To study the catalytic effects of (HO) (n = 1-3), the mechanisms of the reaction HO + HO →O + HO without and with (HO) (n = 1-3) have been investigated theoretically at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ level of theory, coupled with rate constant calculations using the conventional transition state theory. Our results show that upon incorporation of (HO) (n = 1-3) into the channel of HO + O formation, two different reactions, i.e. HO + HO(HO) (n = 1-3) and HO + HO(HO) (n = 1-3), have been observed, and these two reactions are competitive with each other. The catalytic effects of (HO) (n = 1-3) mainly arise from the contribution of a single water vapor molecule; this is because the effective rate constants with water are respectively larger by 2-3 and 3-4 orders of magnitude than those of the reactions with (HO) and (HO). Furthermore, the catalytic effects of the water monomer mainly arise from the HOHO + HO reaction, and the enhancement factor of this reaction is obvious within the temperature range of 240.0-425.0 K, with the branching ratio (k'(RW)/k) of 17.27-80.77%. Overall, the present results provide a new example of how water and water clusters catalyze gas phase reactions under atmospheric conditions.

In the incorporation of the catalyst (H2O)n (n = 1–3) into the HO2 + HO2 → H2O2 + 3O2 reaction, the catalytic effect of water, water dimers and water trimers is mainly derived from the contribution of a single water vapor molecule by a stepwise route.

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Electronic supplementary information (ESI) available: Geometrical parameters for the reaction of HN(NO2)2 to O2NNN(O)OH without and with catalyst X (X = H2O, (H2O)2, HCOOH and H2SO4,) optimized at the CBS-QB3 level of theory respectively describes in Figure S1 and Figure S2, respectively. Wiberg bond indices (WBI) and Atom-atom overlap-weighted NAO bond order (ANBO) for X-Y bond of the TSn (n = 3-6) in the isomerization of HON(O)NNO2 to ON(OH)NNO2 with HCOOH, H2SO4, HN(NO2)2 and HON(O)NNO2) calculated for the model compounds at the CBS-QB3 level describes in Table S1.

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