Ab initio MO study on direct production of H2O, N2O and CO3 from the respective CH2OO “Bee-sting-like” attack at H2, N2 and CO2

Context We have computationally elucidated the mechanism for formation of H2O, N2O and CO3 from the reactions of CH2OO with H2, N2 and CO2, respectively, by the direct attack of the terminal O atom of CH2OO. This unique mechanism, which is characteristically “bee-sting-like” in nature, was found to be closely parallel to their reactions with the O(1D) atom. Reactions with H2 and CO2 take place by side-on attack, while the N2 reaction occurs by end-on attack with predicted barriers, 19.4, 13.1 and 25.3 kcal.mol−1, respectively. The CO2 reaction with CH2OO was found to occur by producing the C2v CO3, O = C < (O)O, instead of its D3h conformer, essentially similar to the O(1D) + CO2 reaction. The rate constants for the three reactions have been computed by the transition state theory (TST) based on the predicted potential energy profiles. We have also utilized the isodesmic nature of the dative bond exchange in the N2 reaction, CH2O → O + N2 = CH2O + N2 → O, to estimate the heat of the formation of CH2OO. Based on the heat of reaction computed at the highest level of theory employed, we obtained ΔfHo0 (CH2OO) = 27.5 kcal.mol−1; the value agrees with the recent results within ± 1 kcal.mol−1. Methods All calculations were performed using Gaussian 16 software. Geometry, frequency, and IRC analysis calculations were conducted at the M06-2X/aug-cc-pVTZ level of theory. The heats of reaction have been evaluated at the highest level, CCSD(T)/CBS(T,Q,5)//M06-2x/aug-cc-pvTz. Supplementary Information The online version contains supplementary material available at 10.1007/s00894-024-06065-1.


Introduction
There have been voluminous publications since Welz et al. discovered in 2012 a convenient and clean method of producing the simplest Criegee intermediate (CI), CH 2 OO, by the CH 2 I + O 2 → CH 2 OO + I reaction [1], which allowed experimentalists to monitor its kinetics cleanly.The kinetics and mechanisms of reactions of various CIs have been reviewed by many [2,3].Osborn and Taatjes [2] reviewed the physical chemistry of CIs in general in the gas phase.Vereecken and Francisco [3] discussed CIs' complicated roles in the chemistry of troposphere.More recently, Chhantyal-Pun et al. detailed the production, detection and reactivity of various CIs [4].
Mechanistically, most of the reported reactions of atmospheric interest centered on bimolecular processes occurring via association complexes to be followed by fragmentation of these complexes, including the very fast head-to-tail self-reaction of the CH 2 OO zwitter-ionic species [5].Truhlar and coworkers [6,7] have recently carried out high-level computational studies on several atmospherically important CI reactions with a comprehensive listing of references for various pollutants, and H 2 O and its dimers, among many others.They put forth a triplelevel strategy for prediction of atmospheric kinetics by employing a near complete-basis limit couple cluster theory with a new hybrid meta density functionals (MO6CR) optimized for CIs and a systematic treatment for the complex-forming kinetics [7].Kumar and Francisco[8] theoretically examined the activation of X-H bonds by CIs for a series of molecules including H 2 , CH 4 , CH x F 4-x (x = 1-3) and SiH 4 , all taking place by the complexforming mechanism.We will therefore not rehash these well-reported complex-forming bimolecular reactions in the present study.
In one of our computational studies on the thermal unimolecular decay of CH 2 OO [9], we postulated that the extension of the O-O bond following thermal excitation, the terminal O atom exhibited the O( 1 D)-atom character and was capable of inserting into one of the C-H bonds to form highly excited HCOOH with more than 110 kcal.mol−1 exothermicity, which enthalpically helped drive the formation and fragmentation of HCOOH to give various products, H 2 + CO 2 , H 2 O + CO, among others [9].A similar intramolecular insertion reaction was also illustrated for CH 3 HOO.
In the present study, we specifically investigated by a high-level quantum chemical calculation the O( 1 D)-atom character of the terminal O atom in bimolecular processes using the reactions of CH 2 OO with H 2 , N 2 and CO 2 as examples.Significantly, we discovered that H 2 O, N 2 O and CO 3 could be formed directly from the respective reaction by a Bee-sting-like (BSL) mechanism without the need for very high activation energies.In nature, it is well-known that when a bee stings a person, its stinger detaches from its body and leaves inside the skin of the victim.To our knowledge, this type of unique bimolecular reaction mechanism involving two molecules has not been reported previously and is illustrated for the first time in this study.Parenthetically, we should mention that aside from the mechanistic elucidation of the BSL processes, we have also utilized the enthalpic change associated with the dative bond exchange, from CH 2 O → O to N 2 giving CH 2 O + N 2 → O in the CH 2 OO + N 2 reaction, to reliably evaluate the enthalpy of CH 2 OO formation.The results of this computational study are reported herein.

Computational details
The mechanisms for the reactions of CH 2 OO with H 2 , N 2 and CO 2 have been studied by quantum-chemical calculations.The geometries of the reactants, products, and transition states were optimized by the M06-2X method [10] with the aug-cc-pVTZ basis set [11,12] using the Gaussian 16 software package [13].The optimized geometries at the M06-2X/aug-cc-pVTZ level were used to establish the potential energy surfaces (PESs) of the 3 reaction systems employing the coupled-cluster level of molecular orbital theory, CCSD(T), incorporating all the single and double excitations plus perturbative corrections for the triple excitations [14].The zero-point energy (ZPE) corrections to the relative energies were also made at the M06-2X/aug-cc-pVTZ level.For the heats of reaction, we have also extrapolated the energies to the complete basis set (CBS) limit [15], based on the M06-2x/aug-cc-pvTz optimized geometries to obtain the CCSD(T)/CBS limit energies.The CBS energies were estimated using a three-point extrapolation scheme based on the CCSD(T) method, with the aug-pVXZ (X = T, Q, and 5) basis sets of Dunning [11].
Calculations of the kinetics for the direct exchange reactions, the conventional transition state theory (TST) [16] was employed by using the CHEMRATE code of NIST [17].Tunneling corrections based on Eckart's model have been made for H-transfer reactions [18].The predicted reaction rates were obtained using the frequencies without scaling.All molecular parameters of the TSs, reactants, and products are listed in Table S1 of the SI section.

Results and discussions CH 2 OO + H 2
Figure 1 presents the potential energy profile of the CH 2 OO + H 2 reaction including the direct terminal O-insertion step giving H 2 O via T H S1 and those occurring by ring-TSs found in this work and in the work by Kumar and Francisco [8].Our calculations were performed at the CCSD(T)/ CBS//M06-2X/aug-cc-pVTZ level as aforementioned.For comparison, we have listed in Table 1 all the TS values and those of Kumar and Francisco's reaction channels predicted at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ level.For the lowest energy barrier at T H S4, our result 13.7 kcal.mol −1 agrees closely with theirs, 13.4 kcal.mol−1 ; the CH 3 OOH product thus formed was predicted to lie 55.2 kcal.mol −1 below the reactants, which also agrees excellently with their value of 55.4 kcal.mol−1 .We found another interesting reaction channel occurring by a ring TS, initiated by the H 2 -catalyzed isomerization CH 2 OO → H 2 C < (O)O (dioxirane) via T H S2 with a barrier of 20.2 kcal.mol−1 .The dioxirane isomer further reacts with H 2 via T H S3 (11.4 kcal.mol −1 ) to produce CH 2 O + H 2 O; this reaction path has been confirmed by an IRC analysis.Significantly, the insertion barrier at T H S1, 19.4 kcal.mol−1 , lies between T H S2 (20.2 kcal.mol−1 ) and T H S4 (13.7 kcal.mol−1 ).The good agreement between our values evaluated at the CCSD(T)/ CBS//M06-2X/aug-cc-pVTZ level with Kumar and Francisco's result obtained at the CCSD(T)/aug-cc-pVTZ//M06-2X/ aug-cc-pVTZ level for the barrier at T H S4 and the heat of reaction producing the CH 3 OOH product suggests that both methods are suitable for the CH 2 OO + H 2 system, and the result for the direct BSL reaction via T H S1 is expected to be reasonable.The IRC analysis carried out for the reaction producing H 2 O by direct insertion is shown in Fig. S1.

CH 2 OO + N 2
To our knowledge, there has been no prior reported study on N 2 reactions with CIs, CH 2 OO particularly.Our predicted PES of the CH 2 OO + N 2 reaction at the CCSD(T)/CBS// M06-2X/aug-cc-pVTZ level is depicted in Fig. 2 with the energies summarized in Table 2.The barrier for the direct reaction of the terminal O atom with N 2 at T N S1, 25.3 kcal.mol −1 , is higher than that of the analogous H 2 reaction, 19.4 kcal.mol−1 , at T H S1 by about 6 kcal.mol−1 .The IRC analysis of the reaction channel is shown in Fig. S2

CH 2 OO + CO 2
Figure 3 shows the potential energy profile of the CH 2 OO + CO 2 reaction forming CO 3 by T C S1 and the lower energy product channels taking place by initial ring complex formation as reported by Kumar and Francisco [19] and Lin et al. [20].Our values for the complex forming path obtained at the CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level are listed in Table 3 for comparison with the results of Kumar and Francisco predicted at the CCSD(T)/aug-cc-pVTZ// M06-2X/aug-cc-pVTZ level [19] and the experimentally validated values of Lin et al. computed at the QCISD(T)/CBS// B3LYP/6-311 + G(2d,2p) level [20].The barrier at T C S3, 7.8 kcal.mol−1 , the energies for the pre-reaction (LM C 1) and postreaction (LM C 2) intermediates, -3.6 kcal.mol−1 and -27.9 kcal.mol−1 , respectively, all agree closely their values as presented in Table 3.The collision-induced isomerization of CH 2 OO to CH 2 < (O)O, akin to those occurring via T H S2 and T N S2 mentioned above, was found to have an energy barrier of 17 kcal.mol−1 above the reactants at the M06-2X/ aug-cc-pVTZ level; no further calculations were performed because of the high barrier.
For the reaction channel of interest to this work, the direct formation of CO 3 by the terminal O-atom attack at CO 2 , the mechanism turns out to be quite interesting.The initial CO 3 product was found to have the C 2v structure, O = C < (O)O, formed by side-on attack; O = C < (O) O isomerizes readily to its D 3h conformer with a small barrier of 4.3 kcal.mol−1 .The IRC analysis of the reaction channel is shown in Fig. S3.This mechanism turns out to be similar to that of the O( 1 D) + CO 2 reaction predicted by Mebel and coworkers [21], in which the C 2v CO 3 was found to be produced directly.The C 2v to D 3h CO 3 isomerization barrier was reported to be 4.4 kcal.mol−1 at the MRCI + Q(16,13)/6-311 + G(3df) level of theory,  in very good agreement with our value, 4.3 kcal.mol−1 , computed at the CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level as aforementioned.Parenthetically, we should mention that the singlet CO 2 -oxide, O = CO → O, was found to be theoretically unstable.

Heat of Formation of CH 2 OO
The isodesmic nature of the dative bond exchange in the N 2 reaction, as alluded above, is ideal for estimation of the heat of formation of CH 2 OO using the reliably predicted heat of the reaction (Δ    The O( 1 D)-like character of the terminal O atom exhibited in these bimolecular reactions indirectly corroborates our previous study on the unimolecular decay of CH 2 OO by intramolecular insertion of the terminal O atom into one of its C-H bonds forming HCOOH very exothermically [9].We have utilized the isodesmic characteristics of the dative bond exchange in the N 2 reaction, for estimation of the heat of formation of CH 2 OO.We believe that this is perhaps one of the most reliable schemes for evaluation of the heat of CH 2 OO formation theoretically because of the well-established thermochemistry of CH 2 O and N 2 O, and the potential computational-error cancellation from each side of the reaction as well.Based on the heat of the above reaction evaluated with our highest level of theory, CCSD(T)/CBS(T,Q,5)//M06-2x/aug-cc-pvTz, the heat of formation of CH 2 OO was predicted to be 27.5 kcal.mol−1 .The value agrees with the best recent estimates [22][23][24] approximately within ± 1 kcal.mol−1 .

Fig. 1
Fig.1The potential energy surface for the CH 2 OO + H 2 reaction by the direct terminal O-insertion step giving H 2 O via T H S1 computed at the CCSD(T)/CBS//M06-2X/augcc-pVTZ level (energies are in kcal.mol.−1 ) r H o ) and the experimentally well-established heats of formation of CH 2 O and N 2 O.The energy balance of the reaction gives rise to: Δ f H o (CH 2 OO) = Δ r H o + Δ f H o (CH 2 O) + Δ f H o (N 2 O) at 0 K. Based on the values of Δ r H o predicted at the 3 different levels of theory, we obtained: I, at the CCSD(T)/CBS(D,T,Q)//M06-2x/aug-cc-pvTz level, 28.1 kcal.mol−1 ; II, at the CCSD(T)/CBS(T,Q,5)//M06-2x/ aug-cc-pvTz level, 27.5 kcal.mol−1 ; and III, at the M06-2x/ CBS(D,T,Q)//M06-2x/aug-cc-pvTz level, 29.3 kcal.mol−1 ; the 3 closely banded values: 28.1, 27.5 and 29.3 kcal.mol−1 are presented in Table4.Our highest level result, 27.5 kcal.mol −1 , lies closely within the recently predicted value of Nguyen et al.[22], 28.1 kcal.mol−1 acquired at the CCSD(T)/ CBS(D,T,Q)//CCSD(T)/aug-cc-pvTz level, and the most recent high-level prediction, 26.5 kcal.mol−1 , determined at the CCSDTQ/CBS(D,T,Q,5,6) + Δ//CCSD(T)/ANO2 level of theory[23].It is worth mentioning that above results are also in reasonable agreement with the earlier value of 27.0 at 298 K (or 28.7 kcal.mol−1 at 0 K) reported by Cremer and coworkers[24], obtained by the CCSD(T)/ [4s3p2d1f/3s2p1d] calculation.CH 2 O → O + N 2 = CH 2 O + N 2 → OConclusionsIn this study, we have explored the reactivity of the terminal O atom of CH 2 O → O toward H 2 , N 2 and CO 2 directly producing H 2 O, N 2 O and CO 3 , respectively, by the beesting-like mechanism without going through formation of complexes.This unique reaction mechanism involving two singlet molecular species has not been reported before.The reaction paths have been clearly illustrated by IRC analyses (see Figs. S1, S2 and S3).Concurrently, we also examined most, if not all, of the processes taking place by indirect complexing mechanisms.Comparison of the energetics involved in many of these processes previously investigated by several authors with our values obtained from calculations at the CCSD(T)/CBS(D,T,Q)//M06-2x/aug-cc-pvTz level of theory agrees very closely.For the direct reactions, H 2 O was found to be formed by insertion of the terminal O atom into H 2 side-on after the extension of the O → O bond at transition state T H S1 with the barrier energy of 19.4 kcal.mol−1 , while N 2 O and CO 3 were formed by the attack of the terminal O atom, end-on and side-on at T N S1 and T C S1, respectively, with largely different barriers of 25.3 and 13.1 kcal.mol−1 .Significantly, the predicted rate constants at 300 K (see Fig. 4) were found to correlate qualitatively with the rate constants for the O( 1 D) atom reactions with H 2 , N 2 and CO 2 at 300 K.The similarity was even more vividly illustrated by the mechanism of the CH 2 OO + CO 2 reaction, as shown in Fig.3, that the C 2v CO 3 , O = C < (O)O, instead of its D 3h conformer, was initially formed in the reaction, akin to that occurs in the O( 1 D) + CO 2 reaction reported by Mebel and coworkers[21].

aFig. 4
Fig. 4 Predicted rate constants for CH 2 OO reactions with H 2 , N 2 and CO 2 by direct "bee-sting-like" attacks of the terminal O-atom producing H 2 O, N 2 O and CO 3 , respectively

Table 1
All TSs and intermediates of the reaction of CH 2 OO + H 2 were computed at the CCSD(T)/CBS//M06-2X/aug-cc-pVTZ level

Table 2
All TSs and intermediates of the reaction of CH 2 OO + N 2 were computed at the CCSD(T)/CBS//M06-2X/ aug-cc-pVTZ level

Table 3
All TSs and intermediates of the reaction of CH 2 OO + CO 2

Table 4
Heat of Formation of CH 2 OO predicted by different authors (in kcal.mol−1 at 0 K)