Computational Studies of Rubber Ozonation Explain the Effectiveness of 6PPD as an Antidegradant and the Mechanism of Its Quinone Formation

The discovery that the commercial rubber antidegradant 6PPD reacts with ozone (O3) to produce a highly toxic quinone (6PPDQ) spurred a significant research effort into nontoxic alternatives. This work has been hampered by lack of a detailed understanding of the mechanism of protection that 6PPD affords rubber compounds against ozone. Herein, we report high-level density functional theory studies into early steps of rubber and PPD (p-phenylenediamine) ozonation, identifying key steps that contribute to the antiozonant activity of PPDs. In this, we establish that our density functional theory approach can achieve chemical accuracy for many ozonation reactions, which are notoriously difficult to model. Using adiabatic energy decomposition analysis, we examine and dispel the notion that one-electron charge transfer initiates ozonation in these systems, as is sometimes argued. Instead, we find direct interaction between O3 and the PPD aromatic ring is kinetically accessible and that this motif is more significant than interactions with PPD nitrogens. The former pathway results in a hydroxylated PPD intermediate, which reacts further with O3 to afford 6PPD hydroquinone and, ultimately, 6PPDQ. This mechanism directly links the toxicity of 6PPDQ to the antiozonant function of 6PPD. These results have significant implications for development of alternative antiozonants, which are discussed.


List of Tables
where 1 ⟨Ŝ 2 ⟩ SC and 3 ⟨Ŝ 2 ⟩ are the expectation values of the total spin operator for the spincontaminated (SC) singlet reference state and a high-spin triplet state, respectively. This parameter is then used to project energetic contributions from the high-spin state out of the targeted singlet reference, affording the corrected energy using the energies of the triplet and spin-contaminated singlet reference states, 3 E and 1 E SC .
Both SC and AP energies are reported for all reactive oxygen species, including ozone, singlet oxygen, and various intermediates and transition states that were determined to resemble these molecules on the basis of the values of ⟨Ŝ 2 ⟩ for computed reference states.

S1.1 Benchmark values for vdW complexes
In contrast to transition structures and reaction energies, both spin contaminated and approximate projection (AP) 2 schemes yield adequate results for van der Waals (vdW) complexation energies (∆E vdW ) with O 3 (Table S1). Reference values obtained from Ref. 1 were computed using CCSDT(Q) and extrapolated to the complete basis set limit. Results using the ωB97X-V 3 and ωB97M-V 4 density functionals, as well as the κ-OOMP2 method (κ = 1.45), 5 are within chemical accuracy for almost all species. Furthermore, while not employed here for the sake of simplicity, we expect even better agreement could be achieved Table S1: Errors in spin-contaminated (SC) and approximate projection (AP) single-point energies for benchmark van der Waals (vdW) complexation energies. For κ-OOMP2 (κ = 1.45) results, no spin polarization was observed for O 3 or any vdW complex, so "SC" does not apply and AP corrections are identically zero. Reference values are CCSDT(Q) results extrapolated to the CBS limit obtained from Ref. 1. Highlighted boxes represent the best performing methodology for a given parameter at a given basis set truncation.

S1.2 The effect of regularizer strength in κ-OOMP2
The strength of the regularizer (κ) has been shown to strongly influence the performance of the κ-OOMP2 method, and different values of κ are appropriate for different applications. 5,9,10 In particular, like OOMP2 itself (κ → ∞), overly weak regularizers (κ too large) have been shown to result in artificial symmetry restoration in strongly correlated systems.
Stronger regularizers (lower κ values) are necessary to recover essential spin polarization that is associated with systems exhibiting strong correlation. At the other extreme, excessively strong regularization leads to artificial symmetry-breaking, as is well-known for mean-field Hartree-Fock (i.e. κ = 0). where spin-polarization is recovered in κ-OOMP2 with far weaker regularization, 11 or in transition-metal containing systems. 10 In other words, the k-OOMP2 results suggest that O 3 at its equilibrium geometry is not strongly correlated because it does not exhibit essential symmetry breaking for κ values in the recommended range. 10 As a corollary, the use of too-strong regularizers overly dampens the effects of dynamic correlation, and this effect is apparently significant for the O 3 systems here, such that κ = 0.8 results in poor agreement with benchmark energies (Table S2). Instead, the best agreement with CCSDT(Q) benchmarks 1 is achieved with κ = 1.45. Even still, the ωB97X-V and ωB97M-V DFAs outperform κ-OOMP2. In particular, none of the tested parameterizations of κ-OOMP2 achieve chemical accuracy for the thermodynamics of O 3 splitting (O 3 → 1 O 2 + O(3 p)), which has been put forth as a test system for ozone modeling. 1 As a result, we do not use κ-OOMP2 for any of the main results of this paper, despite its success for other strongly correlated systems.

S1.3 Understanding spin contamination in DFA energies
The disparity in the accuracy of predictions for barrier heights and reaction energies, as well as the poor performance of κ-OOMP2, stems from changes in the extent of multireference character of various species across the ozonation PES. Stationary points corresponding to reactant states exhibit strong correlation and spin symmetry breaking due to the biradicaloid nature of O 3 . In formation of a vdW complex, the electronic structure of O 3 does not change drastically, and both SC and AP schemes treat the complexation energy in a balanced way.
As a result, all methods achieve chemical accuracy, i.e. errors less than 1 kcal mol −1 , for predictions of ∆E vdW (Table S1). The situation is materially different for computations of  12 and we remind the reader that the extent of spin-contamination in DFT is measured for the fictitious reference system of non-interacting electrons, rather than the physical system of interacting electrons.

S2 Conformer specifications
Our computational work utilized a number of distinct isomers and conformers for all derivatives of 4-aminodiphenylamine (4ADPA, 2) and N -methyl-N ′ -phenyl-p-phenylenediamine (MePPD, 3), and only results corresponding to the minimum-energy conformers are reported in the main text. We include structural details for each conformer in the molecular S8 coordinate (.xyz) files accompanying the SI, and energies for these in the corresponding spreadsheet. The labeling scheme for these conformers is defined in Figures S1-S4. Conformers for quinone diimine (QDI) structures follow the same ordering, though they are not explicitly included in the figures below.