The Atmospheric Oxidation of HONO by OH, Cl, and ClO Radicals

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The Atmospheric Oxidation of HONO by OH, Cl, and ClO Radicals Josep M Anglada, and Albert Sole J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10715 • Publication Date (Web): 28 Nov 2017 Downloaded from http://pubs.acs.org on November 29, 2017

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The Journal of Physical Chemistry

The Atmospheric Oxidation of HONO by OH, Cl, and ClO Radicals Josep M. Anglada, *a and Albert Solé b a) Departament de Química Biològica i Modelització Molecular, (IQAC – CSIC), Jordi Girona, 18-26, E-08034 Barcelona. E-mail: [email protected]. b) Departament de Ciència de Materials i Química Física, i Institut de Química Teòrica i Computacional (IQTCUB). Universitat de Barcelona, Martí i Franqués, 1, E-08028 Barcelona. E-mail: [email protected]

Abstract The atmospheric oxidation of nitrous acid by hydroxyl radical, chlorine atom and chlorine monoxide radical has been investigation with high level theoretical methods. Nitrous acid has two conformers (cis- and trans-) and we have found a reaction path for the oxidation of each one of these conformers with the radicals considered. In all cases, the oxidation of the cis- conformer is much more favorable than the oxidation of the trans- conformer. Interestingly all transition states in these oxidation processes follow a proton coupled electron transfer mechanism. Our computed rate constant at 298 K for the reaction of cis-HONO + •OH is 4.83 x 10-12 cm3 molecule-1 s-1, in excellent agreement with their experimental values (4.85 x 10-12 and 6.48 x 10-12 cm3 molecule-1 s-1). For the trans-HONO + •OH reaction our calculated rate constant at 298 K is 9.05 x 10-18 cm3 molecule-1 s-1, and we have computed an effective rate constant for the oxidation of the whole nitrous acid by hydroxyl radical of 1.81 x 10-12 cm3 molecule-1 s1 . For the oxidation of nitrous acid by chlorine atom we predict greater rate constants (7.38 x 10-11, 3.33 x 10-15, and 2.76 x 10-11 cm3 molecule-1 s-1, for the cis-, the transconformers, and for the whole HONO), these results suggesting that this reaction should contribute to the tropospheric oxidation of nitrous acid, especially in marine boundary areas, and to the formation of tropospheric ozone. For the oxidation of nitrous acid by chlorine monoxide we predict rate constants roughly six orders of magnitude smaller than the oxidation by chlorine atom and therefore we consider that this process should play a minor role in the troposphere. Introduction Nitrous acid (HONO) is an important trace gas in the Earth’s atmosphere. Different field

measurements report atmospheric concentrations of HONO ranging between 1.05 and

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9.71 ppb,1-5 and it has been proven that HONO would lead to increased ozone concentration since their atmospheric decomposition products (NO and NO2, see below) are precursors of the atmospheric formation of O3.6-7 Furthermore, it plays an important role in the morning formation of secondary aerosols.2 In addition, it is proposed that nitrous acid can act as a harmful pollutant with direct impact on human health.8-9 Nitrous acid is directly emitted to the atmosphere by combustion processes, vehicle exhaust, and from biogenic sources,

10-15

but it can also be formed by the direct

homogenous reaction 1, by the heterogeneous reactions 2, and 3, and by the photolysis of adsorbed nitrate or nitric acid (reaction 4).3, 6, 16-21 NO + •OH → HONO (1) 2NO2(g) + H2O(ads) → HONO(g) + HNO3(ads) (2) NO2 + (C-H)(surf) → HONO(g) + (C)(surf) (3) HNO3/NO3- + hυ → HONO/NO2- + O (4) The main atmospheric fate of nitrous acid is its photolysis as described in reaction 5. HONO absorbs light in the actinic region, and constitutes and important tropospheric source of hydroxyl radicals.6 This reaction is endothermic by 49.66 ± 0.04 kcal·mol-1, 22

and it has a photolysis rate constant of 1.9 x 10-3 s-1.23

HONO + hν (λ < 400 nm) → •OH + NO (5) Moreover, it is known that its homogeneous reaction with hydroxyl radical (reaction 6) also contributes to the sink of HONO in the troposphere. 3, 6, 19 HONO + •OH → NO2 + H2O (6) For the cis-HONO + OH reaction, it has been reported experimental rate constant values, at room temperature, of 4.85 x 10-12 cm3 molecule-1 s-1,23-24 and 6.48 x 10-12 cm3 molecule-1 s-1. 23, 25 Both articles report very close rate constants at 298 K but there is a controversy regarding the dependence of k on the temperature. DeMoore at al.,23-24 report the Arrhenius equation k = 1.79 x 10-11 exp(-0.78/RT) with a positive dependence of the rate constant on the temperature, whereas Atkinson et al.,

23, 25

report the

Arrhenius equation k = 2.71 x 10-12 exp(0.52/RT) with a negative dependence of the rate constant on the temperature. From a theoretical point of view, there is a single work


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in the literature by Xia and Lin,26 reporting an extensive ab-initio and RRKM study on this reactions. In this work, we have restricted ourselves in the lower energy reaction paths, focusing our attention in the electronic features of the investigated processes and in obtaining accurate rate constants. HONO + Cl• → NO2 + ClH

(7)

HONO + ClO• → NO2 + ClOH

(8)

In addition, we have also considered the study of the oxidation of nitrous acid by chlorine atom and chlorine monoxide radical (reactions 7 and 8). The main tropospheric precursor of Cl• is sea salt aerosol,27-28 whereas ClO• can be formed by oxidation of hypochlorous acid by hydroxyl radical.

29

Recently, there has been measured

5

concentrations of these species of 3 x 10 and 1 x 107 molecules·cm-3 in the marine boundary layer, along with the 6 x 105 molecules·cm-3 measured for hydroxyl radical.30 It is well known that chlorine atoms is a strong oxidant and, for instance, the rate constants for the reactions of Cl• with alkanes are about two orders of magnitude greater than those of the reactions with •OH radicals.

28, 30-32

ClO• also reacts quite fast with

species as HO2•,33 and all these data suggest that reactions 7, and 8 may also have potential atmospheric relevance and deserve to be investigated. Theoretical Methods In a first step, we have employed the density functional methods B3LYP,34 BH&HLYP,35 and M06-2X,36 with the 6-311+G(2df,2p) basis set37-38 to optimize the stationary points on the potential energy surfaces (PES) investigated. At this level of theory, we have performed harmonic vibrational frequency calculations to confirm the nature (minima or saddle points) of the stationary points, and to calculate the zero-point energy and the thermal contributions to enthalpy and Gibbs energy as well. In addition, we have carried out intrinsic reaction coordinate (IRC) calculations39-41 in order to confirm the connectivity between a given transition state structure (TS) and the corresponding reactant and product. In a second step, the most relevant stationary points have also been re-optimized at CCSD(T) level of theory42 employing the 6-311+G(2df,2p) basis set.



The final energies have been obtained by carrying out single point energy calculation at CCSD(T) level of theory employing the aug-cc-pVTZ and aug-cc-pVQZ basis sets, and considering the extrapolation to the complete basis set (CBS) limit, according to the extrapolation scheme by Helgaker et al.

43

The reliability of these results, regarding to

the possible multi-reference character of the corresponding wave function, have been checked by looking at the T1 diagnostic value of the CCSD wave function. In all cases the T1D values (up to 0.045) lie among the standards reported in reference 44, with the exception of the transition state for the reaction between cis-HONO and ClO•, for which we got a T1D value of 0.060. In this case, we have also calculated the corresponding energy barrier by performing large scale MRCI+Q/aug-cc-pVTZ level of theory (multireference CI calculations including the Davidson extrapolation to quadruple excitations) and the calculated MRCI+Q barrier agrees very well with the CCSD(T) value. The kinetic study has been performed using the variational (VTST) transition state theory, considering energies obtained at the CCSD(T)/CBS energies and partition functions computed at M06-2X/6-311+G(2df,2p) level of theory. The tunneling effects have been obtained with the small curvature approach. The quantum chemical calculations carried out in this work were performed by using Gaussian45 and ORCA program packages.

46

The Molden47 and VMD48 programs were

employed to visualize and plot the geometric and electronic features. The kinetic study was done by using the Polyrate program.49 Results and discussion. Hydrogen atom abstraction by radicals. Proton coupled electron transfer versus hydrogen atom transfer mechanisms. Hydrogen atom abstraction by radicals (reaction 9) is one of the most common reactions in the atmosphere. X-H + ·Y → X· + H-Y (9) It is well stablished that in many cases, the reaction proceeds by the concerted breaking and forming of the covalent bonds involving the hydrogen atom being transferred. (i.e. X-H and H-Y). In this process, when the ·Y radical approaches the X-H bond, the


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unpaired electron interacts with the hydrogen atom, and the formation of the H-Y bond occurs whereas the X-H bond breaks homoliticaly. A model example of this kind of reaction mechanism is the reaction of H2O with •OH,50 and in Figure 1a we have plotted the most relevant features of this process. At the transition state, a three center three electron electronic structure is formed, which is shown by picture of the HOMO and SOMO orbitals, indicating that the spin density is shared between the X and Y atoms that are involved in the transfer of the hydrogen atom (the two oxygen atoms in this case). It is also a common belief that the energy barrier associated to this reaction depends on the strength of the X-H bond, and Zavitsas and co-workers 51-54 pointed out that this is related to the triplet repulsion energy of the X·/·Y pair at the transition structure.

Figure 1. Pictorial representation of the main electronic features of the hydrogen atom transfer (left side, Figure 1a), and proton coupled electron transfer mechanisms (right side, Figure 1b). There are however situations, where the hydrogen abstraction by radicals occurs in a different manner, involving a proton coupled electron transfer process. An example of this kind of reaction mechanism is the gas phase oxidation of the acidic hydrogen atom of formic acid by hydroxyl radical.55 In figure 1b we have depicted a scheme of this reaction mechanism which shows that in the molecule to be oxidized, there is a group Z (the oxygen atom of the carbonyl group in this case) with a lone pair of electrons facing



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the unpaired electron of the attacking radical Y (the oxygen atom of the hydroxyl radical), whereas a lone pair of the radical is directed over the hydrogen atom (the acidic hydrogen in Figure 1b) of the molecule to be oxidized. In such a situation, the reaction can proceed by a transfer of an electron from Z to Y and, simultaneously a jump of the X-H proton to Y in a proton coupled electron transfer mechanism. The electronic features, also depicted in Figure 1b, show that the electronic density, and the spin density as well, are now shared between the Z and Y atoms where the electron transfer occurs, which clearly differentiates from the conventional hydrogen atom transfer mechanism. Further examples of this kind of processes have been also reported in the literature for the atmospheric oxidation of organic and inorganic acids by radicals.55-62 The gas phase nitrous acid. There are two conformers (cis- and trans-) of the gas phase nitrous acid and Figure S1 of the supplementary information shows the most relevant geometrical parameters of their optimized structures. Both conformers are almost degenerate and our results displayed in Table 1 show that our calculations predict the trans conformers to be 0.30 kcal·mol-1 more stable than the cis conformer, in good agreement with the 0.50 kcal·mol-1 reported in reference.26 Their relative enthalpy at 298 K is computed to be 0.26 kcal·mol-1 in very good agreement with the experimental values (0.34 ± 0.09 kcal·mol-1).22 Our computed geometrical parameters and relative energies are also in excellent agreement with experimental63 and theoretical calculations64-65 from the literature. These values suggest that both conformers of HONO should be considered in studying the reactivity of this species, and our results allow to calculate the equilibrium constant between them. At room temperature, the equilibrium constant between the cisand transconformers is computed to be 1.669, which means that the population of the

trans- and cis- conformers are 63% and 37%, respectively. The whole values computed at different temperatures are collected in Table S2 of the supplementary information. Table 1: Relative energies, energies plus ZPE (Zero Point Energy), (in kcal·mol-1), enthalpies, and free energies (in kcal·mol-1, at 298 K) calculated for the reactions investigated in this work. Compound

∆E

∆ (E+ZPE)

∆Η (298K)


∆G(298K)

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HONO a trans-HONO

0.00

0.00

0.00

0.00

cis-HONO

0.33

0.30

0.26

0.30

•

cis-HONO + OH → NO2 + H2O a cis-HONO + OH

0.00

0.00

0.00

0.00

ACR1

-4.99

-3.48

-3.84

3.64

ACR3 b

-4.77

-3.03

-3.47

4.35

ATS1

-1.42

-1.38

-2.59

6.96

ATS3 b

15.75

14.31

12.66

23.44

ACP1

-42.90

-40.91

-40.57

-35.15

NO2 + H2O c

-40.65

-39.86

-39.67

-39.93

trans-HONO + •OH → NO2 + H2O b trans-HONO + OH

0.00

0.00

0.00

0.00

ACR2

-4.28

-2.33

-2.80

4.97

ATS2

9.18

9.63

8.40

17.96

ACP1 a

-42.57

-40.61

-40.31

-34.85

•

cis-HONO + Cl → NO2 + ClH a cis-HONO + Cl

0.00

0.00

0.00

0.00

BCR1

-3.64

-3.30

-3.60

2.95

BTS1

-0.23

-3.04

-3.84

4.05

BCP1

-23.36

-25.07

-24.81

-20.00

NO2 + ClH c

-22.13

-25.27

-24.79

-26.27

trans-HONO + Cl• → NO2 + ClH b



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trans-HONO + Cl

0.00

0.00

0.00

-11.62

BCR2

-3.67

-2.94

-3.18

-8.43

BTS2

8.62

6.29

5.51

1.64

BCP2

-23.23

-25.54

-25.53

-31.87

cis-HONO + ClO• → NO2 + ClOH a cis-HONO + ClO

0.00

0.00

0.00

0.00

CCR1

-4.24

-3.44

-3.36

4.25

CTS1

12.72

10.65

10.22

19.38

CCP1

-18.76

-17.82

-17.42

-10.64

NO2 + ClOH c

-16.90

-17.09

-16.89

-17.47

•

trans-HONO + ClO → NO2 + ClOH b trans-HONO + ClO

0.00

0.00

0.00

0.00

CCR2

-4.34

-3.49

-3.32

4.02

CTS2

21.94

20.26

19.85

28.85

CCP2

-19.47

-18.60

-18.19

-11.93

a) CCSD(T)/CBS//CCSD(T)/6-311+G(2df,2p) energies with ZPE and thermodynamic corrections computed at M06-2X/6-311+G(2df,2p) level of theory (see text). b) CCSD(T)/CBS//M06-2X/6-311+G(2df,2p) energies with ZPE and thermodynamic corrections computed at M06-2X/6-311+G(2df,2p) level of theory (see text). c) The experimental reaction enthalpies (∆rxnH298) for the reaction between cisHONO and ·OH, Cl·, and ClO·, are -40.05; -24.35, and -15.95 kcal·mol-1, respectively.66

The reaction of HONO with OH, Cl, and ClO. We have found one elementary pathway for the reaction of each of the two conformers (cis- and trans-) of HONO with the ·X radicals (X= ·OH, Cl·, and ClO·), leading to


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the formation of NO2 + HX (HX= H2O, ClH and ClOH) (reactions 6, 7, and 8). Each elementary reaction begins with the formation of a pre-reactive complex followed by the transition state, which leads to the formation of a post reactive complex before the release of the products. Figures 2, 4, and 5 display a schematic profile of the corresponding potential energy surfaces of these reactions, and in Figure 3 we have depicted the most relevant geometrical parameters of the corresponding transition states along with their electronic features. Table 1 contains the corresponding relative energies, which shows that our calculated reaction enthalpies are in excellent agreement with the experimental values. In the text, we have named the transition states by the letters TS, the pre-reactive complexes by CR, and the post-reactive complexes by CP, followed by a number. In order to distinguish the reaction of nitrous acid with the different radicals investigated, each stationary point is preceded by the letters A, B, or C for the reaction with the ·OH, Cl·, and ClO· radicals, respectively. Thus, for instance, ATS1 corresponds to transition state for the reaction of nitrous acid with hydroxyl radical while BTS1 corresponds to a transition state for the reaction of HONO with Cl· atom. ∆(E+ZPE)/Kcal·mol-1 14.61 ATS3 9.63

cis-HONO + OH 0.30

ATS2

0.00

-1.08

trans-HONO + OH

ATS1 -3.18/-2.33

cis-HONO + OH 0.30

-3.18 ACR1 -39.56 -40.61 NO2 + H2O

ACR1

ACR2

ACP1

Figure 2. Schematic potential energy surface for the reaction between HONO and ·OH.



For the reaction of nitrous acid with hydroxyl radical (reaction 6), the interaction of cisHONO with OH proceeds through the formation of the ACR1 pre-reactive complex, which is followed by the ATS1 transition state and the ACP1 post-reactive complex, occurring previous to the formation of the NO2 and H2O products. Table 1 and Figure 2 show that ACR1 has a binding energy of 3.48 kcal·mol-1. It has a planar structure (CS, 2

A’’) where both cis-HONO and OH moieties are held together by two hydrogen bonds,

one between the hydrogen atom of the acid and the oxygen atom of the radical, and the other between the hydrogen atom of the radical and the terminal oxygen atom of cisHONO. The ATS1 transition state lie just 2.10 kcal·mol-1 above the ACR1 complex, but below the energy of the reactants. These results compare with the values reported by Xia and Lin,26 although we predict a slightly larger stability for the stationary points probably due to the different theoretical approach employed in both works. In terms of free energy both, ACR1 and ATS1 lie above the reactants (3.64 and 6.96 kcal·mol-1, respectively (see Table 1). Figure 3 shows that, at the ATS1 transition structure, the •

OH radical approaches the cis-HONO molecule in such a way that the unpaired

electron of •OH faces the lone pair of the terminal oxygen atom of nitrous acid whereas a lone pair of the oxygen atom of the radical is directed to hydrogen atom of cis-HONO so that the transition state has a five-member ring structure. This approach facilitates the transfer of one electron from the terminal oxygen atom of the acid to •OH and, simultaneously, the jump of the proton from the acid to the radical, which corresponds to a proton coupled electron transfer mechanism. The picture of the HOMO and SOMO orbitals displayed in Figure 3 shows clearly this situation. The electron density is shared between the terminal oxygen atom of cis-HONO and the OH radical and the spin density as well, as described in a previous section. In the ACP1 post reactive complex at the exit channel, the two moieties, NO2 and H2O, are held together by a van der Waals interaction occurring between the oxygen atom of water and the nitrogen atom of nitrogen dioxide (see Figure 2). Here it is also worth mentioning that along ACR1, the M06-2X functional also predicts a further pre-reactive complex (ACR3, See Table 1), which is almost degenerate with ACR1, in which the OH of the radical moiety lies out of plane by 62°. However, this complex has not been found at CCSD(T) level and therefore no further discussion is done on this issue.


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1.122 [1.093] (1.146)

1.304 [1.347] (1.241)

[1.109] (1.139) {1.091}

2.264 [2.296] (2.351)

ATS1

HOMO

1.591 [1.606] (1.593) {1.631} 1.161 [1.145] (1.143) {1.140}

SOMO

[2.255] (2.294) {2.437}

ATS2

SOMO

HOMO

[1.162] (1.139) {1.161}

2.558 [2.611] (2.652) {2.694}

BTS1

BTS2

HOMO

SOMO [1.155] (1.154) {1.146}

2.396 [2.723] (2.870) {2.827} [2.626] (2.618) {2.835}

1.177 [1.147] (1.149) {1.135}

HOMO

[1.614] (1.621) {1.624}

[2.593] (2.621) {2.745}

SOMO

HOMO

1.232 [1.246] (1.221) {1.286}

[1.336] (1.261) {1.380}

CTS1

[1.236] (1.218) {1.272}

CTS2

SOMO

HOMO

SOMO

Figure 3. Relevant geometrical parameters, and electronic features of the transition states involved in the oxidation of HONO by the ·OH, Cl·, and ClO· radicals. Plain values correspond to optimized geometries at CCSD(T) level; values in brackets,



parenthesis, and braces, correspond to M06-2X, BH&HLYP, and B3LYP optimized structures. Distances are in Angstroms. In addition to the ATS1, we have also found and additional reaction path, which starts from the ACR1 pre-reactive complex, goes through the ATS3 transition state and continues via ACR1 before the release of the products cis-HONO + OH (see Figure 2). This is a silent reaction where reactive and products are the same species. This process involves a double proton transfer reaction so that the hydrogen atom of the acid is transferred to the hydroxyl radical and, simultaneously, the hydrogen of the radical is transferred to the terminal oxygen atom of cis-HONO. ATS3 has a planar structure (C2v, 2

B1 electronic state) and the unpaired electron is mainly localized over the oxygen atom

of the radical moiety, perpendicular to the symmetry plane containing all atoms and therefore it does not participate in the reaction, in a similar way as described for the oxidation of formic acid, nitric acid and sulfuric acid by hydroxyl radical. 55, 57-58 The reaction of trans-HONO with ·OH occurs through the ATS2 transition state, and is mediated by the ACR2 pre-reactive complex and by the ACP1 post-reactive complex. For ACR2, we have computed a binding energy of 2.33 kcal·mol-1, and the •OH and

trans-HONO moieties are held together by an hydrogen bond between the hydrogen atom of the acid and the oxygen atom of the radical (see Figure 2). Our calculations predict the transition state ATS2 to lie 9.63 kcal·mol-1 above the energy of the transHONO + •OH reactants, that is, 10.71 kcal·mol-1 higher than the energy of ATS1, suggesting that this reaction mechanism should not play an important role in the atmospheric oxidation of nitrous acid. The analysis of the electronic structure of ATS2 indicate that this elementary reaction also follows a proton coupled electron transfer mechanism. Figure 3 shows that the unpaired electron of the radical faces the lone pair of the nitrogen atom of nitrous acid and the lone pair of the OH moiety is directed towards the hydrogen atom of the acid so that an electron from the nitrogen atom is transferred to the oxygen atom of the radical, while the proton from the acid is transferred to the oxygen atoms of the radical moiety. This kind of reaction mechanism implies a four-member ring structure for ATS2, which is much more strained that ATS1 (see above), and imply the higher energy barrier of this reaction path.


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∆(E+ZPE)/Kcal·mol-1

6.29 cis-HONO + Cl

BTS2

0.30 -2.74

0.00

trans-HONO + Cl

BTS1 -3.00/-2.94

-24.77/ -25.54

-24.97 NO2 + ClH

BCR1

BCR2

BCP1

BCP2

Figure 4. Schematic potential energy surface for the reaction between HONO and Cl·. The reaction of HONO with Cl· and ClO· have the same features as those described for the reaction with hydroxyl radical, except the double proton transfer mechanism occurs in the reaction with ·OH only. Thus, for the reaction of cis-HONO + Cl· (ClO·), the reaction(s) path follows the sequence BCR1 (CCR1) → BTS1 (CTS1) → BCP1 (CCP1) → NO2 + ClH (ClOH), and for the reaction of trans-HONO + Cl· (ClO·), the corresponding transition state BTS2 (CTS2) is mediated by the pre-reactive complex BCR2 (CCR2) and by the post-reactive complex BCP2 (CCP2) (see Figures 4 and 5). Regarding the electronic features of these processes, Figure 3 shows that all transition states follow a proton coupled electron transfer mechanism, in a similar manner as described for ATS1 and ATS2 in the reaction with hydroxyl radical. In the case of reaction 7, the chlorine atom is involved in the electron and proton transfer processes while in the case of reaction 8, the oxygen of the chlorine monoxide radical participates in the simultaneous transfer of the electron and the proton. Figure 3 also shows that BTS1 and CTS1 have a five-member ring structure whereas BTS2 and CTS2 have a four-member ring structure in a similar way as described above for ATS1 and ATS2, respectively.



Page 14 of 26

With respect to the reaction with chlorine atom our results predict that BTS1 lie just 0.26 kcal·mol-1 above the energy of the pre-reactive complex BCR1, and 3.04 kcal·mol1

below the energy of the separate reactants cis-HONO + Cl·, suggesting that the

reaction through this channel should be very fast. The reaction between trans-HONO +Cl·, through BTS2, has a much higher energy barrier according to its more strained structure as described for ATS2 above (see Table 1). ∆(E+ZPE)/Kcal·mol-1 20.26 CTS2 10.95 cis-HONO + ClO CTS1 0.30 0.00 trans-HONO + ClO

-16.79

-17.52/ -18.60

-3.14/-3.49

NO2 + ClOH

CCR1

CCR2 CCP1

CCP2

Figure 5. Schematic potential energy surface for the reaction between HONO and ClO·. Regarding the reaction with chlorine monoxide, our calculations predict quite high energy barriers for both CTS1 and CTS2 (10.65 and 20.26 kcal·mol-1, respectively, relative to the corresponding separate radicals, see Table 1 and Figure 5), which contrast with the reactions of nitrous acid with hydroxyl and chlorine radicals. Finally, we have to mention that any effort to find reaction paths involving a conventional hydrogen atom transfer mechanism were unsuccessful, which indicates that if they exist, should have a much higher energy barrier. From an energetic point of view, the computed reaction enthalpies at 298 K, for the reaction of cis-HONO with ·OH, with Cl·, and with ClO·, are -39.67, -24.79, and -


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16.89 kcal·mol-1, in excellent agreement with the experimental values, namely -40.05 ± 0.09, -24.79 ± 0.09, and -15.95 ± 0.09 kcal·mol-1, respectively. 22 Finally, it is also worth mentioning several technical aspects of the calculations. Throughout this investigation, we have used different theoretical approaches including different DFT functionals and the CCSD(T) method in the case of the stationary points involved in the oxidation of cis-HONO by the three radicals considered. In Figure 3 we have collected the most relevant parameters of all TS1 and TS2 transition states obtained with the different methods employed. At first glance, the most critical geometrical parameter is the distance between the two atoms where the electron transfer takes place, and for all TS1 transition states we take as the most accurate optimized geometries those obtained at the CCSD(T) level of theory. For ATS1 this O···O distance is computed to be 2.264 Å whereas the M06-2X and BH&HLYP predict distances 0.032 and 0.087 Å longer, respectively (see Figure 3). The O···H and H···O distances of the hydrogen being transferred are computed to be 1.122 and 1.304 Å, respectively at CCSD(T) level of theory, with differences up to 0.06 Å employing the BH&HLYP functional. These geometrical parameters are in good agreement with the corresponding proton coupled electron transfer transition states involved in the oxidation of formic and nitric acid by hydroxyl radical.55, 58 With the B3LYP approach we were not able to find this transition state. For BTS1 Figure 3 shows the calculated O···Cl distance at CCSD(T) level of theory is 2.558 Å and the corresponding computed distance at M06-2X, BH&HLYP, and B3LYP are 0.053, 0.094, and 0.136 Å longer, respectively. For CTS1, the computed O···O distance is 2.396 Å but the three DFT functionals employed perform worse, with errors between 0.327 and 0.474 Å (see Figure 3), which is probably due to the fact that in CTS1 the unpaired electron is mainly delocalized between the O and Cl atoms of the radical moiety. Despite these geometry differences, the energy barriers computed at CCSD(T)/aug-cc-pVTZ//M062X/6-311+G(2df,2p) and CCSD(T)/aug-cc-pVTZ//CCSD(T)/6-311+G(2df,2p) levels of theory compare quite well, with differences smaller than 0.9 kcal·mol-1. The TS2 transition states have only been optimized using the DFT methods because its higher energy barriers, but we are confident that the errors computed employing the different functionals should follow the same trends, since the O···N distance in ATS2 compares quite well with the corresponding O···N distance in the proton coupled electron transfer transition state of the HNO3 + •NH2 reaction.61-62 In any case, these results suggest that



the M06-2X functional performs better than BH&HLYP in predicting the geometry of these transition states while the B3LYP approach performs worse. However, it is also worth mentioning that the ACR2, CCR1 and CCR2 are predicted to have one imaginary frequency at M06-2X level of theory, even after performing an optimization with a very tight option.

Reaction Kinetics The kinetic study has been done taking into account that all reactions investigated in this work begin with the formation of a pre-reactive complex (CR), which is in equilibrium with the reactants, and occurs before the transition state and the release of the corresponding products (Reaction 10) HONO + •X ⇌ CR → NO2 + HX

(10)

According to this reaction scheme, and taking into account that all transition states lie higher in terms of free energy than the reactants (see Table 1), the kinetic model employed in the calculation of the rate constants have been done according equation 1.

=

=

[1]

where Keq is the equilibrium constant of the pre-reactive complex and k2 is the rate constant of the unimolecular reaction between the pre-reactive complex to the reaction product. The Keq values have been calculated according to equation 2.

=

( )

[2]

where the Q values correspond to the partition functions and EC and ER are the energies of the complex and reactants. For k2, we have used the canonical variational transition state theory (CVTST),67-69 following equation 3.

=

(∗)

(!∗) "

[3]

where s* is the free energy maximum along the reaction path at temperature T, Q Complex is the partition function of the pre-reactive complex, Q GT(s*) is the generalized transition state partition function and V(s*) is the potential energy and κ is the tunneling


Page 16 of 26

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parameter, that has been computed with the small curvature approach. For the reaction via TS1, these calculations have been done employing the Hessian matrices computed at M06-2X/6-311+G(2df,2p)

level

of

theory

CCSD(T)/CBS//CCSD(T)/6-311+G(2df,2p).

For

and the

energies reactions

calculated via

TS2,

at these

calculations have been carried out using hessian matrices computed at M06-2X/6311+G(2df,2p) level of theory and energies calculated at CCSD(T)/CBS//M06-2X/6311+G(2df,2p). In all cases, the partition functions have been calculated from a rigid rotor harmonic oscillator approximation. The Polyrate program has been employed in the kinetic calculations.

The reaction mechanisms discussed in the previous section have shown that there is a reaction path for the reaction of each of the two conformers of HONO with the X radicals which leads to the formation of NO2 + HX products. Accordingly, the reaction rate is given by v = kTS1[cis-HONO][ •X] + kTS2[trans-HONO)[ •X] [4] In a previous section, we have already pointed out that the two conformers of nitrous acid are almost degenerate so that an equilibrium cis-HONO and trans-HONO can be established in the atmosphere thorough

cis-HONO ⇌ trans-HONO (11) and the corresponding equilibrium constant is

#$%&% =

[()*+,#$%&%] [./,#$%&%]

[5]

Taking into account this equilibrium, and considering the whole concentration of nitrous acid as: [HONO] = [cis-HONO] + [trans-HOHO]

[6]

the reaction rates (4) can be written as v =

!

012345 6

[7898][:] +

!;

The Atmospheric Oxidation of HONO by OH, Cl, and ClO Radicals

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