. Plausible reasons for the preference toward the latter set are given in terms of the characteristics of the minimum energy crossing point (MECP) and the stability of an intermediate formed (after the MECP) in the quartet surface. These unique results show that these two pathways are associated with a bifurcation, yielding spin‐dependent products.

The Haber–Weiss (HW) reaction:1

$${\displaystyle \mathrm{O}{}_2{}^{·-}+\mathrm{H}{}_2\mathrm{O}{}_2\to \mathrm{O}{}_2+\mathrm{HO}{}^{•}+\mathrm{HO}{}^{-}}$$ (1)

has been the focus of much attention over the decades, because it can be a potential precursor of reactive oxygen species. Yet, the actual role of this reaction in biological processes and its suppression by the superoxide dismutase enzyme have been a matter of considerable controversy.2 Reaction (1) is known to proceed readily in the presence of Fe³⁺ ions (or other transition‐metal ions) via a chain mechanism, but becomes very slow3 or negligible4 in aqueous solutions under physiological conditions. Surprisingly, it has recently been observed to be very facile in the gas‐phase under low‐pressure conditions and to proceed directly in the absence of any solvent effects or catalyst.5 This finding suggests that the intrinsic HW reaction occurs with little or no activation energy and that it could occur easily in a hydrophobic environment. Two main features are particularly striking about the results obtained for the gas‐phase reaction:5 1) the rate constant amounts to 29 % of the limiting‐collision rate constant and 2) the nature and distribution of products, which are displayed in Scheme 1.

Scheme 1.

Products identified by Blanskby et al.5 for the gas‐phase reaction between superoxide and hydrogen peroxide.

Owing to the wide interest in the HW reaction and the unusual gas‐phase results, the mechanism of this reaction poses some intriguing questions and provided the impetus for our investigation. Two possible mechanisms were originally envisioned for Reactions (2 a) and (2 b) in Scheme 1: initial formation of a stable ion‐neutral complex [O₂ ^⋅−⋅⋅⋅H₂O₂] followed by either a hydrogen atom or proton transfer, or by an electron transfer. In both cases, a series of putative intermediates were proposed to account for the final products. However, both mechanisms must overcome some formal unfavorable energetics. Proton transfer from H₂O₂ to O₂ ^⋅− is endothermic by 23 kcal mol⁻¹ in the gas phase;6 whereas an electron transfer from O₂ ^⋅− to H₂O₂ is also expected to be endothermic, because the electron affinity of H₂O₂ is presumably negative.7 In fact, experimental work as well as theoretical calculations for the [H₂O₂]⁻ potential energy surface (PES) lead either to O⁻(H₂O) or OH⁻(OH^⋅) structures or to total dissociation.7, 8 In addition, Reaction (2 a) is exothermic, provided O₂ is formed in the ³∑_u ⁻ ground state. This suggests that the major product of the intrinsic HW reaction proceeds through a spin‐forbidden reaction pathway.9 By comparison, Reaction (1) in solution gives rise to singlet oxygen (¹Δ_g ⁻).10

Herein, we report a detailed theoretical investigation of the relevant features of the PES for the O₂ ^⋅−/H₂O₂ reaction to properly address the mechanism of the intrinsic HW reaction. Although the full computational details are described in the Supporting Information (Section S1), our discussion will be centered around the results obtained at the ROB2PLYP‐D3/aug‐cc‐pVTZ//UB2PLYP‐D3/aug‐cc‐pVTZ level of theory. This functional has been shown to yield comparable results with CCSD(T) for calculating reaction energies and transition states in a recent study of anion/neutral reactions.11 Dispersion corrections were included for cases involving large distances between fragments. Although the nature of this problem suggests a multiconfigurational approach, attempts to describe these reactions at the CASSCF/MR‐CISD level proved unsatisfactory, owing to difficulties in defining the same active space for all regions. However, the single reference approaches used here are shown to yield a correct description of the feasibility of these reactions and good agreement with experimental reaction enthalpies, as shown below. Similar single reference approaches have been applied successfully to other spin‐forbidden reactions.19d

Figures 1 and 2 illustrate the calculated energy profile and the optimized structures for the reactants (R), products (P), reactant complex (RC), product complexes (PC), intermediates (Int), transition states (TS), and the minimum‐energy crossing point (MECP) between the doublet and quartet energy surfaces for the electron‐transfer mechanism. The calculated reaction enthalpies at the ROB2PLYP‐D3//UB2PLYP‐D3/aug‐cc‐pVTZ level were estimated to be −12.6 kcal mol⁻¹ for the ²[O^⋅−(H₂O)]+³O₂ reaction and −28.2 kcal mol⁻¹ for the ²O₃ ^⋅−+¹H₂O products, in good agreement with the experimental reaction enthalpies.5

Figure 1.

Calculated energy profile at the ROB2PLYP‐D3//UB2PLYP‐D3/aug‐cc‐pVTZ level for the electron‐transfer mechanism of the O₂ ^⋅−+H₂O₂ reaction. Relative energies of ⁴TS‐1 and ⁴Int‐1 (represented by the dashed thin line) do not include zero‐point energies. ²P′ corresponds to the products with singlet dioxygen, ²[O^⋅−(H₂O)]+¹O₂. Refer to Figure 2 for the notation used.

Figure 2.

Calculated structures at the UB2PLYP‐D3/aug‐cc‐pVTZ level for the electron‐transfer mechanism of the O₂ ^⋅−+H₂O₂ reaction. The main geometrical parameters (distances in Å and ϕ_{H1‐O2‐O3‐H4} dihedral angles in degrees) are included in the structures.

The reaction is predicted to proceed by the initial formation of a reactant complex, ²RC, between hydrogen peroxide and the superoxide anion (see Figures 1 and 2). This complex is calculated to be 31.7 kcal mol⁻¹ more stable than the reactants. This energy is considerably higher than the solvation energy of O₂ ^⋅− with water that has been measured to range between 18.4 and 19.6 kcal mol⁻¹ from different experiments,12 and can be attributed to the larger number of hydrogen bonds in the ²RC complex. The optimized structure for ²RC reveals that the dihedral angle of H₂O₂ calculated to be approximately 113° for the isolated molecule is significantly decreased to almost 0.1°. Furthermore, the O⋅⋅⋅H distances are calculated to be 1.70 Å, which are indicative of strong hydrogen bonds.13 From the ²RC complex, the electron‐transfer pathway (Figure 1) proceeds through transition state ²TS‐1 located 3.1 kcal mol⁻¹ below the energy of the reactants. The transition state ²TS‐1 is characterized by partial charge transfer from the superoxide to the H₂O₂ moiety, as inferred from the approximately −0.4 NBO charge (calculated at the UB2PLYP‐D3 level) on the superoxide anion. An analysis of the Kohn–Sham HOMO orbital (see Figure S4) with beta spin in the TS‐1 doublet structure indicates a large contribution from the σ* orbital of the O−O peroxide bond, and accounts for the increase in the bond distance. In the region between ²TS‐1 and PC, the main rearrangements involve a combination of stretching of the hydrogen peroxide O−O bond, change in the relative orientation of the two OH groups, and migration of the O₂ moiety (see Figure 2), leading to a higher entropy for ²TS‐1 when compared with the tight ²RC structure (see Table S1). From ²TS‐1, this pathway leads to intermediate ²Int‐1 calculated to be 9.2 kcal mol⁻¹ below the energy of the reactants, with a structure corresponding to a loose nonlinear [O₂⋅⋅⋅O(H)⋅⋅⋅O(H)]⁻ complex. After ²Int‐1, our results predict the system to evolve in the direction of products via a flat PES, with a topology that resembles a bifurcation containing a spin‐forbidden pathway. On the one hand, formation of the ²O₃ ^⋅−+¹H₂O products (labeled as ²P) proceeds along the doublet surface through ²Int‐1 → ²TS‐2 → ²PC, which is characterized by a very low barrier (less than 1 kcal mol⁻¹). But, on the other hand, formation of ²[O^⋅−(H₂O)] + ³O₂ (labeled as the ⁴P products) takes place via the ²Int‐1 → ^2/4MECP → ⁴Int‐2 → ⁴TS‐2 → ⁴PC route, consisting of a spin‐forbidden pathway. The MECP structure connects two intermediates (²Int‐1 and ⁴Int‐2), one on each PES, with an energy difference of less than 1 kcal mol⁻¹ between MECP and ²Int‐1.

Single‐point calculations were performed for the ²TS‐1, ²Int‐1, ⁴Int‐2, and ⁴TS‐2 structures to identify the spin‐crossing region by changing the multiplicity from doublet to quartet and vice‐versa (see the dashed thin line in Figure 1). Occurrence of a spin change, from ²Int‐1 to ⁴Int‐2, along with the quasi‐degeneracy between the doublet and quartet states in the region between these two stationary points, suggests the presence of MECP (see Figures 1 and 2) between these two states after the ²TS‐1 region. The NBO charges calculated for the MECP structure (taken as the average between the doublet and quartet charges) indicate complete charge transfer between the superoxide and the [OHOH] moiety, with approximately equal charges on the two OH groups. Thus, the presence of O₂ leads to a charge separation with the negative charge in the H acceptor OH group, which is the reverse of what was predicted in the photodetachment experiments.8b

From a structural point of view, the main difference between the two intermediates (²Int‐1 and ⁴Int‐2) is the relative position of the O₂ molecule. Although O₂ is almost in the same plane as the OH group closest to it in the doublet surface, O₂ is almost equidistant from the two OH groups in the quartet surface. Their NBO charges again indicate almost complete charge transfer between superoxide and the [OH⋅⋅⋅OH] moiety, with approximately equal charges in the two OH groups. These two intermediates then lead to their corresponding product complexes, namely O₃ ^⋅−⋅⋅⋅(H₂O) and O₂⋅⋅⋅O^⋅−(H₂O), and finally to the O₃ ^⋅− and O^⋅−(H₂O) anions identified experimentally.5 In summary, our results indicate that O₃ ^⋅− originates from the doublet surface, whereas the O^⋅−(H₂O) anion is formed from the quartet surface (see Figures 1 and 2).

The larger O−O bond distances (see Figure 2) of O₂ in ²Int‐1 and ²TS‐2, when compared with those in ⁴Int‐2 and ⁴TS‐2, are consistent with singlet and triplet dioxygen in the doublet and quartet surfaces, respectively.14 This feature may account for the larger stability of the two points on the quartet surface (see Figure 1).

Accounting for the branching ratio that favors the preferential formation of [O^⋅−(H₂O)]+³O₂ cannot be solely explained by the calculated energetics. This situation is similar to that described in Ref. 9b, where a stable species (in our case ²Int‐1) can either yield one set of products on the same PES (doublet) after passing through ²TS‐2 (see Figure 1), or can form different products on another PES (quartet), with a spin change occurring at a crossing point (MECP in Figure 1). Although the ⁴Int‐2 species is more stable than the ²Int‐1, and may explain the preference for this pathway,9b the energies of ²TS‐2 and ^2/4MECP are essentially identical. In this case, the probability of the transition from the doublet to the quartet surface becomes important. Although a relatively small spin‐orbit coupling matrix element can be expected for light elements, high probabilities of spin conversion can be achieved, depending on the characteristics of the two PES at the MECP15, 16 and on the velocity of the system at the MECP.17 According to the transition probability based on the Landau–Zener model applied to spin‐forbidden reactions, if, for instance, relatively low velocities (in comparison with the spin‐orbit coupling between the two spin states) are achieved, the probability of spin conversion can be increased, as can be seen from Equation (1) of Ref. 17. A preference for a spin‐forbidden pathway has been observed previously for a reaction between species containing light elements,18 and many cases have been illustrated in gas‐phase ion chemistry.19

A potential energy calculation along the O⋅⋅⋅O bond distance of hydrogen peroxide and one of the O⋅⋅⋅OH bond angles shows a flat region involving ²Int‐1, ²TS‐2, and ^2/4MECP (see Figure 3). Recent studies of dynamics simulations suggest that the initial vibrational energy distribution and energy exchange between different degrees of freedom can determine the mechanisms and selectivity of reactions that occur on a PES with a flat topography.20 Figure 3 also displays two vibrational frequencies of the ²Int‐1 related to the bending mode around the O⋅⋅⋅OH bending angle, which is consistent with the ²Int‐1 → ²TS‐2 route, and to the stretching mode responsible for separating the O₂⋅⋅⋅O(H)⋅⋅⋅O(H) groups, associated with the ²Int‐1 → ^2/4MECP pathway. Thus, preference for the spin‐forbidden pathway for the O₂ ⋅ ⁻+H₂O₂ reaction can be rationalized by the flatness of the doublet PES in combination with the fact that the stretching mode (285.3 cm⁻¹) is energetically more readily accessible than the bending mode (825.9 cm⁻¹).

Figure 3.

Contour map of the PES along the O⋅⋅⋅O bond distance of hydrogen peroxide and one of its O⋅⋅⋅OH bond angles, calculated by the relaxed‐scan procedure at the ROB2PLYP‐D3//UB2PLYP‐D3/aug‐cc‐pVTZ level.

An alternative mechanism involving proton abstraction after the initial complex ²RC has also been explored, which is fully described in the Supporting Information (see Section S3). Although the initial proton abstraction goes through a transition state below the energy of the reactants, the subsequent steps involve energies that are substantially higher than the energy of the reactants, either on the doublet or quartet surfaces. Thus, this mechanism is unlikely to be feasible under the experimental conditions of the gas‐phase experiment,5 and cannot account for the ease of Reaction (2).

Our present study shows conclusively that the intrinsic HW reaction proceeds along a quartet and a doublet surface to yield O^⋅−(H₂O)+O₂ and O₃ ^⋅−+H₂O, respectively. The ease of these two pathways is associated with the larger stability of the stationary points and transition states compared to the isolated reactants and a very favorable crossing point between the two surfaces, with the experimentally observed preferred products corresponding to a spin‐forbidden reaction. A particularly interesting observation is that the two pathways are derived from a bifurcation starting at the same transition state (²TS‐1, see Figure 3). To the best of our knowledge, it is the first time that a bifurcation yielding spin‐dependent products is identified.

An initial comparison of the electron‐transfer mechanism for the HW reaction in aqueous solution was also carried out using single‐point calculations with the PCM continuum model.21 Although the calculated reaction free energy suggests that these channels are thermodynamically feasible, the obtained free energy of activation, corresponding to the first step, ²RC → ²TS‐1, is very high, (ca. 31.3 kcal mol⁻¹; see Table S1). This result agrees with the fact that the HW reaction is suppressed in aqueous solution.

Conflict of interest

The authors declare no conflict of interest.

Supporting information

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Supplementary

E. F. V. Leitão, E. Ventura, M. A. F. de Souza, J. M. Riveros, S. A. do Monte, ChemistryOpen 2017, 6, 360.