Theoretical studies of reaction mechanisms for potential reactions of HNCO with HO 2 radicals

Abstract

The reaction mechanism of HNCO with HO₂ radicals is investigated by means of the B3PW91/6-311+G(d,p) method to determine a more reasonable pathway. Four possible entrance patterns are designed; however, only three situations are finally confirmed. When HNCO and HO₂ are close to each other, they first form an intermediate a2. Then, the terminal O atom in HO₂ connects with the C atom of HNCO along with the H atom transferring from HO₂ to the O atom of HNCO. After that the C–O bond ruptures again to form i. Finally, product P6(NCO + HOOH) is generated from i via H atom transfer. P6 is the most accessible product with the simplest steps and lowest barrier height. In addition, the energy of several of the routes is refined at the CCSD(T)/6-311+G(d,p) level based on the optimized geometries. Although there are some differences, the most favorable product is still P6. It is expected that this study would be helpful in further studies on HNCO and in understanding its reactions.

Introduction

Isocyanic acid, HNCO, is an important species for life and synthetic chemistry, since it is the simplest molecule with four elements including H, C, N, and O. As early as 1830, HNCO has been synthesized. ¹ Up to now, it has been identified in various media. ² Besides the abundance, its special importance arises from the role it plays in urban air pollution and toxicity. HNCO is a major emission from cars with gasoline and diesel engines. ³ In addition, HNCO is also a constituent of cigarette smoke, ⁴ which not only has negative effects on the atmosphere but also poses health risks.

Numerous theoretical and experimental studies have been performed on the reactions of HNCO. From 1840 to 1850, geometrical information on HNCO was descended in various reports,^5–8 with studies have focused on its decomposition. Certainly, HNCO can react with radicals and atoms in the atmosphere, such as H, ⁹ O₃, ¹⁰ and CH₂CH. ¹¹ However, its reaction with HO₂ has never been reported. The HO₂ radical is an important species in atmospheric chemistry. The subsequent reaction pathway of HO₂ would affect the composition of the troposphere. Therefore, reactions involving HO₂ have been extensively studied with HX (X = F, Cl, Br, I), ¹² H₂CO, ¹³ XCHO (X = F, Cl), ¹⁴ and HCNO. ¹⁵ However, to our best knowledge, the reaction of HO₂ and HNCO has never been reported. Since they are abundant and important species in the atmosphere, they would also be expected to react with radicals and atoms in the atmosphere, and this aspect deserves to be elucidated. The HO₂ species is theoretically studied by density functional theory (DFT). Our ultimate goal is to find the major product, which would be helpful to determine its effect in the air.

Computational details

All the quantum chemical calculations were carried out using the Gaussian 09 program. ¹⁶ The molecular geometries of the title compounds for the HNCO + HO₂ reaction were fully optimized by Becke’s three-parameter exact exchange functional combined with the Perdew and Wang (B3PW91)^17,18 and 6-311+G(d,p) basis sets. ¹⁹ At the same level, the vibrational frequency was calculated to confirm the nature of the stationary point and to make the zero-point energy correction. The minimum is confirmed to be all positive frequencies and the transition state has only one imaginary frequency. Starting from the transition states, the minimum energy path (MEP) was constructed from the intrinsic reaction coordinate (IRC) to ensure that two desired minima were connected with the transition state. Finally, the energy of some of the stationary points were corrected by Correlation-Coupled Cluster Theory with single and double excitations with perturbative inclusion of the triple excitation (CCSD(T)) method^20,21 with the 6-311+G(d,p) ²² basis set on the basis of the optimized geometries.

Results and discussion

Six products, P1(H₂NO + CO₂), P2(H₂O + NO + CO), P3(NO + CO₂ + H₂), P4(CO₂ + HNOH), P5(NCOO + H₂O), and P6(NCO + HOOH); 17 intermediates, a1, a2, a3, b, c, d, e, f, g, h, i, j, k, l, m, n, and o; 30 transition states, TSa1/b, TSa2/f, TSa3/j, TSb/d, TSb/g, TSc/f, TSc/j, TSc/k, TSd/e, TSe/g, TSf/h, TSf/i, TSf/j, TSf/n, TSf/P5, TSg/l, TSh/k, TSi/P6, TSj/P1, TSk/l, TSl/m, TSl/n, TSl/P2, TSm/o, TSn/o, TSn/P3, TSo/P1, TSo/P4, TSR/c, and TSR/o; and 46 reaction pathways are confirmed in the reaction. The optimized structures of reactants and products are shown in Figure 1 along with the available experimental results;^23–27 the optimized structures of intermediates are shown in Figure 2, and the optimized structures of transition states are shown in Figure 3. For reactant HNCO, the bond lengths and angles calculated at the B3PW91/6-311+G(d,p) level are in good agreement with the corresponding experimental values.^5–8 Besides the reactants, the calculated geometries of the products H₂O, HOOH, H₂, NO, and CO are also consistent with the experimental results,^24,26,27 indicating that the geometric parameters determined at the B3PW91/6-311+G(d,p) level are reasonable.

Figure 1.

Optimized structures of the reactants and products at the B3PW91/6-311+G(d,p) level. The numbers in parentheses are the experimental values.^22–26

Figure 2.

Optimized structures of the intermediates at the B3PW91/6-311+G(d,p) level.

Figure 3.

Optimized structures of the transition states at the B3PW91/6-311+G(d,p) level.

The schematic potential energy surface of reaction HNCO + HO₂ calculated at the B3PW91/6-311+G(d,p) level is shown in Figure 4, in which TSx/y indicates that the transition state connects with two minima, x and y. The total energy of HNCO + HO₂ is set to as zero for reference. The relative energy is calculated by the following relationship: ΔE(relative energy) = E(transition state/complex) − E(reactant). The barrier height is defined by the difference between the transition state and the corresponding intermediate. The relative energies of the reactants and products are shown in Table 1. The rate-determining barrier heights of each pathway are listed in Table 2.

Figure 4.

Potential energy surface of the HNCO + HO₂ reaction calculated at the B3PW91/6-311+G(d,p) level.

Table 1.

The relative energies of the reactants and products (in kcal/mol).

Species	Relative energy
HNCO + HO2	0
P1(H2NO + CO2)	−55.40
P2(H2O + NO + CO)	−25.96
P3(NO + CO2 + H2)	−43.10
P4(CO2 + HNOH)	−46.51
P5(NCOO + H2O)	39.43
P6(NCO + HOOH)	27.36

Table 2.

The rate-determining barrier heights of the most favorable route to form each product (in kcal/mol).

	B3PW91/6-311 + G(d,p)	CCSD(T)/6-311 + G(d,p)//B3PW91/6-311 + G(d,p)
P1(H2NO + CO2)	50.59	81.47
P2(H2O + NO + CO)	31.08	51.84
P3(NO + CO2 + H2)	61.96	81.47
P4(CO2 + HNOH)	34.61	51.84
P5(NCOO + H2O)	75.65	73.99
P6(NCO + HOOH)	22.16	23.18

Initial process

When HNCO and HO₂ are close to each other, there are several possible attaching positions. The direct hydrogen abstraction route is omitted in this article, since this pathway is simple enough and the product information is obvious. Besides the direct hydrogen abstraction route, four attaching models have been designed by us, that is, the terminal O of HO₂ attaching to the C of HNCO, the middle O of HO₂ attaching to the C of HNCO, and the terminal O and the middle O of HO₂ attaching to the N of HNCO, respectively. Unfortunately, the pathway involving the middle O of HO₂ attaching to the N of HNCO is not successfully confirmed. For other situations, there is a common property, that is, they skip a transition state to complete the attaching process. Subsequently, they would produce other intermediates and final products.

Formation of P1(H₂NO + CO₂)

Seventeen reaction channels are confirmed to form P1 (Figure 5). Route P1-16 and P1-17 is the simplest one with only two steps. First, the middle O of HO₂ is connected with HNCO to form o via TSR/o. Next, the C–N bond is broken along with transfer of the O atom to the N atom. As a result, CO₂ and H₂NO are produced. Although only two steps are involved, the barrier height to form o is as high as 68.77 kcal/mol. Moreover, it is the highest in all the transition states, which is difficult to overcome. Route P1-16 is also a two-step pathway. Initially, the terminal O atom of HO₂ is close to the C atom of HNCO. At the same time, the H atom of HO₂ transfers to the N atom of HNCO leading to j via TSa3/j with a barrier height of 6.58 kcal/mol. After that, rupture of the C–N bond and formation of an N–O bond are completed by TSj/P1 leading to P1. The rate-determining barrier height is 59.39 kcal/mol for route P1-16. The remaining 15 routes start from three intermediates, a1, a2, and c. It is interesting that all the intermediates would convert into j or o leading to P1. In other words, the j and o are critical intermediates in the pathway to produce P1. Since all pathways have to overcome the barrier height of TSj/P1 (59.39 kcal/mol) or TSo/P1 (50.59 kcal/mol), P1 would not be the major product due to the high barrier height.

Figure 5.

The reaction routes to produce P1. Red values are the energy barriers (kcal/mol) of the rate-determining step for each path.

Formation of P2 (H₂O + NO + CO)

There are five routes to form P2 starting from three intermediates, a1, a2, and c (see Figure S1 in the supplemental material). Formation of f is the easiest via TSa2/f with a barrier height of 15.16 kcal/mol, which is much lower than those of the routes to form b and c. Only route P2-5 is discussed, while other routes are omitted. The H atom connected with N atom is transferred to the O atom via TSf/h with a barrier height of 31.08 kcal/mol. Then h would dissociate into NC(O)O and H₂O with O–H bond fission. Next, the H₂O is kept. The O atom of NC(O)O is shifted from the C atom to the N atom via TSk/l resulting in l. Intermediate l then undergoes rupture of the N–C bond to form NO and CO. In the whole pathway, the f → h step is the rate-determining step with a barrier height of 31.08 kcal/mol. The route to form P2 is more competitive than that to form P1.

Formation of P3(NO + CO₂ + H₂), P4(CO₂ + HNOH), and P5(NCOO + H₂O)

The reaction routes to form P3, P4, and P5 are discussed together (see Figures S2–S4 in the supplemental material), since they have some common features: (1) the rate-determining step is too highfor them to be favorable routes. Correspondingly, they would be unfavorable products. (2) Whatever the entry species is, they would convert into the same intermediate leading to the final product, such as, n for P3, o for P4, and f for P5. (3) The route is very complex with many steps except for the two-step route P4-9 to form P4, the two-step route P5-2 to form P5, and the three-step route P5-1 to form P5. (4) There is overlap among different routes to form the final product.

Formation of P6(NCO + HOOH)

As shown in Figure 6, P6 could be produced by two possible reaction routes, route P6-1 and route P6-2. The only difference between them is that there is one more step in the entrance to route P6-1. After the intermediate f, route P6-1 and route P6-2 are merged into one route to form P6. The rate-determining step is f → i via TSf/i with the barrier height of 22.16 kcal/mol. In TSf/i, rupture of the C–O bond is accompanied with transfer of the H atom from N to O, appearing as the recombination of HNCO with the help of HO₂. The final step is migration of the H atom from O to O via TSi/P6 leading to P6.

Figure 6.

The reaction routes to produce P6. The values in red are the energy barriers (kcal/mol) of the rate-determining step for each path.

Favorable routes

P6 is the most favorable product. In contrast, there is little chance to form P3, P1, P4, and P5. P2 is the second favorable product. There are two competitive pathways, P2-3 and P2-5, to form P2 with the same rate-determining step. However, route P2-5 is more favorable due to the two following reasons. One is that route P2-5 has fewer steps, while route P2-3 has one more step. The other reason is that route P2-3 has three steps with a barrier height over 20 kcal/mol, which is larger than that of route P2-5. Therefore, route P2-5 is more competitive than route P2-3. To confirm the correctness of the most favorable route, the barrier heights of the most favorable route for each product are refined at the CCSD(T)/6-311+G(d,p) level on the basis of the respective optimized geometries. As shown in Figure 7 and Table 2, P6 is still the most favorable product with a rate-determining barrier height of 23.18 kcal/mol. After correction, the rate-determining step of P1-8 and P3-6 becomes the same, which is the step transferring from f to n with a barrier height of 81.47 kcal/mol. The barrier height is too high to be completed. In addition, P1-8 and P3-6 are not the most favorable routes to form P1 and P3, respectively, which are changed to be P1-10 and P3-7. Similarly, the rate-determining step of route P4-7 has changed to be f → h, which is the same as that of route P2-5. Therefore, P4 could also be secondary possible products. Although there is variation in the rate-determining step, the most favorable product is still retained.

Figure 7.

Potential energy surface of the HNCO + HO₂ reaction at the CCSD(T)/6-311+G(d,p)//B3PW91/6-311+G(d,p) level.

Conclusion

In this work, the reaction mechanism of HNCO and HO₂ is theoretically explored at the B3PW91/6-311+G(d,p) level. As a result, 46 pathways, 17 intermediates, 30 transitions, and 6 products are determined. It is a process without barrier height when the terminal O of HO₂ attaches to the C of HNCO to form a2 and a3. While there is transition state to form other intermediates, a2 produces the intermediate f via TSa2/f resulting in P6(NCO + HOOH). This is the most favorable pathway with the most favorable product P6. P2 is the second most favorable product. Because of the high barrier heights, there is little chance to form P1(H₂NO + CO₂), P3(NO + CO₂ + H₂), P4(CO₂ + HNOH), and P5(NCOO + H₂O). After the energy is corrected at the CCSD(T)/6-311+G(d,p) level, P6 is still the most favorable product. However, P4 could also be a possible product just like P2 after the energy is refined.

Supplemental Material

Supporting_Information – Supplemental material for Theoretical studies of reaction mechanisms for potential reactions of HNCO with HO2 radicals

Supplemental material, Supporting_Information for Theoretical studies of reaction mechanisms for potential reactions of HNCO with HO2 radicals by Beibei An, Fuhua Huang, Ke Chen, Jiamin Jiang, Jianbin Xu and Li Wang in Journal of Chemical Research