From O2â-Initiated SO2 Oxidation to Sulfate Formation in the Gas

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A: Kinetics, Dynamics, Photochemistry, and Excited States

From O2--Initiated SO2 Oxidation to Sulfate Formation in the Gas-Phase Narcisse Tchinda Tsona, Junyao Li, and Lin Du J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b03381 • Publication Date (Web): 20 Jun 2018 Downloaded from http://pubs.acs.org on June 22, 2018

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The Journal of Physical Chemistry

From O2--Initiated SO2 Oxidation to Sulfate Formation in the Gas-Phase Narcisse T. Tsona, Junyao Li and Lin Du* Environment Research Institute, Shandong University, Shanda South Road 27, 250100 Shandong, China

Corresponding Author * E-mail: [email protected], Tel: +86 531 883 660 72.

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Abstract We have investigated the chemical fate of O2SOO-, the immediate product of the reaction between sulfur dioxide (SO2) and the superoxide ion (O2-), by reactions with nitrogen oxides (NO and NO2) using high-level theoretical calculations. Both reactions with NO and NO2 lead to exergonic formation of adducts, which subsequently overcome low energy barriers to form SO3 + NO3- and SO4- + NO, with rate constants of 6.9 × 10-10 and 6.3 × 10-10 cm3 molecule-1 s-1, respectively. Reactions with water are ~15-23 times slower than corresponding naked reactions at ambient conditions, hence not slow enough to be prevented at these conditions. The studied reactions are not only useful for understanding ionic SO2 oxidation in the atmosphere and in chamber experiments but also provide a new mechanism for the gas-phase formation of sulfate from an ion-induced mechanism. These reactions may enhance our understanding of the early stages of secondary aerosol formation.

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1. Introduction The formation of atmospheric aerosol particles is controlled by different processes, starting from the aggregation of gaseous molecules forming small molecular clusters, to their growth to sizes where they affect global climate.1-2 Despite the intensive research in the field of aerosol science since recent decades, the complete mechanisms and the identity of the different species involved in atmospheric aerosol formation are still uncertain. It is, however, well established that sulfuric acid (H2SO4) is the central species responsible for the aggregation of small molecules in the early stages of aerosol formation,3-4 while the growth stage is mainly controlled by organics.5-6 It was shown that the concentration of atmospheric H2SO4 correlates well with the nanoparticles formation rate7-8 and, yet until recently, the known concentration of H2SO4 was unable to explain the observed particle formation rates.9-13 However, due to the high climatic impact of aerosols,14 any deficiency of H2SO4 formation rates in climate models causes large uncertainties, e.g. on temperature predictions.8 The concentration of sulfuric acid used in climate models is mainly estimated from oxidation of sulfur dioxide (SO2) by the OH radical15 and the Criegee intermediates16-17 in electrically neutral mechanisms. During the last decade, the enhancing effect of ions in aerosol formation was evidenced from chamber studies,18-19 and few mechanisms of H2SO4 formation from ion-induced SO2 oxidation were recently proved theoretically.20-21 Ion-induced SO2 reactions remain weakly explored, probably due to their complexity. Ions are highly reactive (anions are more reactive than cations22-23) and each ion may likely trigger new reactions or recombine with oppositely charged counterparts under relevant atmospheric temperatures and humidity to form neutral particles.24 Most anions readily react with atmospheric trace constituents and reactions involving SO2 form more oxidized sulfur-containing anions,25-26 which likely end up as H2SO4, the terminal oxidation species of sulfur in the atmosphere. It was also evidenced from experiments that high oxidized sulfur-containing anions readily form in ionized SO2/NH3/H2O/air and SO2/H2O/air mixtures, 3



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as a result of SO2 ionization by reactions with primary negative ions.27-28 Of considerable interest in these processes is the reaction between SO2 and the superoxide ion (O2-), SO2 + O2- → O2SOO-

(1)

O2- is continuously produced in the gas-phase upon ionization by galactic cosmic rays and in most experimental setups.29-30 Due to the high electron affinity and high concentration of O2 in the atmosphere, free electrons can bind to O2 molecules and form O2- in a few nanoseconds. As a primary anion formed upon ionization by galactic cosmic rays, the production rate of O2- can be approximated to the typical ion production rate in the atmosphere, 2 to 100 cm-3 s-1 depending on the altitude.24,31 O2- plays a fundamental role in the negative ion transformation processes in the atmosphere.32 Reaction (1) has repeatedly been explored in laboratory studies25-26,33-36 and the structure of its most likely product was recently assigned using ab initio calculations.37 Having a peroxy structure, the product of reaction (1), O2SOO-,

was found to be prevented from

isomerizing to the sulfate radical ion (SO4-) by 30 kcal mol-1 energy barrier, and although a second SO2 molecule was found to lower the energy barrier to 21 kcal mol-1, the formation of SO4- from reaction (1) was still hindered.37 Atmospheric half-lives of O2SOO-, 109 s and 3 × 102 s, based on its conversion rate constants in the absence and the presence of a second SO2 molecule, respectively, indicate that this molecular ion would live long enough to experience collisions with most abundant atmospheric trace oxidants such as ozone (O3), nitric oxide (NO), and nitrogen oxide (NO2). The collision with NO2 was formerly explored in a laboratory study by Fehsenfeld and Ferguson and the following reaction pathways were found, with approximate measured rate constants of 6×10-11 and 4×10-11 cm3 molecule-1 s-1 for reactions (2a) and (2b), respectively, at 1.5 % relative humidity (RH).25 O2SOO- + NO2 → NO2- + SO2 + O2 → NO3- + SO3 4


(2a) (2b)

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Reaction (2b) is particularly important since the formation of SO3 (the precursor of H2SO4) and NO3- hereby closes the oxidation process of reaction (1). Although water effect was not examined in the study of reaction (2b) by Fehsenfeld and Ferguson,25 its impact on atmospheric processes is well established,38-39 and should not be disregarded in this reaction. Upon formation, O2- quickly hydrates and is thermally stabilized at typical atmospheric conditions with at least five water molecules.32,38 Moreover, the inclusion of three water molecules in reaction (1) indicated that O2SOO- and O2SOO-···H2O are the most abundant products formed from O2- + SO2 reaction at ambient conditions.37 This shows the necessity to include water in reaction (2b) under realistic atmospheric conditions. Moreover, in polluted areas with high concentrations of NOx, the fate of O2SOO- would also depend on the reaction with NO.

2. Methods 2.1 Electronic structure calculations When treating charged species, special care must be taken when selecting the appropriate computational method. Related to this, a series of studies involving highly oxidized sulfur anions have successfully employed the CAM-B3LYP functional with the Dunning type basis sets40 to investigate reaction energetics and kinetics, and found good agreement with high level computational methods and experiments.20,37-39,41 In particular, CAM-B3LYP is superior to B3LYP by inclusion of an increasing amount of Hartree-Fock exchange at increasing distances.43 To account for dispersion forces often ill described by most density functionals, the D3 correctional scheme was used in conjunction to CAM-B3LYP.44 This functional was used with the 6-31+G(d,p) basis set to perform all initial configurational scans and geometries optimizations. Optimized geometries at this level of theory were re-optimized with the CAM-B3LYP-D3/aug-cc-pVTZ method. Although when using the Dunning type 5



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basis sets for sulfur-containing species it is recommended to include extra d functions for the sulfur atom, it was recently shown that this is not desirable for charged species, especially when

used

in

conjunction

with

the

CAM-B3LYP

functional.20

The

CAM-B3LYP-D3/aug-cc-pVTZ method is particularly suitable to study charged systems as both the density functional and the basis set have the ability to accurately reproduce the diffuse nature of the extra electron at increasing distances.40,43 Vibrational frequencies, zero-point vibrational energies (ZPVE), and thermal contributions to energies were calculated at the CAM-B3LYP-D3/aug-cc-pVTZ level of theory under the rigid rotor-harmonic oscillator approximation (RRHO) at 298.15 K and 1 atm. Under the RRHO approximation, the accurate determination of the Gibbs free energies can be affected by two factors: the inclusion of low-lying and anharmonic vibrational frequencies.45 While the anharmonic treatment of vibrational frequencies in the determination of the partition function leads to more accurate results, it makes the calculations to be computationally unaffordable. A usual way to solve for the anharmonicity is to determine anharmonic scaling factors for harmonic frequencies, which however, generally applies only for small systems.46-48 Another difficulty is that derived scaling factors depend on inter- and intra-molecular vibrations of specific systems and hence, may lead to erroneous results when applied to other systems. Since our systems are relatively large, coupled to the lack of experimental results, neither scaling factors nor anharmonic vibrational frequencies analyses were considered in this study. Although this omission may lead to errors in Gibbs free energies, these errors rarely exceed 1 kcal mol-1.49 Transition states (TS) structures were obtained by first scanning the configurational space of the reactants states along the reaction coordinate, and then refining the best TS guesses using the Synchronous Transit Quasi-Newton method.50 Intrinsic reaction coordinate calculations51 were further performed on the TS structures to insure they connected the reactants to desired products. Single-point energy calculations for electronic energies correction were performed on the CAM-B3LYP-D3/aug-cc-pVTZ optimized geometries 6


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using the coupled-cluster method at the UCCSD(T)/aug-cc-pVTZ level of theory. All calculations were carried out using the Gaussian 09 package program.52

2.2 Kinetics Reaction rate constants were determined by considering pseudo steady-state approximation on the adduct: it is assumed that the main processes for the adduct are its formation from the collision of separate reactants, and its decomposition either to form new products or by evaporating back to the separate reactants, O2SOO- + NO/NO2 ↔ Adduct → Products

(3)

so that the change in its concentration with time is always equal to zero (d[Adduct]/dt = 0). This leads to the following expression for the bimolecular rate constant,

kbimol = kcoll ×

(4)

where kcoll is the collision rate constant of the reactants of Equation (3), kuni is the unimolecular rate constant of the adduct reaction to form the products, and kevap the rate constant of its evaporation to form initial reactants. Further details to obtain Equation (4) can be found in Section S2 of the Supporting Information. As most collisions of ions with polar molecules are barrierless, they are usually modelled using capture theories, which assume that the reaction rate is governed by long-range interactions, whereas the short-range reaction probability is unity.53 The capture theory was first developed by Langevin in early twentieth century and led to an expression of the rate constant that is independent of the temperature. From classical trajectory calculations, Su and Chesnavich parametrized an improved temperature-dependent rate constant based on the Langevin capture theory, which was used to determine the collision rate constant of the

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reactants in this study.54 By its definition, the parametrization of Su and Chesnavich is the Langevin capture rate constant, scaled by a temperature-dependent term and is given as:

= ×

. .

+ 0.9754&

(5)

where kL = qµ−1/2(πα/ε0)1/2 is the Langevin capture rate constant, x = µD/(8πε0αkBT)1/2, q is the charge of the ion, µ is the reduced mass of the colliding species, ε0 is the vacuum permittivity, α and µD are the polarizability and dipole moment of the polar molecule, and kB is Boltzmann’s constant. The rate constant (kevap) of evaporation of the adduct back to initial reactants was calculated using the detailed balance condition as ∆3

'()* = × +),- × exp − & 45

(6)

where ρatm is the standard density (at T = 298.15 K and p = 1 atm, ρatm = 2.5 × 1019 molecule cm-3), R is the molar gas constant, and ∆G is the Gibbs free energy change of the formation of initial reactants of Equation (3) from the adduct. The unimolecular rate constant (kuni) of the conversion of the adduct to the products was calculated using the harmonic transition state theory,55 given by the following equation

678 =

∏ :;; > ∏ :

From O2â-Initiated SO2 Oxidation to Sulfate Formation in the Gas

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