A Barrier-Free Atomic RadicalMolecule Reaction: N (2D) ⫹ NO2 (2A1) Mechanistic Study MING-HUI ZUO, HUI-LING LIU, XU-RI HUANG, JIN-HUI ZHAN, CHIA-CHUNG SUN State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China Received 4 October 2007; accepted 30 December 2007 Published online 4 March 2008 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/qua.21621

ABSTRACT: The reaction of N (2D) radical with NO2 molecule has been studied theoretically using density functional theory and ab initio quantum chemistry method. Singlet electronic state [N2O2] potential energy surfaces (PES) are calculated at the CCSD(T)/aug-cc-pVDZ//B3LYP/6-311⫹G(d) ⫹ ZPE and G3B3 levels of theory. All the involved transition states for generation of (2NO) and (O2 ⫹ N2) lie much lower than the reactants. Thus, the novel reaction N ⫹ NO2 can proceed effectively even at low temperatures and it is expected to play a role in both combustion and interstellar processes. On the basis of the analysis of the kinetics of all pathways through which the reactions proceed, we expect that the competitive power of reaction pathways may vary with experimental conditions for the title reaction. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem 108: 1309 –1315, 2008

Key words: reaction mechanism; potential energy surface; N2O2

Correspondence to: X.-R. Huang; e-mail: theorychem@gmail. com Contract grant sponsor: National Natural Science Foundation of China. Contract grant numbers: 20773048 and 20643004. Contract grant sponsor: Excellent Young Foundation of Jilin Province and Technology Development Project of Jilin Province. Contract grant number: 20050906-6. Contract grant sponsor: Excellent Young Teacher Foundation of the Ministry of Education of China.

International Journal of Quantum Chemistry, Vol 108, 1309 –1315 (2008) © 2008 Wiley Periodicals, Inc.

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1. Introduction

N

itrogen oxides (NOx) are a class of environmentally important species involved in the stratosphere ozone depletion process and in the formation of acid rain and smog in the troposphere [1]. Photochemical processes involving the atomic radical N and NOx (NO and NO2) molecules play a crucial rule in the terrestrial and planetary atmospheres [2–5]. The discharge flow technique has been used with resonance fluorescence detection of N atoms to study the fast radical–radical reaction of ground state nitrogen atoms with NO and NO2 [6]. As efficient routes to the reduction of NO2 to form N2 and O2 are sought, the N ⫹ NO2 reaction has been studied using various kinetics techniques to determine the important channels and the product branching ratios [7–10]. The reactions of metastable atomic nitrogen, N (2D), with NO2 are also of interest relevant to the chemistry in the perturbed thermosphere. There exists a general interest in measuring reactivities of these metastable states because they may well play significant roles in phenomena associated with energy deposition [11]. The N2O2 species are considered in terms of their roles as reactive intermediates in the N ⫹ NO2 chemical reactions. The N (2D) ⫹ NO2 reaction are of particular interest because they may be related to the nitrogen-recycle processes. They are also relevant to the study of the reverse reaction, the NO and NO2 reduction to N2 and O2, a useful model for the understanding of selective catalytic processes of environmental significance [12]. Since N2O2 was suggested as a possible intermediate in the detonation of nitric oxide, its potential applications as a highenergy density material (HEDM) and its relevance to important research areas have stimulated much theoretical and experimental work [13–36]. Two N2O2 isomers containing N2/O2 and NO/NO subunits, respectively, were detected by neutralizationreionization mass spectrometry (NRMS) as metastable species with lifetimes exceeding 1 ␮s [37]. N2O2 bears on the important issue of the missing sources of NOx in the odd-nitrogen budget of the Earth’s lower atmosphere. Laboratory studies revealed indeed an unexpected route to NOx from the O2/N2 photolysis, suggesting N2O2 as the key intermediate of excited states reactions [38, 39]. In this article, singlet electronic state [N2O2] PES are calculated at the ab initio quantum chemistry method. Furthermore, theoretical studies predicted several high-energy isomers N2O2, which are ther-

modynamically unstable, but kinetically stable toward both dissociation and isomerization to more stable isomers due to the existence of sizable barriers. Some conclusions made in the present article may be helpful for further theoretical and experimental studies of the N (2D) ⫹ NO2 reaction. Understanding this reaction mechanism may be of great importance in reducing the environmental pollution caused by nitric oxide.

2. Computational Methods All geometries of the reactants, complexes, intermediates, transition states (TSs), and products were located and properly characterized by the calculation of harmonic frequencies, utilizing the Gaussian 03 program package [40]. The calculations reported in the present investigation were carried out using the density functional theory (DFT) functional B3LYP [41– 43], and unrestricted Møller-Plesset second-order perturbation UMP2 method with 6-311⫹⫹G(d,p) basis set [44-45]. Tran et al. and Zuo et al. have previously reported the success of the B3LYP method in predicting geometries of unsaturated chain structures, and this method produces optimized structures, at low computational cost, that compared favorably with higher level calculations [46, 47]. Geometries of the reactants, products, intermediates, and transition states have been fully optimized with the MP2 and B3LYP method using the 6-311⫹⫹G(d,p) basis set. Vibrational frequencies calculated at the same level of theory, have been used to characterize stationary points and zero-point energy (ZPE) correction. All the stationary points were identified for local minima (with the number of imaginary frequencies equal to zero) or transition states (each with one imaginary frequency). To confirm that the transition states connect between designated intermediates, intrinsic reaction coordinate (IRC) calculations were performed at the B3LYP/6-311⫹⫹G(d,p) level of theory [48]. Zero-point vibrational energy has been calculated in the harmonic application without sealing. To obtain a more reliable energy, further calculations with large basis sets and high levels of electron correlation could be employed. Thus, the multilevel method G3B3 [49], and the coupled-cluster theory including single and double excitations and perturbative inclusion of triple excitations [CCSD(T)] method with triple-zeta basis sets of Dunning (cc-pVTZ) were used as standard [50 –52]. The B3LYP/6-311⫹⫹G(d,p) optimized geometries

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3. Results and Discussion The optimized structural parameters of the reactants, intermediate isomers, transition states, and products for the N (2D) ⫹ NO2 reaction on the singlet electronic state are shown in Figure 1. The total energies of all the species involved in the reaction are listed in Table I. Figure 2 show schematic plots of the relative energies of the singlet a potential energy surface (PES), where the values are the G3B3 relative energies. The symbol TSx-y is used to denote a transition state; x and y are the corresponding isomers or products. 3.1. ISOMERIZATION AND DISSOCIATION There are two products, six intermediate isomers, and 10 transition states present on the singlet potential energy surface. The corresponding optimized geometries and energies are shown in Figure 1, and Table I, respectively. For the singlet reaction N (2D) ⫹ NO2, there are two initial attack channels to form the isomers 1 N(NO)O (⫺90.18), and 3 (⫺88.43), respectively. The values in parentheses are G3B3 relative energies in kcal/mol with reference to R N (2D) ⫹ NO2 (0.0). Clearly, isomers 1 N(NO)O is an energy-rich species and may make the reaction easier to go through the subsequent reaction steps. From the isomer 1, there are five isomerization and dissociation pathways that can be expressed as follows: Path RP1 (1): R 3 1 3 TS1–2 3 2 3 TS2–P1 3 P1

Path RP1 (2): R 3 1 3 TS1– 4 3 4 3 TS4 –5 3 5 3 TS5–P1 3 P1 Path RP2 (1): R 3 1 3 TS1– 4 3 4 3 TS4 –P2 3 P2 Path RP3 (1): R 3 1 3 TS1– 4 3 4 3 P3 Path RP1 (3): R 3 1 3 TS1–P1 3 P1 First, from the isomer 1 N(NO)O with the energy of ⫺90.18 kcal/mol, the pathway RP1(1) can reach the products P1 (2NO) easily by going through TS1–2, isomer 2 ONNO, and TS2–P1 in succession with the energies of ⫺85.28, ⫺119.43, ⫺114.75 kcal/ mol, respectively. It is an N-insertion and O-rock mechanism. Since all the energies of the transition

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FIGURE 1. Optimized geometries (Å, °) of the reactants, intermediates, transition states, and products for the N (2D) ⫹ NO2 reaction. Numbers in roman type show the structures at the B3LYP/6-311⫹⫹G(d,p) level of theory. Numbers in parentheses show the structures at the G3B3 level of theory. Italicized numbers denote the structures at the MP2/6-311⫹⫹G(d,p) level of theory. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

states and isomers in the pathway RP1 (1) are lower than that of the reactants, the rate of this pathway should be very fast. It is both thermodynamically and kinetically much more competitive than the other pathways. Second, for pathway RP2 (1), 1 transforms to P2 (1O2 ⴙ N2) by going successively through TS1– 4 (⫺51.16), 4 (⫺73.30), TS4 –P2 (⫺70.98), and P2 (⫺149.89). Isomer 1 can transform to P2 (O2 ⴙ N2) through a successive O-rock and decomposition process. It is also of interest to give

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⫺259.6399596 ⫺259.8633132 ⫺259.8686496 ⫺259.7071333 ⫺259.7850384 ⫺259.8415210 ⫺259.7778852 ⫺259.7623469 ⫺259.7882597 ⫺259.7348486 ⫺259.7774245 ⫺259.7137688 ⫺259.6770710 ⫺259.8311635 ⫺259.7112168 ⫺259.6619690 ⫺259.7348494 ⫺259.7584367 ⫺259.7267519 ⫺259.7536495 (0.00) (⫺140.16) (⫺143.51) (⫺42.15) (⫺91.04) (⫺126.48) (⫺86.55) (⫺76.80) (⫺93.06) (⫺59.54) (⫺86.26) (⫺46.32) (⫺23.29) (⫺119.98) (⫺44.71) (⫺13.81) (⫺59.54) (⫺74.35) (⫺54.46) (⫺71.34)

0.008789 0.009018 0.009294 0.011009 0.012806 0.012702 0.013964 0.011757 0.013867 0.010524 0.011015 0.010946 0.009686 0.010692 0.01006 0.00971 0.010397 0.009356 0.010812 0.01147

ZPE ⫺259.2138928 (0.00) ⫺259.4335574 (⫺137.70) ⫺259.4546495 (⫺150.76) ⫺259.2894523 (⫺52.93) ⫺259.3586428 (⫺88.31) ⫺259.4019753 (⫺115.57) ⫺259.361461 (⫺89.35) ⫺259.3290892 (⫺70.42) ⫺259.3700647 (⫺94.81) ⫺259.3199971 (⫺65.49) ⫺259.345192 (⫺80.99) ⫺259.2961286 (⫺50.25) ⫺259.2396416 (⫺15.59) ⫺259.392273 (⫺110.74) ⫺259.2851741 (⫺43.93) ⫺259.2405905 (⫺16.18) ⫺259.319983 (⫺65.56) ⫺259.3235205 (⫺68.44) ⫺259.2924755 (⫺48.04) ⫺259.3342286 (⫺73.83)

CCSD(T)/cc⫺pVTZ// B3LYP/6⫺311⫹⫹G(d,p) ⫺259.4557555 ⫺259.6725008 ⫺259.6946187 ⫺259.5404173 ⫺259.5994661 ⫺259.6460734 ⫺259.5966775 ⫺259.5725725 ⫺259.6052416 ⫺259.5595118 ⫺259.5916638 ⫺259.5372888 ⫺259.4825500 ⫺259.6386186 ⫺259.5309366 ⫺259.4825307 ⫺259.5596690 ⫺259.5688743 ⫺259.5392817 ⫺259.5721151

0K (0.00) (⫺136.01) (⫺149.89) (⫺53.13) (⫺90.18) (⫺119.43) (⫺88.43) (⫺73.30) (⫺93.80) (⫺65.11) (⫺85.28) (⫺51.16) (⫺16.81) (⫺114.75) (⫺47.18) (⫺16.80) (⫺65.21) (⫺70.98) (⫺52.41) (⫺73.02)

G3B3

⫺259.449501 ⫺259.665890 ⫺259.688006 ⫺259.534398 ⫺259.594963 ⫺259.641074 ⫺259.592610 ⫺259.567448 ⫺259.601109 ⫺259.554539 ⫺259.586962 ⫺259.532518 ⫺259.477883 ⫺259.643182 ⫺259.526590 ⫺259.478169 ⫺259.555522 ⫺259.565703 ⫺259.535164 ⫺259.568050

(0.00) (⫺135.79) (⫺149.66) (⫺53.27) (⫺91.28) (⫺120.21) (⫺89.80) (⫺74.01) (⫺95.14) (⫺65.91) (⫺86.26) (⫺52.09) (⫺17.81) (⫺121.54) (⫺48.37) (⫺17.99) (⫺66.53) (⫺72.92) (⫺53.75) (⫺74.39)

298 K

Theoretical predication of the total energy (hartrees), harmonic ZPE (hartrees), relative energies (kcal/mol) for products, intermediates and transition states of N (2D) ⫹ NO2 reaction at different levels of theory.

R(2N ⫹ NO2) P1(2NO) P2(1O2 ⫹ N2) P3(1O ⫹ 1N2O) 1 2 3 4 5 6 TS1–2 TS1–4 TS1–P1 TS2–P1 TS3–P1 TS3–6 TS6–P1 TS4–P2 TS4–5 TS5–P1

Energy (0 K)

B3LYP/6⫺311⫹⫹G(d,p)

TABLE I ________________________________________________________________________________________________________________________________ Theoretical predication of the total energy (hartrees), harmonic ZPE (hartrees), relative energies (kcal/mol) for products, intermediates and transition states of N (2D) ⴙ NO2 reaction at different levels of theory.

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FIGURE 2. Schematic representation of the spin-allowed reaction mechanism. Singlet electronic state potential energy surface (PES) for the N (2D) ⫹ NO2 reaction at the G3B3 levels of theory. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.] the most feasible pathways for some other products. It is creditable that the TS4 –P2 can transform to the P2 (1O2 ⴙ N2) on the singlet surface. We should mention here that the bond lengths of the P2 (1O2 ⴙ N2) are according to our IRC calculation at the B3LYP/6-311⫹⫹G(d,p) level of theory as shown in Figure 3. Moreover, isomer 4 OONN can transform to products P3 (⫺53.13) directly in pathway RP3 (1). While the dissociation process from isomer 4 to the products P3 have to absorb a great deal of energy.

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On the other hand, isomer 4 can also transform to P1 through a successive O-rock and four-center ring formation-decomposition process. Because the rate-determining energy barrier (39.01) of Path RP1 (2) is higher than the ones of Path RP1 (1) (4.89), pathway Path RP1(2) should be less competitive than pathway Path RP1(1). For pathway RP1 (3), isomer 1 can overcome a 41.81 kcal/mol energy barrier (TS1–P1), directly to educts P1. Isomerization from 1 to P1 has to overcome a very high energy transition state TS1–P1 (⫺16.81) can be ne-

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ZUO ET AL. should be more competitive than RP2 (1) at low temperature ranges. Consequently, NO is the major product of the singlet reaction N (2D) ⫹ NO2.

3.2. COMPARISON WITH EXPERIMENTS

FIGURE 3. Bond dissociation curve calculated via IRC calculations at the B3LYP/6-311⫹⫹G(d,p) level of theory. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

glected. Because the rate-determining energy barrier (73.46) of Path RP1 (3) is higher than the ones of Path RP1 (1) (4.89), pathway Path RP1 (3) should be less competitive than pathway Path RP1 (1). Furthermore, we have also studied a related four center cyclic ring structure 3. It is a stable six ␲ electrons four-center ring with a planar. Our understanding of aromatic molecules rests primarily on the 4n ⫹ 2 ␲-electron criterion, known as Hu¨ckel’s rule, describing the delocalization of ␲-electrons. Isomer 3 has stability and aromatic character. From the isomers 3, there are two isomerization and dissociation pathways that can be expressed as follows: Path RP1 (4): R 3 3 3 TS3–P1 3 P1 Path RP1 (5): R 3 3 3 TS3– 6 3 6 3 TS6 –P1 3 P1 For pathway Path RP1 (4), isomer 3 can also transform to P1 through a four-center cage decomposition process. 3 can be directly dissociated to P1 via transition state TS3–P1 (11.45). Because further isomerization from Isomer 3 to P1 has to overcome a very high energy transition state TS3– 6 (41.83), Path RP1 (5): R 3 3 3 TS3– 6 3 6 3 TS6 –P1 3 P1 can be neglected. For pathway Path RP1 (4), isomer 3 can overcome a 43.0 kcal/mol energy barrier (TS1–P1), directly to educts P1. This is a four-center ring decomposition process. To briefly summarize, pathway Path RP1 (1) and Path RP2 (1) are major pathways among all pathways mentioned earlier. The pathway Path RP1 (1)

The reactions of metastable atomic nitrogen, with NO2 are also of interest relevant to the chemistry in the perturbed thermosphere [11]. For the N ⫹ NO2 reaction, other channels forming 2NO, N2 ⫹ O2, 3O ⫹ N2O, and N2 ⫹2O are energetically possible. However, those channels are suggested to be of minor importance as related to products [6]. According to our results, it is shown that the most feasible pathway should be the atomic radical N attacking the NO bonding of the NO2 molecule first to form the adduct 1 N(NO)O, followed by one of the NO bonding broken to give intermediate 2 ONNO, and then to the major products P1 (2NO). Since there is no barrier for this pathway, the title reaction is expected to be very fast. The other reaction pathways are less competitive due to thermodynamical or kinetic factors. This is qualitatively consistent with the experimental result [6, 11]. Thus, the novel reaction N ⫹ NO2 can proceed effectively even at low temperatures and it is expected to play a role in both combustion and interstellar processes.

4. Conclusions The mechanism of the N (2D) ⫹ NO2 reaction is elucidated by means of ab initio calculations at the CCSD(T)//B3LYP and G3B3 levels of theory. The major pathway is Path RP1 (1): R 3 1 3 TS1–2 3 2 3 TS2–P1 3 P1 on the singlet potential energy surface. The major pathway is barrier-less. Both kinetic and thermodynamic considerations support the viability of such channels. Other pathways on the singlet PES may be less competitive for both kinetic and thermodynamic reasons. Further theoretical and experimental studies are desirable to provide some useful insight into the mechanism of the N radical reaction.

ACKNOWLEDGMENTS The authors are thankful for the reviewers’ invaluable comments.

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