Mechanism of the Chemiluminescent Reaction between Nitric Oxide

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Mechanism of the Chemiluminescent Reaction between Nitric Oxide and Ozone Mahesh Gudem, and Anirban Hazra J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08812 • Publication Date (Web): 31 Oct 2018 Downloaded from http://pubs.acs.org on November 4, 2018

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The Journal of Physical Chemistry

Mechanism of the Chemiluminescent Reaction between Nitric Oxide and Ozone Mahesh Gudem* and Anirban Hazra* Department of Chemistry, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Pune 411008, Maharashtra, India ABSTRACT: The gas phase reaction of nitric oxide with ozone to give chemiluminescence is used extensively for detection of nitrogen oxides. The molecular mechanism of chemiluminescence in this reaction is not known. So far, the only chemiluminescent systems studied in depth are certain cycloperoxides, which emit light following decomposition. Given our understanding of the mechanism of chemiluminescence in those molecules, one would expect by extension that in the NO+O3 reaction the chemiluminescent species — NO2 in this case — is formed in the excited state through a reaction pathway that diverges from the ground state pathway near the transition state. A systematic search for such a pathway leads us to conclude that such a mechanism is unlikely. Instead, our study suggests that chemiluminescence in the NO+O3 reaction is due to emission from the NO2 vibronic states associated with the ground (𝑋 2A1) and first excited (𝐴 2B ) electronic states, which are populated in the nascent NO produced in the reaction. The vibronic coupling between 2 2 the 𝑋 2A1 and 𝐴 2B2 states of NO2 is due to a conical intersection (CI), which is geometrically and energetically close to the 𝐴 2B2 minimum energy geometry and only 1.3 eV higher than ground state NO2. Further, the CI is 1.2 eV lower than the energy of the NO+O3 reactants and therefore thermodynamically accessible following the reaction. An analysis of the product energy distribution indicates that the major fraction of the reaction energy is channeled into the vibrational modes of NO2, sufficient to populate the vibronic states of NO2 around the 𝑋/𝐴 CI. These vibronic states show dipoleallowed emission in a frequency range that is consistent with the observed broad chemiluminescence spectrum.

INTRODUCTION Chemiluminescence is the emission of light as a consequence of a chemical reaction. This process brings to mind fireflies and glow sticks where the mechanism of light emission is entirely different from the commonly observed emission of radiation from a hot body. Moreover, chemiluminescence stands out from most other chemical reactions because it involves both ground and excited molecular electronic states, yet is a thermally activated reaction rather than a photo-induced one. There has been significant interest recently in exploring the mechanism of chemiluminescence, with several theoretical studies exploring the reaction in models representing firefly dioxetanone1-12. In those systems, which are four-membered-ring peroxides there exists a conical intersection between the ground and excited states near the transition state. On accessing this conical intersection, the molecule gets populated in both ground and excited states, and the excited state product gives light while decaying to the ground state. However, no other class of chemiluminescent reactions, particularly non-enzymatic reactions, has been examined in depth and the general principles of the mechanism of chemiluminescent reactions are yet to be established.

oxide with ozone to produce nitrogen dioxide and oxygen (Scheme 1). This reaction is routinely used commercially for quantitative determination of NOx (NO and NO2) in gas mixtures. It also plays a crucial role in the atmospheric ozone budget13-15. In this reaction, it is thought that oxygen is produced in the ground electronic state, while NO2 is formed in both the ground and excited electronic states (with majority fraction in the ground state), and the process of relaxation of excited NO2 leads to chemiluminescence16-23. The molecular details of this reaction are yet largely unknown. Being a gas phase process and because of the relatively small size of the reacting molecules, one might expect that accurate quantum mechanical methods can be easily applied to describe this reaction. However, because of multiple challenges discussed below, this has not been the case. In the present work, we have sought to obtain a detailed and fundamental understanding of the mechanism of the reaction in Scheme 1 — in particular the process of chemiluminescence — with the help of high-level quantum chemical calculations.

In the gas phase, perhaps the most well-known and widely applied chemiluminescent reaction is that of nitric

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Scheme 1. Reaction of nitric oxide with ozone.

A detailed study of any reaction mechanism requires a knowledge of potential energy surfaces (PES) and nuclear dynamics going from reactant to product. Although the NO + O3 chemiluminescent reaction has been known for long, such fundamental aspects have barely been explored due to several theoretical challenges specific to this reaction: (1) There is coupling between nuclear and electronic motion, and consequent breakdown of the Born-Oppenheimer approximation due to the presence of energetically close electronic states typical of chemiluminescent reactions. This requires a treatment of the nuclear dynamics with the inclusion of non-adiabatic effects. (2) In bond stretching situations (when a bond is broken and another formed) and sometimes in regions where states are very close energetically, the electronic wave function of the system cannot be described by commonly used single-reference electronic structure methods. (3) Three of the molecules involved in the reaction are open shell systems — NO and NO2 are doublets, and O2 is a triplet. The fourth molecule O3 is known to have multi-reference character even in the ground state24. So closed shell single reference methods with a Hartree-Fock reference function or density functional theory methods which are relatively easy to apply are not suitable. (4) Unlike the well-studied chemiluminescent systems which involve intra-molecular reactions, the present system has two molecules as reactants and two others as products. This makes it especially difficult to correlate the state character between reactant and product electronic states, and understand changes in electronic structure as the reaction proceeds. In essence, a proper description of this system requires the use of multi-reference electronic structure methods to obtain the PES, and careful analysis of the state characters to obtain reaction pathways. The current knowledge about this system is now summarized. Chemiluminescence from NO + O3 mixtures was observed in the visible region of the electromagnetic spectrum as early as 191122, but these were later attributed to the reaction of NO with atomic oxygen21. Chemiluminescence for the reaction in Scheme 1 was first reported in the red and infrared regions of the electromagnetic spectrum (590-1085 nm) by Greaves and Garvin18, and a more extended intensity distribution (6003000 nm) was presented by Clough and Thrush25. There have been only a handful of studies on understanding the mechanism of this reaction. The ground state reaction mechanism has been explored using single-reference methods like unrestricted Hartree-Fock theory (UHF)26, unrestricted Møller-Plesset second-order perturbation theory (UMP2)26-27, density functional theory (DFT)27 and the coupled cluster singles and doubles method (CCSD)28.

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Nonetheless, as explained earlier, single-reference methods are inadequate. Redpath et. al., using minimal state correlation diagrams have proposed two different mechanisms for the reaction20: (a) the end-atom approach — NO abstracts the terminal oxygen atom of ozone, and (b) the middle-atom approach — NO approaches O3 in the plane which bisects the O3 bond angle and abstracts the central oxygen atom of ozone. The first pathway is energetically favourable, while only the second can explain the absence of excited O2 in the products, rendering the discussion inconclusive given the complexity of the NO + O3 system and the available experimental results. A recent experimental study by Savarino et al. suggests that the end-atom approach has a higher probability than the middle-atom approach, with probability of the latter pathway being (8±5) %.29 In summary, the present understanding of the reaction exists only in pieces and leaves a lot to be desired. In this paper we have used multi-reference electronic structure methods to investigate the molecular details of the NO + O3 reaction. Our goal is to explore the thermally relevant minimum energy paths, reproduce the activation energy barrier, and to explain the broadchemiluminescence associated with the NO + O3 reaction. We have restricted ourselves to studying the end-atom approach which is the experimentally suggested major reaction pathway29. The mechanism of chemiluminescence in this reaction is found to be distinct from the cycloperoxide systems that have been studied previously1-12.

COMPUTATIONAL METHODS The complete active space self-consistent field (CASSCF)30-32 method, perhaps the most widely applied multi-reference electronic-structure method, has been used to explore the ground and excited state PES of the reaction. Dynamical electron correlation has been accounted for perturbatively. No symmetry constraints have been imposed. The key to the successful application of the CASSCF method for reactions is the proper selection of the active space (active electrons and orbitals) that describes the system along the whole reaction path. The ideal active space in our case would consist of 19 electrons in 15 orbitals [CAS(19-in-15)]. This comprises of nitric oxide's σ/σ* orbitals (2-in-2) plus two sets of π/ π* orbitals (5-in4), and ozone's two sets of σ/σ* orbitals (4-in-4), three π orbitals formed from three p-orbitals (4-in-3) plus the two lone pairs on the terminal oxygen atoms (4-in-2). In terms of atomic orbitals, the 15 orbitals can be thought of as all the valence p orbitals of nitrogen and oxygen. However, exploring reaction pathways with this large active space is computationally untenable and we have used a more reasonable active space for our calculations by excluding the σ/σ* orbitals of O1-N2 and O4-O5 bonds from the space (refer Figure 1. for atom numbering and definitions of rN-O and rO-O). This is not expected to lead to any significant loss of accuracy because during the reaction, the O3-O4 bond dissociates and the N2-O3 bond is formed, whereas


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the O1-N2, O4-O5 bonds are not affected significantly. Representative calculations bear this out (Tables S1 and S2 of the Supporting Information). The active space that we have finally used for all calculations consists of 15 electrons in 11 orbitals [CAS(15-in-11)] and the corresponding active orbitals are shown in Figure S1 of the Supporting Information. The active space used for calculations on NO2 consists of 17 electrons in 12 orbitals where all the valence orbitals have been included. The 6311++G(2df, 2pd) basis set has been used. This relatively large basis set is necessary to correctly describe the decomposition process in O333-35. All calculations have been performed using the MOLPRO-2012 suite of programs36.

Figure 1. Schematic representation of the NO + O3 system showing the atom numbering and the important reaction coordinates namely the rN-O and rO-O bond lengths.

We have taken four electronic states with equal weights in the state-averaged CASSCF (4SA-CASSCF) wave function to describe the reaction. The state averaging helps in providing a balanced description of the states included in the wave function and also helps with convergence of the CASSCF calculation. The nature of the four states and the rationale for them being a good choice is based on an analysis of the electronic character of the lowest few reactant and product states and is discussed on page S9 of the Supporting Information. For the calculations of only NO2 a 2SA-CASSCF wave function with the ground and first excited state has been used. The conical intersection optimizations of NO2 were performed starting from the ground state geometry using the gradient projection algorithm of Bearpark et al 37. The minimum energy path (MEP) of the reaction was obtained using the method of Sun and Ruedenberg38-39 to follow the intrinsic reaction coordinate (IRC) as implemented in MOLPRO-201236. The reactant and product geometries taken for energy calculations were the two end points of the MEP calculations. To account for dynamical correlation, single point energies on the corresponding CASSCF optimized geometries were computed with multi-state complete active space secondorder perturbation method (abbreviated as MSCASPT2)40-41. Given the impracticality of geometry optimization using CASPT2, this CASPT2//CASSCF approach has been the method of choice for several mechanistic studies of chemical reactions6, 9, 42-49. In the MS-CASPT2 method, an imaginary level shift of 0.3 a.u. has been used to avoid the intruder state problem50. No IPEA correction has been applied. To estimate the disposal of reaction energy into the product modes, the sudden vector projection (SVP) model developed and

successfully applied to various reactions by Guo and coworkers has been used51-60.

RESULTS AND DISCUSSION Pathways from reactant to product. In the well-studied chemiluminescent system dioxetanone, the ground and excited state products are produced through two different paths2, 6-7. For the NO + O3 reaction, there is consensus in the literature that the emissive species is NO216-23. There are however contrasting views about whether the ground (𝑋 2A1) and first excited (𝐴 2B2) electronic states of NO2 are formed through the same or different electronic channels in the reaction19, 25, 61-63. We have investigated the lowest two PES of the NO + O3 reaction starting from the side of the reactants in an attempt to resolve this issue. The ground state of the reactant, when NO and O3 molecules are far apart, is doubly degenerate corresponding to an electron occupying either the 𝜋𝑦∗ or 𝜋𝑧∗ orbital of NO (Figure S2 and S3 of the Supporting Information). These two orbitals are oriented perpendicular to each other and interact differently with the HOMO of O3 as the NO and O3 molecules approach each other (Figure 2). We will refer to the electronic state of the reaction complex characterized by the interaction of the singly occupied 𝜋𝑧∗ orbital of NO with the HOMO of O3 as the 𝜋𝑧∗ state, and the complementary state as the 𝜋𝑦∗ state. As one would expect, the double degeneracy breaks as the reactants approach giving two energetically distinct states. We have performed relaxed scans using 4SA-CASSCF on both these states by following their respective characters while constraining rN-O in steps starting from large values corresponding to the reactant going to small values corresponding to the product (Figure S4 of the Supporting Information). The main difference in the wave functions along the two paths is in one of the orbitals, which is either 𝜋𝑦∗ or 𝜋𝑧∗ , in the respective leading determinants. In the case of the 𝜋𝑧∗ scan the energy increases up to rNO=2.12 Å and then begins to decrease till rN-O = 2.06 Å (black line in Figure S4 of the Supporting Information). For rN-O < 2.06 Å, say rN-O = 2.04 Å, constrained optimization leads to a very different geometry compared to the starting geometry, with the O3-O4 bond breaking giving well separated NO2 and O2. We initiated a transition state (TS) optimization from the highest point on the relaxed scan curve corresponding to rN-O=2.12 Å which led to a converged TS geometry. The geometrical parameters of the optimized TS is presented in Table 1 and the structure is shown in Figure S5(a) of the Supporting Information. The reported geometry from a CCSD calculation28 (Figure S5(b) and Table S3 of the Supporting Information) is presented alongside for comparison. There are significant differences in the optimized structure between the two methods, particularly in the rN-O distance and δ(O1N2O3O4) dihedral angle. Given that the NO + O3 system is known to have multireference character, this difference can be presumably attributed to an inadequate description of the non-dynamical electronic correlation in CCSD, which is a single reference method.


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The MEP connecting the reactants to the products was calculated on the 𝜋𝑧∗ state. Interestingly, the geometry of the reactant O3 obtained along the MEP is not precisely symmetric (Table 1). This is an artefact of the exclusion of the σ/σ* orbitals of O4-O5 from the active space. The asymmetry in geometry is not significant enough to make a difference in the overall description of the reaction path. A similar situation exists in the product geometry for NO2 due to the exclusion of the σ/σ* orbitals of O1-N2 (penultimate column of Table 1). The 15-in-11 active space used here attempts to balance accuracy of description and computational feasibility, and using larger active spaces would not be practical, especially for the 4-state-MSCASPT2 calculations of energy, which are performed along the 4SA-CASSCF MEP. The energies of four lowest electronic states along the reaction MEP are shown in Figure 3. The energy of the product is 58.9 kcal/mol lower than that of the reactant. This value compares reasonably well with the experimentally measured reaction enthalpy of 49 kcal/mol61. CCSD on the other hand gives a very different ∆𝐸 of 26.9 kcal/mol28 demonstrating, once again, the necessity of a multi-reference description. The activation energy for the reaction on the ground state is found to be 3.3 kcal/mol which is in good agreement with the experimental estimate that ranges from 2.4–3.2 kcal/mol61, 64-65.

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correlation diagram in Figure S7. At geometries where the 𝜋𝑦∗ state becomes the fourth adiabatic excited state, it is no longer included in the lowest four states of SA-CASSCF calculation. From the nature of the 𝜋𝑦∗ molecular orbital at rN-O = 1.8 Å (Figure 2b), the 𝜋𝑦∗ state appears to correlate with a B1 symmetry orbital of NO2, which characterizes a higher excited state of NO266-67. Energies at the 4-state-MS-CASPT2 level of theory were calculated at the points on the relaxed scan curve up to rN-O = 1.8 Å (Figure 4). The energy on this path is much higher than the barrier on the ground state, and it is therefore unlikely that this path would be thermally accessed with any significant probability.

Figure 3. Calculated 4-state-MS-CASPT2//4-SA-CASSCF energies of the four lowest states along the ground state MEP connecting reactants to products of the NO + O3 reaction.

Figure 2. Orbitals characterizing the 𝜋𝑦∗ and 𝜋𝑧∗ electronic states in the reactant (a and c) and product (b and d) regions. In the reactant region these are the 𝜋𝑦∗ and 𝜋𝑧∗ orbitals of NO which are oriented perpendicular to each other. In the product region, the O3-NO complex has different structures in the two states to maximize the orbital overlap leading to bond formation. There is lateral 𝜋-type overlap in the 𝜋𝑦∗ state and head-on 𝜎-type overlap in the 𝜋𝑧∗ state.

The 𝜋𝑦∗ relaxed scan curve (red line in Figure S4 of the Supporting Information) was obtained up to rN-O = 1.8 Å. For smaller rN-O, for example rN-O = 1.7 Å, the constrained optimization leads to the breaking of O3-O4 bond. We analysed the electronic states on the constrained optimization path and the 𝜋𝑦∗ -character state was found to increase in energy and cross another electronic state. The O3-O4 bond breaking takes place on this latter lower energy state. At larger O3-O4 distances, the 𝜋𝑦∗ state crosses other electronic states and corresponds to a much higher excited state. This is consistent with the state

Figure 4. Calculated 4-state-MS-CASPT2//4SA-CASSCF energy of the 𝜋𝑦∗ state along the relaxed scan path of NO + O3 reaction with rN-O as constraint starting from the reactants. The geometry and energy of the optimized transition state on the 𝜋𝑧∗ state marked with a blue triangle


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Table 1. Relative energies and key structural parameters of important geometries on the potential energy surface of the NO + O3 reaction.

Relative Energies (kcal/mol)

Bond lengths (Å)

Bond angles (deg)

Product

Product

(NO2 in 𝑿 2A1)

(NO2 in 𝑨 2B2)

3.3

-58.9

-24.4

1.14

1.13

1.16

1.26

3.45

2.12

1.20

1.27

1.32

1.40

3.30

3.30

1.22

1.24

1.18

1.18

O1-N2-O3

93.0

107.9

134.4

101.6

N2-O3-O4

112.4

100.2

92.1

106.7

O3-O4-O5

116.2

112.8

126.5

96.8

Reactant

Transition state

4-state-MS-CASPT2// 4-SA-CASSCF

0.0

O1-N2 N2-O3 O3-O4 O4-O5

Since we were unable to find a path for NO2 formation in the 𝐴 2B2 state starting from the reactants, we attempted to find such a path starting from the product side, i.e., from the optimized NO2–O2 complex where NO2 is in the 𝐴 2B2 state, O2 in the ground state and rO-O = 3.3 Å (last column of Table 1). A relaxed scan with rO-O as constraint was performed. Points on the curve were obtained till rO-O = 3 Å. However, for a smaller rO-O, say rOO = 2.9 Å, the optimization of the other coordinates invariably led to the 𝑋 2A1 product geometry. Therefore all commonly used approaches to find a path for the formation of NO2 in the 𝐴 2B2 state from NO + O3 proved elusive. It is well established that the 𝑋 2A1 and 𝐴 2B2 states are strongly vibronically coupled68-78. In fact the 𝑋/𝐴 conical intersection (CI) is geometrically and energetically close to the 𝐴 2B2 state minimum and because of the complex topologies around a CI, it is possible that there is no minimum energy adiabatic path on the PES to access the 𝐴 2B2 minimum, which is not influenced by the 𝑋 2A1 state. In other words it is possible that in this case the only way to access the 𝐴 2B2 state is through its vibronic manifold, which is of 𝑋 – 𝐴 mixed character. Energy distribution in the products. We explore the possibility of formation of vibronically excited NO2 in the NO + O3 reaction. The calculated energy of the reaction (58.9 kcal/mol) is greater than the energy of the first electronically excited state of NO2 (34.5 kcal/mol) implying it is possible for the 𝐴 2B2 NO2 to be formed in the course of the reaction depending on how the released energy is partitioned. It would require crossed molecular beam experiments and full quantum dynamical calculations to accurately quantify this partitioning. Such experiments on this system have not been reported. Full quantum calculations appear computationally impracticable since both dynamical and non-dynamical electron correlation have to be treated to get accurate PES and couplings, and in our experience, a calculation of energy at a single point at the 4-state-MS-CASPT2 level

with 15-in-11 active space and 6-311++G(2df, 2pd) basis set with parallelization over 4 processors takes several days indicating the enormous computation cost of simulating the quantum dynamics. We thus resort to more approximate methods, which can provide an estimate of the energy distribution. The SVP method has been demonstrated as a promising way of estimating energy disposal in reactions in the various product modes. It gives comparable results to experiment and more accurate theoretical methods for a variety of systems51-60. The SVP model is based on the premise that the timescale of the collisions that lead to reaction or product internal conversion is shorter than the timescale of intramolecular vibrational energy distribution. The extent of overlap of the reaction coordinate at the transition state with the various product modes is proportional to the amount of energy disposed in those modes following the reaction. We have applied the SVP approach to the present reaction. The SVP analysis showing the largest contributions to the energy distribution in the products of the NO + O3 reaction is presented in Figure 5 and the full distribution is presented in Table S4 of the Supporting Information. The reaction coordinate and all the product modes are shown in Figure S6 of the Supporting Information. A geometry on the MEP corresponding to NO2 and O2 being sufficiently far away from each other for their interaction to be negligible (rO-O=3.30 Å) is used to represent the products in the SVP analysis. It turns out that the three vibrational normal modes of NO2 constitute 75% of the projection (sum of squares of overlaps) of the reaction coordinate at the transition state. This suggests that the majority of the energy of the reaction flows into the vibrational modes of NO2, particularly in the symmetric stretch vibration. While for most reactions, products are formed in vibrationally excited states of the ground electronic state and they cool primarily by collisions, NO2 has a rather unique electronic structure, which is discussed in the next subsection, whereby vibrational

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cooling can also take place through radiative relaxation to give chemiluminescent emission. Origin of the chemiluminescent emission. The energy of the equilibrium geometry on the 𝐴 2B2 state of NO2 is calculated to be 1.29 eV higher than the ground state equilibrium geometry at the 2-state-MS-CASPT2//2SACASSCF level of theory (Table S5), consistent with previous calculations using other methods77-79. We must clarify that in the previous subsection the energy of the reaction product in the first excited state, which can be expected to be the same as the energy of NO2 in the 𝐴 2B2 state, was stated as 34.5 kcal/mol (1.50 eV). This difference is because that calculation was of NO2 + O2 and used a smaller number of active orbitals for NO2. The ground state PES intersects the 𝐴 2B2 PES close to its minimum energy geometry. The CI is present for NO2 in C2v symmetry and different pairs of values of NO distance and ONO bond angle77-78. The degeneracy breaks when the C2v symmetry is broken. The 𝑋/𝐴 CI and the 𝐴 2B2 minimum are very similar geometrically and energetically (Table S5) and this leads to strong vibronic effects between the 𝑋 2A1 and 𝐴 2B2 states. The nascent NO2 from the reaction can be expected to be, based on the energy partitioning analysis above, highly vibrationally excited and be formed in the 𝑋 ― 𝐴 vibronic states. Delon, Jost and co-workers have through a series of studies of NO2 in a supersonic jet, systematically characterized the nature of the vibronic states of this molecule73-76. They have explained the laser induced dispersed fluorescence spectrum (LIDFS) in terms of the emission from the states near the 𝑋 ― 𝐴 conical intersection by considering strong vibronic coupling between the dense set of high vibrational levels of the 𝑋 2A1 state and the sparser isoenergetic vibrational levels of the 𝐴 2B2 state. The overall symmetry of the emitting vibronic states studied by them is B2 which are a combination of b2 (asymmetric stretch) vibrational levels of the 𝑋 2A1 state and the a1 (symmetric stretch and bend) vibrational levels of the 𝐴 2B2 state. They considered only the B2 vibronic states because these are the only ones to which absorption is allowed76, 80. Further, they showed that the vibronic states below and around 2 eV are well described as a linear combination of one dominant vibrational level of 𝐴 2B2 and a few highly excited vibrational levels of the 𝑋 2A1. Following the notation of Delon et. al.76, such vibronic states can be written as,

|𝐵2(vibronic)〉 ∝ |𝐴 2B2 ; 𝜈′1, 𝜈′2, 𝜈′3(even)〉 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑙𝑒𝑣𝑒𝑙𝑠

+

∑

𝐶𝜈𝑖|𝑋 2A1 ; 𝜈1, 𝜈2, 𝜈3, (odd)〉

𝜈𝑖 ' ' where 𝜈1, 𝜈2, 𝜈3 (𝜈' 1, 𝜈2, 𝜈3) are the number of quanta in the symmetric stretch, bending and asymmetric stretch normal modes respectively of the ground (excited) state. The asymmetric stretch is a basis for the 𝑏2 irreducible representation of the C2v point group. The even number of quanta 𝜈′3 in 𝐴 2B2 and the odd number of quanta 𝜈3 in 𝑋 2A ensures B symmetry of the vibronic state. 1 2

Figure 5. Projections of the product modes onto the reaction coordinate vector at the transition state. 𝑣1, 𝑣2, and 𝑣3 correspond to symmetric stretch, bend and asymmetric stretch of NO2. 𝑣4 corresponds to the O2 stretch and, 𝑣5 𝑣8 and 𝑣9 correspond to intermolecular motion.

We hypothesize that the chemiluminescence is due to formation of NO2 molecules in 𝑋 2A1 – 𝐴 2B2 vibronic states which subsequently emit light. The emission process is much like that in the LIDFS, except that in the case of chemiluminescence the vibronic states are populated in the course of a chemical reaction after thermally crossing a barrier rather than by absorption of light. A product NO2 formed in the 𝑋 2A1 state with odd (even) 𝜈3 will be of B2 (A1) vibronic symmetry and can mix with a 𝐴 2B2 state with even (odd) 𝜈' 3. The uniqueness of NO2 is in the vibronic mixing of the ground and first excited electronic states, due to which vibrational hot molecules are actually in the mixed 𝑋 2A1 – 𝐴 2B2 vibronic states, from which emission to lower vibrational states is significant. This can be contrasted with typical vibrationally hot molecules where excitation is to the vibrational levels of the ground electronic state. If such a hot molecule is produced in a chemical reaction, it mostly relaxes through collisions because vibrational emission is subject to the selection rule ∆𝜐𝑖 =± 1 and is slow because of the small Einstein A coefficient, which determines the rate of spontaneous emission. This is because the A coefficient is proportional to the cube of the energy difference between the two states: Emission to the immediately lower vibrational state is of relatively small frequency corresponding to a small rate compared to an electronic or vibronic transition which is of relatively higher frequency. Moreover, A is proportional to the transition dipole moment which is generally much smaller in a vibrational transition than in an electronic transition81. The energies of the proposed emissive vibronic states can be at most equal to 2.6 eV, the energy of the reaction, and are expected to be somewhat lower because part of the energy is distributed in degrees of freedom other than the NO2 vibrational modes. This is consistent with the NO + O3 emission spectrum (Figure S8 of the Supporting Information) which spans energies from 0.4 to 2.0 eV with a peak near 1.1 eV. The quantum yield of the chemiluminescence is estimated to be ~0.06-0.1861, 63-64. The yield reduction can be due to competing collision induced relaxation pathways in NO2 and the distribution


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of reaction energy in degrees of freedom other than the NO2 modes.

CONCLUSIONS The chemiluminescent reaction of NO + O3 to give NO2 + O2 has been studied using the 4-state-MS-CASPT2//4SACASSCF method. The MEP of the reaction has been obtained. The TS barrier is found to be 3.3 kcal/mol in good agreement with experiment. The reactant ground electronic state is doubly degenerate and splits into two paths as the reactants approach. The barrier on the higher path is much greater than the TS barrier on the MEP and is thermally inaccessible. The reaction is highly exothermic and the majority of the reaction energy is disposed in the vibrational modes of NO2. This molecule has an energetically accessible CI between the ground (𝑋 2A ) and first excited (𝐴 2B ) electronic states, and these 1 2 two states are strongly vibronically coupled. The excess energy in the nascent NO2 populates its vibronic states. The typical ∆𝜐𝑖 =± 1 vibrational selection does not apply to these states and emission to the lower states is allowed, which explains the broad chemiluminescence. The mechanism of chemiluminescence in the NO + O3 reaction is very different from that in cycloperoxides, the only type of chemiluminescent system explored in depth till now, and the results provide fundamental new insights on the phenomenon of chemiluminescence.

ASSOCIATED CONTENT Supporting Information. Active space orbitals. Molecular orbital diagram for NO. Degenerate HOMOs of nitric oxide. Relaxed potential energy scans on 𝜋𝑧∗ and 𝜋𝑦∗ states along rNO. Comparison of reaction TS structure obtained in this work with the previously reported CCSD TS structure. All the product modes and the reaction coordinate mode. State correlation diagram. Experimentally observed chemiluminescence spectrum. Discussion on contrition and consequences of the state correlation diagram. Tables with occupation numbers and the comparison of geometrical parameters obtained with bigger and reduced active space. Comparison of geometrical parameters of TS optimized in this work with the previously reported TS. Projections of product modes onto the reaction coordinate. Geometrical parameters and relative energies of critical points on two lowest electronic states of NO2. Cartesian coordinates for the critical geometries along the reaction MEP. “This material is available free of charge via the Internet at http://pubs.acs.org.”

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] *E-mail: [email protected]

Notes Any additional relevant notes should be placed here.

ACKNOWLEDGMENT

For financial support we acknowledge the Science and Engineering Research Board, Department of Science and Technology, Government of India (Project code GAP/DSTSERB/CHE-12-0086). We also acknowledge the Centre for Development of Advanced Computing (C-DAC) for providing computing time on National PARAM Supercomputing Facility. We are grateful to Dr. Debashree Ghosh, Indian Association for the Cultivation and Science, Kolkata, India for helpful discussions.

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Mechanism of the Chemiluminescent Reaction between Nitric Oxide

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