Influence of Ammonia and Water on the Fate of Sulfur Trioxide in the

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Influence of Ammonia and Water on the Fate of Sulfur Trioxide in Troposphere: Theoretical investigation of Sulfamic Acid and Sulfuric Acid Formation Pathways Saptarshi Sarkar, Binod Kumar Oram, and Biman Bandyopadhyay J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b09306 • Publication Date (Web): 22 Mar 2019 Downloaded from http://pubs.acs.org on March 22, 2019

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The Journal of Physical Chemistry

Influence of Ammonia and Water on The Fate of Sulfur Trioxide in Troposphere: Theoretical Investigation of Sulfamic Acid and Sulfuric Acid Formation Pathways Saptarshi Sarkar, Binod Kumar Oram, and Biman Bandyopadhyay∗ Department of Chemistry, Malaviya National Institute of Technology Jaipur, Jaipur, 302017,India E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1

Abstract

Reaction of ammonia with SO3 as a potential source of sulfamic acid in troposphere has been investigated by means of electronic structure and chemical kinetic calculations. Besides, the hydrolysis reaction, which is known to be a major atmospheric decay channel of SO3 , has also been investigated. The catalytic effects of ammonia and water on both the reactions have been studied. Rate coefficients for all the studied reaction channels were calculated using transition state theory employing pre-equilibrium approximation. Calculated rate coefficients for a number of catalyzed hydrolysis and ammonolysis processes were found to be much higher (by ∼ 105 to ∼ 109 times) than the gas kinetic limit at ambient temperature. With decrease in temperature, due to negative temperature dependence of rate coefficients, that difference became even larger (up to ∼ 1016 times). Therefore, in order to remove the discrepancies, rate coefficients for all the studied reaction channels were calculated by means of master equation. The results showed marked improvements with only one channel showing slightly higher rate coefficient above the gas kinetic limit. The rate coefficients for catalyzed channels obtained from master equation also showed negative temperature dependence, albeit to much smaller extent. The uncatalyzed ammonolysis reaction, similar to the corresponding hydrolysis, was found to be too slow to have any practical atmospheric implication. For both reactions, ammonia catalyzed pathways have higher rate coefficients than water catalyzed ones. Between hydrolysis and ammonolysis, the latter showed higher rate coefficient. In spite of that, ammonolysis is expected to have negligible contribution in the tropospheric loss process of SO3 due to large difference in concentration values between water and ammonia in troposphere.

2

Introduction

SO3 is considered to be one of the major pollutants 1–6 present in Earth’s atmosphere due to its role in the formation of atmospheric aerosols and its contributions towards acid rain via 2


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formation of sulfuric acid, i.e H2 SO4 (SA). 7–10 SO3 is mainly formed in atmosphere by gas phase oxidation of sulfur dioxide (SO2 ). 7,11–13 In atmosphere, SO3 rapidly reacts with water to form SA. SO3 has drawn the attention of atmospheric chemists for a long time because of its pivotal role in the atmospheric acid rain and various nucleation processes. 14–17 Formation of SA through gas phase hydrolysis of SO3 has been extensively studied by various research groups, both experimentally 13,18–25 as well as theoretically. 26–36 Various investigations suggested that SA formation through the reaction between SO3 and water monomer (WM) is unfavorable under atmospheric conditions due to high energy barrier (> 28 kcal mol−1 ). 26–28 As a result, effect of different catalysts, namely water, 13,18–23,25–27,34–36 hydroperoxy radical, 29 formic acid, 30,31 SA (as auto catalyst), 32 nitric acid, 33 and ammonia (AM), 35 on the hydrolysis of SO3 were studied by various research groups. Considering the combined effect of rate constants and catalysts’ concentrations, WM and AM were proposed to have significant contribution in total SA formation in troposphere. Very recently, it has been shown for ketene and SO3 that, similar to the hydrolysis process, ammonolysis could also be an important tropospheric loss channel. 37,38 In fact, Li et al. 38 showed that AM can self catalyze the ammonolysis of SO3 , similar to the widely known self catalysis of SO3 hydrolysis by WM. Therefore, keeping in mind that SO3 is known to form stable complex with AM 13,23,39–44 as well as react with it, and also the fact that AM and WM is closely connected to the atmospheric fate of SO3 , it becomes imperative that ammonolysis of SO3 be studied and compared with the already established route of hydrolysis in a detailed manner. Mechanistically, ammonolysis is very similar to hydrolysis; both involve initially formation of pre-reactive complexes (RCs) followed by unimolecular transformations to form the final products. Ammonolysis of SO3 results in formation of sulfamic acid i.e, HSO3 NH2 (SMA) in troposphere.

SO3 + WM

SA

SO3 + AM

SMA 3



SMA plays an important role as scavenger of nitrous acid and has got various industrial applications. 45 It may act as an effective nucleation agent for the formation of atmospheric aerosols and cloud particles. 13,40,42,44,46 There exist a number of experimental 13,23,39,40 and theoretical 38,41–44,47 studies on the formation of SMA through ammonolysis of SO3 in the gas phase. Lovejoy and Hanson 13 experimentally measured the effective second order rate coefficient for the reaction to be 2 × 10−11 cm3 molecule−1 s−1 at 295 K under 1 atm N2 pressure, which indicates that ammonolysis could be a potential atmospheric loss channel for SO3 . However, existing theoretical studies suggested that SMA formation via ammonolysis of SO3 is unfavorable due to high reaction barrier (28.6 kcal mol−1 ). 41,47 Very recently Li et al. 38 have shown that an additional AM as self-catalyst and SMA as auto-catalyst could facilitate the reaction and the rate coefficient was reported to be ∼ 10−10 cm3 molecule−1 s−1 at ambient temperature. They also suggested that the discrepancy between experimental and theoretical results was mainly due to the presence of facilitator molecules. There exist a number of theoretical investigations on the reaction and possible complex formation involving SO3 , WM and AM. 41–43 Pawlowski et al. 42 have shown that stabilization energy of the RC (SO3 -AM) for ammonolysis of SO3 increases with increasing number of additional WM. This result strongly indicates that ammonolysis of SO3 could be effective for atmospheric nucleation process and cloud formation in presence of WM. Very recently, Li et al. 38 studied the self-catalytic effect on the ammonolysis of SO3 by means of energy calculation and rate calculations. Except this, there exists no detailed theoretical investigations on the SMA formation through ammonolysis of SO3 under atmospheric conditions to the best of our knowledge. So, a detailed investigation of the reaction of SO3 with AM and assessment of its atmospheric implications are carried out by investigating the catalytic effect of WM and AM on the reaction. Possibility of other catalysts certainly remains under tropospheric conditions, but we have focused on the catalytic effects of WM and AM on ammonolysis of SO3 in this work. This is due to the fact that hydrolysis of SO3 has been shown to be mostly facilitated by WM and AM.

4


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3 3.1

Methodologies Electronic structure calculation

Geometries of isolated reactants, RCs, transition states (TSs), pre-product complexes (PCs) and isolated products have been optimized at B3LYP/cc-pV(T+d)Z level of theory. Molecular geometries with all positive normal mode of frequencies represent minima on potential energy surface (PES) while, the geometries containing single imaginary frequency represent TSs. To improve the reaction energetics, single point energies of all the species were calculated at CCSD(T)/cc-pV(T+d)Z level of theory, using geometry optimized at B3LYP/ccpV(T+d)Z level of theory. Previous theoretical investigations on the WM catalyzed hydrolysis of SO3 were carried out by means of electronic structure calculations at CCSD(T)/ccpV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory 32,35 and the reported rate coefficients were found to be consistent with experimentally measured values. 24 Additionally, we have carried out calculations for the WM catalyzed hydrolysis channel at MP2 level using aug-cc-PVDZ and cc-pVTZ basis sets, followed by single point energy calculations at CCSD(T) level using the same basis sets. Relative ZPE corrected energies (kcal mol−1 ) with respect to isolated reactants and rate coefficients (cm3 molecule−1 s−1 ) values at 298 K calculated using these two different levels of theories are listed in Table S1 and S2, respectively. When viewed against the results obtained from CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory, these values clearly indicate that B3LYP results match better with experimental values over MP2. 24 Therefore, we have carried out the calculations for all the studied reaction channels using CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory. Intrinsic reaction coordinate (IRC) calculations were carried out for confirmation of correct connectivity between TSs and the corresponding RCs and PCs. All these calculations were carried out using Gaussian 09 suites of programs. 48 All the energy values reported here are calculated 5



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at CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z levels of theory with zero point energy (ZPE) correction done at B3LYP/cc-pV(T+d)Z level, unless otherwise stated.

3.2

Chemical kinetics calculation

The reaction scheme for uncatalyzed addition of X (where, X = WM and AM for hydrolysis and ammonolysis, respectively) to SO3 is shown in Scheme 1. kfX

SO3 + X

krX

SO3 -X

X kuni

P

Scheme 1: Reaction scheme for addition of X to SO3 (X = WM and AM)

Assuming, SO3 -X is in equilibrium with isolated reactants and then SO3 -X undergoes unimolecular transformation through corresponding TS to form P (P = SA or SMA when X = WM or AM, respectively), the reaction rate under pre-equilibrium approximation can be written as -

Rate = kX [SO3 ][X]

X X X Where, kX = Keq kuni , and Keq =

(1)

kfX krX

From Scheme 1, the two possible reaction channels are as follows: For X = WM, P = SA SO3 -WM

Channel A: SO3 + WM

SA

For X = AM, P = SMA SO3 -AM

Channel B: SO3 + AM

SMA

Under the influence of a catalyst (Y), the addition of X to SO3 could follow two different paths; either SO3 -X complex reacts with Y or SO3 reacts with X-Y complex. When SO3 6


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X reacts with Y, they initially form an RC, i.e, SO3 -X-Y which undergoes unimolecular transformation to form P-Y (Scheme 2).

SO3 -X + Y

kfX+Y krX+Y

SO3 -X-Y

XY kuni

P-Y

Scheme 2: Reaction scheme for addition of Y to SO3 -X (X,Y = WM and AM)

Here, similar to the uncatalyzed reaction, we have assumed that SO3 -X-Y complex is in equilibrium with the reactants SO3 -X and Y. Then it undergoes unimolecular transformation through corresponding TS to form P-Y. Under pre-equilibrium approximation rate of the reaction is given by-

Rate = kX+Y [SO3 − X][Y ] X+Y X+Y XY = kuni , and Keq Where, kX+Y = Keq

(2)

kfX+Y krX+Y

From Scheme 2, there are four different reaction pathways possible; two each for SA and SMA formation by varying X and Y as followsFor X = WM, Y = WM, P = SA Channel C:

SO3 -WM + WM

SO3 -WM-WM

SA-WM

SO3 -WM-AM

SA-AM

For X = WM, Y = AM, P = SA Channel D:

SO3 -WM + AM

For X = AM, Y = WM, P = SMA Channel E:

SO3 -AM + WM

SO3 -AM-WM

SMA-WM

SO3 -AM-AM

SMA-AM

For X = AM, Y = AM, P = SMA Channel F:

SO3 -AM + AM 7



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The other reaction channel involving SO3 , X and Y is when SO3 reacts with X-Y complex (Scheme 3).

SO3 + X-Y

kfX−Y krX−Y

SO3 -X-Y

XY kuni

P-Y

Scheme 3: Reaction scheme for addition of X-Y to SO3 (X,Y = WM and AM)

Here, we have assumed that SO3 -X-Y is in equilibrium with reactants SO3 and X-Y, which undergoes unimolecular transformation through corresponding TS to form P-Y. It is important to note that, for the same set of X and Y, both Scheme 2 and 3 proceeds to same RC (SO3 -X-Y) and TS (TSSO3 −X−Y ), i.e. the unimolecular step is same for the both schemes. Under pre-equilibrium approximation the reaction rate is-

Rate = kX−Y [SO3 ][X − Y ] X−Y XY X−Y Where, kX−Y = Keq kuni , and Keq =

(3)

kfX−Y krX−Y

Similar to Scheme 2, from Scheme 3, four different reaction pathways are possible, two each for SA and SMA formation, involving X and Y as followsFor X = WM, Y = WM, P = SA Channel G:

SO3 + WM-WM

SO3 -WM-WM

SA-WM

SO3 -WM-AM

SA-AM

For X = WM, Y = AM, P = SA Channel H:

SO3 + WM-AM

X = AM, Y = AM, P = SMA Channel I:

SO3 -AM-AM

SO3 + AM-AM

For X = AM, Y = WM, P = SMA 8


SMA-AM

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Channel J:

SO3 -AM-WM

SO3 + AM-WM

SMA-WM

It is worth mentioning here that AM-WM complex exhibits a hydrogen bond between N atom of AM and H atom of WM, i.e. WM acts as the proton donor and AM as the acceptor. 49,50 The other possibility, where WM acts as a proton acceptor and AM as proton donor, is never observed and only one geometry is possible for AM-WM complex. Hence, SMA formation through reaction between SO3 and AM-WM (Channel J) is not possible due to the fact that, the free O atom of WM would bind to SO3 leading to the formation of SA instead of SMA. Therefore, effectively there are altogether nine possible pathways for ammonolysis and hydrolysis of SO3 depending upon various combinations of WM and AM as reactant and catalyst. XY X X−Y X+Y X have been calculated using transition state theory (TST) and kuni , kuni , Keq , Keq The Keq

as-

X Keq =

QSO3 −X −(ESO3 −X −ESO3 −EX ) RT e QSO3 QX

(4)

X+Y Keq =

QSO3 −X−Y −(ESO3 −X−Y −ESO3 −X −EY ) RT e QSO3 −X QY

(5)

X−Y Keq =

QSO3 −X−Y −(ESO3 −X−Y −ESO3 −EX−Y ) RT e QSO3 QX−Y

(6)

X XY kuni (, kuni ) = σΓ

kB T QTS −(ETS −ERC ) RT e h QRC

(7)

Here, Q is the product of translational, rotational, vibrational and electronic canonical partition functions of the respective species, E denotes the ZPE corrected energies of respective species. σ represents the reaction symmetry number, Γ is the tunneling correction for the 9



reaction (taken into account by assuming unsymmetrical Eckart barrier). 51 kB , h and R are the Boltzmann constant, Planck constant and ideal gas constant, respectively. T is the temperature in Kelvin. The rate coefficients were calculated using TST with TheRate software. 52,53 Alongside, we have carried out the kinetic calculations for all the studied reaction channels employing master equation based method as implemented in MESMER program package 54 using Bartis-Widom method. 55–58 As discussed earlier, all the hydrolysis and ammonolysis reaction channels proceed via formation of RCs through barrierless bimolecular association reactions between reactants followed by unimolecular transformation through TS to form PC. Inverse Laplace transformation (ILT) method has been used to carry out the kinetic calculations for the barrierless bimolecular reaction steps. In this regard, the required Arrhenius pre-exponential factors associated with the bimolecular reactions (Table S3 in supporting information) were calculated using KTOOLS codes as implemented in MULTIWELL program suites. 59 Rate coefficients for unimolecular reaction channels have been calculated using Rice-Ramsperger-Kessel-Marcus (RRKM) theory as implemented in MESMER software.

4

Results and Discussion

In the present investigation, we have tried to determine the atmospheric fate of SO3 by investigating its ammonolysis and hydrolysis reactions by means of electronic structure and rate coefficient calculations. As discussed in the preceding section, there are altogether nine pathways possible when WM and AM are considered to participate in the reaction scheme as both reactants and catalysts.

10


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4.1 4.1.1

Hydrolysis of SO3 Uncatalyzed hydrolysis

The reaction is initiated by SO3 binding with WM to form SO3 -WM (Figure 1a) with a binding energy of -7.6 kcal mol−1 (Table 1 and Figure 2a), which subsequently forms SA through a four membered cyclic TS with a barrier height of 16.0 kcal mol−1 . Stabilization energy of SA was found to be -19.5 kcal mol−1 with respect to isolated reactants. The energy values match well with the results of earlier investigations. 31–33 The Gibbs free energy (GFE) barrier for this reaction at 298 K was found to be 25.7 kcal mol−1 with respect to isolated reactants (Table 1 and Figure 3a).

4.1.2

Catalyzed hydrolysis

As discussed earlier in Section 3.2, there exist two WM catalyzed Channels (C and G) and two AM catalyzed Channels (D and H). Earlier we carried out a detailed study of the above mentioned four reaction channels using the same level of calculation used here in this work. 35 The molecular structures, energetics and GFE profile are shown in Figure 1, 2 and 3, respectively. The corresponding values (relative energies and GFEs) are given in Table 1. In fact, the relative stabilities of a number of the RCs are so high that, depending on the concentrations of the isolated reactants, they could be actually present in the atmosphere. Barrier height for WM catalyzed channels were found to be 8 kcal mol−1 higher than that of AM catalyzed channel (Figure 2b and c ). Therefore, it can be safely said that energetically AM catalyzed hydrolysis pathways are more favorable over WM catalyzed pathways.

4.2 4.2.1

Ammonolysis of SO3 Uncatalyzed ammonolysis

Uncatalyzed ammonolysis of SO3 (Channel B) also proceeds through formation of RC (SO3 AM) followed by unimolecular transformation through a four membered cyclic TSSO3 −AM to 11



form SMA (Figure 4a). The relative energies of SO3 -AM, TSSO3 −AM and SMA with respect to isolated reactants are -17.6, 9.0 and -18.9 kcal mol−1 , respectively (Table 1 and Figure 5a) and these energy values match well with the earlier findings. 38,47 ZPE corrected relative GFE with respect to isolated reactants for SO3 -AM, TSSO3 −AM and SMA were found to be -5.2, 18.8 and -7.7 kcal mol−1 (Table 1 and Figure 6a). Therefore, energetically the uncatalyzed ammonolysis is more favorable than uncatalyzed hydrolysis of process.

4.2.2

Catalyzed ammonolysis

WM catalyzed: As discussed earlier, unlike WM catalyzed hydrolysis, there is only a single pathway possible for WM catalyzed ammonolysis (Channel E). The reaction proceeds via formation of a RC (SO3 -AM-WM; stabilization energy is -11.7 kcal mol−1 ) through the reaction between SO3 -AM and WM (Figure 4b and 5b). Then SO3 -AM-WM complex forms a six membered cyclic TS (TSSO3 −AM−WM ) to form SMA-WM with stabilization energy -9.1 kcal mol−1 and the corresponding GFE barrier was found to be 10.1 kcal mol−1 (Table 1 and Figure 6b). The reaction is essentially a barrierless process as TSSO3 −AM−WM lies below SO3 -AM and WM in the PES (Figure 5b). AM catalyzed: This reaction, similar to WM catalyzed hydrolysis, could occur via two different pathways. The first pathway (Channel F) involves binding of SO3 -AM with AM to form the RC (SO3 -AM-AM) (Figure 4c). Stabilization energy of SO3 -AM-AM was found to be -12.6 kcal mol−1 with respect to isolated SO3 -AM complex and AM (Figure 5c). In the second pathway (Channel I), SO3 binds with AM-AM to form the same RC (SO3 -AMAM) with stabilization energy is -27.9 kcal mol−1 with respect to SO3 and AM-AM. Then for both channels, SO3 -AM-AM proceeds through a six membered cyclic TS (TSSO3 −AM−AM ) to form SMA-AM with stabilization energy -30.5 kcal mol−1 . Similar to its WM catalyzed counterpart, AM catalyzed ammonolysis also is a barrierless process as is clearly evident from Figure 5c. The unimolecular GFE barrier for this reaction was found to be 5.8 kcal mol−1 (Figure 6c), which matches well with the value reported by Li et al.(5.7 kcal mol−1 ). 38

12


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It is quite clear from the above findings that, similar to hydrolysis, AM acts as a better catalyst than WM for ammonolysis too, as is evident from reaction energetics.

4.3 4.3.1

Rate coefficients: Transition state theory:

TST has been routinely used for calculation of rate coefficients of hydrolysis and ammonolysis of SO3 till date. 32,35,38 So initially rate coefficients for all the studied channels have been calculated using TST within the range 213 to 320 K under tropospheric conditions (Table 2). The rate coefficients for uncatalyzed hydrolysis and ammonolysis of SO3 were found to be 1.4 × 10−23 and 2.7 × 10−18 cm3 molecule−1 s−1 , respectively, both at 298 K. The values match qualitatively with the values available in literature. 38 At 298 K, rate coefficient values given in Table 2 clearly show that, in case of hydrolysis, the rate coefficients of AM catalyzed pathways are significantly higher than the WM catalyzed pathways. Rate coefficient for AM catalyzed ammonolysis process via Channel F and I were found to be 5.6 × 10−9 and 8.6 × 10−1 cm3 molecule−1 s−1 , respectively (Table 2) at 298 K. The rate coefficients are much higher than the same for water catalyzed pathway (Channel E) and it matches well, for Channel F, with values reported by Li et al.(10−10 cm3 molecule−1 s−1 ) for the same channel. 38 It is worth mentioning here that the calculated rate coefficients at 298 K (Table 2) Channels G and F were found to be very close to, whereas, the same for Channels D, H and I were much higher than the gas kinetic limit. In fact, leaving Channels C and F, all the catalyzed reaction channels show rate coefficients above gas kinetic limit at some temperatures encountered in troposphere (Table 2). The PES of the catalyzed reaction channels (Figure 2 and 5) involve low lying TSs and a closer look at them reveals that, for the channels showing rate coefficients above the gas kinetic limit, the TSs are deeply buried below the energies of the isolated reactants. As a result, the pre-equilibrium approximation completely breaks down in these cases resulting in much higher rate coefficients. 13



Besides, the temperature dependence of the rate coefficients for the catalyzed reaction channels also provide additional support to the breakdown of the pre-equilibrium approximation. Normally, reactions having rate coefficients close to the gas kinetic limit show negligible temperature dependence. Nevertheless, rate coefficients for all the catalyzed reaction channels show marked temperature dependence within the temperature window (213 to 320 K) encountered in troposphere (Table 2 and Figure 7). As temperature in troposphere varies by more than 100 K, temperature dependence of rate coefficients is known to play a significant role on the nature of various atmospherically important reactions, exhibited by a number of theoretical 35,37,60–63 and experimental studies. 24,64–67 Therefore, in addition to having correct rate coefficients at ambient temperatures, having proper trend of temperature dependence is also of prime importance from atmospheric viewpoint. This requirement is amplified by the fact that all the existing experimental investigations on both hydrolysis and ammonolysis of SO3 were performed at ambient temperatures (∼ 280 to 340 K) 23,24 with no experimental evidence in the lower temperatures experienced in higher altitudes in troposphere. In addition, earlier theoretical studies did not explicitly discussed the temperature dependence of rate coefficients for these reaction channels.

4.3.2

Master equation:

As evident from the discussions in the preceding section, TST coupled with pre-equilibrium approximation do not provide reliable results to estimate the rate coefficients and their temperature dependence for the catalyzed reaction channels involving hydrolysis and ammonolysis of SO3 . Therefore, we have calculated rate coefficients for all the studied reaction channels using master equation (Table 3). At 298 K, rate coefficients for both uncatalyzed hydrolysis (1.5 × 10−23 cm3 molecule−1 s−1 ) and ammonolysis (1.8 × 10−18 cm3 molecule−1 s−1 ) channels match well with the earlier findings and also with the values calculated using TST. Among the various catalyzed channels, hydrolysis catalyzed by AM were found to have higher rate coefficients (7.2 × 10−10 and 4.7 × 10−12 cm3 molecule−1 s−1 for Channels D and 14


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H, respectively) compared to their WM catalyzed counterparts (1.4 × 10−12 and 9.7 × 10−13 cm3 molecule−1 s−1 for Channels C and G, respectively). Similarly, for ammonolysis, AM catalyzed channels were found to have higher rate coefficients (4.1 × 10−10 and 7.7 × 10−9 cm3 molecule−1 s−1 for Channels F and I, respectively) with respect to the WM catalyzed channel (5.4 × 10−14 cm3 molecule−1 s−1 for Channel E). Therefore, considering both hydrolysis and ammonolysis, the highest values of rate coefficients were found for AM catalyzed ammonolysis among all the studied reaction channels. It must be noted here that rate coefficients for all the studied reaction channels were within the gas kinetic limit at 298 K, except Channel I, which was only marginally higher. This is a significant improvement over the results obtained using TST, which predicted values as high as 109 times higher than the gas kinetic limit. In order to check whether the improvement in values of rate coefficients are at some particular temperatures or throughout the whole temperature range encountered in troposphere, ln(k) vs (1000/T ) was plotted for all the studied reaction channels within the 213-320 K range (Figure 8). Rate coefficients for all the channels, except Channel A, show negative temperature dependence, which is in accordance to what was found for TST. Nevertheless, the absolute changes in rate coefficients over the whole temperature range are remarkably smaller in this case. This is exactly what is to be expected as fast bimolecular reactions approaching the gas kinetic limit shows negligible temperature dependence. At lower temperature limit (213 K), where all the catalyzed reaction show highest rate coefficient values due to the negative temperature dependence, rate coefficients values of Channel H and I were found to be only ∼ 102 times higher than the gas kinetic limit, as against ∼ 1016 times higher (for Channel I) in case of TST. Therefore, in a nutshell, it can safely be inferred from the above findings that, although TST has been widely used for reactions of SO3 with WM and AM in the past, master equation proves to be a much more reliable tool while dealing with these reactions under tropospheric conditions.

15



5

Atmospheric implications:

The overall contribution of a particular reaction in troposphere is determined by the reaction rate. As a result, the rate coefficient alone is not sufficient to predict the atmospheric importance of the reaction as the rate expression also contains concentration terms of reactants participating in the corresponding reaction channel. Therefore, while comparing the hydrolysis and ammonolysis of SO3 as sources of SA and SMA, respectively, in Earth’s atmosphere, concentrations of WM and AM will have to be considered along with the rate coefficients of the respective reactions. Atmospheric abundance of WM is generally expressed in terms of relative humidity (RH), reaching its maximum value at 100 % RH, whereas, mixing ratio of AM is known to vary from 0.1 to 10 ppbv in troposphere. 68–70 When expressed in terms of molecular concentrations, WM concentrations are found to vary within ∼ 1016 − 1017 molecules cm−3 at 0 km altitude when the range of RH is taken within 20-100 %. Similarly, AM concentration, within 0.1 to 10 ppbv range, varies between ∼ 109 − 1011 molecules cm−3 . As a result, even when AM concentration reaches its higher limits (10 ppbv) and humidity is low enough (20% RH), WM concentration would be ∼ 105 times greater than that of AM concentration. Now, in terms of rate coefficients, AM catalyzed ammonolysis is ∼ 103 times faster than WM catalyzed hydrolysis of SO3 . Therefore, when one considers only the rate coefficients, it might appear that ammonolysis might have a significant contribution in the loss mechanism of SO3 . But the large difference in WM and AM concentrations clearly indicates that overall rate of the hydrolysis channel will be at least 102 higher than the same for the ammonolysis channel. As a result, the primary loss mechanism of SO3 in troposphere would be through hydrolysis with negligible contribution from the ammonolysis channel.

6

Summary

Formation of sulfamic acid through ammonolysis of SO3 and catalytic effects of water and ammonia on the reaction have been investigated by means of quantum chemical calculations 16


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at B3LYP and CCSD(T) levels of theory employing cc-pV(T+d)Z basis set. Besides, hydrolysis of SO3 along with the catalytic role of water and ammonia on this reaction have also been revisited at the same level of theory. Rate coefficients for all the reactions were calculated using transition state theory under the pre-equilibrium approximation. It was found that a number of catalyzed reaction channels showed rate coefficients significantly above the gas kinetic limit. In addition, all the catalyzed channels showed appreciably high negative temperature dependence making the rate coefficients even larger at lower temperatures. Therefore, in order to remove the discrepancies, rate coefficients for all the studied channels were calculated using master equation. The rate coefficients calculated using master equation were found to be consistent with only one channel showing slightly higher value than the gas kinetic limit. The master equation based rate coefficients for all the catalyzed reaction channels also showed negative temperature dependence, but the absolute changes in rate coefficients were much smaller. In absence of any catalyst, ammonolysis was found to be more favorable than hydrolysis; both in terms of activation barrier and rate coefficient. Out of water and ammonia, the latter was found to be a better catalyst for both hydrolysis and ammonolysis reactions. Between, hydrolysis and ammonolysis, the latter was found to be faster in terms of rate coefficient values. Although the rate coefficients for ammonolysis were found to be larger than that of the hydrolysis process, the former is expected to have negligible contribution in the atmospheric loss process of SO3 . This is mainly owing to the large difference in atmospheric concentration of water and ammonia, that can more than compensate the difference in rate coefficient values.

7

Acknowledgement

The authors acknowledge Dr. Arijit K. De, IISER, Mohali for Gaussian 09 calculations and Data Centre, MNIT Jaipur for computational facilities. SS and BKO acknowledge

17



MNIT Jaipur for senior research fellowship and junior research fellowship, respectively. BB acknowledge DST, Govt. of India for the financial support through sanctioned project [No. ECR/2016/000280].

8

supporting information

Arrhenius pre-equilibrium constant, tropospheric concentrations of water, ammonia, water dimer, ammonia-water and ammonia dimer, equilibrium constants and unimolecular rate constants, absolute electronic energies, optimized geometries and normal mode frequencies.

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Table 1: Relative energies (with and without ZPE corrections) and free energies (at 298 K) of all the species with respect isolated reactants calculated at CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory. All the values are in kcal mol−1 Pathway A

B

C

D

E

F

G

H

I

Species SO3 -WM TSSO3 −WM SA SO3 -AM TSSO3 −AM SMA SO3 -WM-WM TSSO3 −WM−WM SA-WM SA+WM SO3 -WM-AM TSSO3 −WM−AM SA-AM SA+AM SO3 -AM-WM TSSO3 −AM−WM SMA-WM SMA+WM SO3 -AM-AM TSSO3 −AM−AM SMA-AM SMA+AM SO3 -WM-WM TSSO3 −WM−WM SA-WM SA+WM SO3 -WM-AM TSSO3 −WM−AM SA-AM SA+AM SO3 -AM-AM TSSO3 −AM−AM SMA-AM SMA+AM

4E 4EZP E -9.9 -7.6 15.3 16.0 -23.0 -19.5 -21.0 -17.6 8.3 9.0 -21.7 -18.9 -16.9 -13.7 -9.5 -7.8 -31.1 -27.4 -17.1 -15.7 -18.6 -15.8 -17.4 -15.8 -33.0 -29.9 -15.9 -14.6 -14.5 -11.7 0.0 -0.1 -10.5 -9.1 -0.6 -1.3 -32.3 -27.9 -25.2 -22.3 -34.1 -30.5 -17.9 -16.6 -16.9 -13.7 -9.5 -7.8 -31.1 -27.4 -17.1 -15.7 -18.6 -15.8 -17.4 -15.8 -33.0 -29.9 -15.9 -14.6 -32.3 -27.9 -25.2 -22.3 -34.1 -30.5 -17.9 -16.6

27


4G 4GZP E -0.2 2.0 25.0 25.7 -10.6 -7.1 -8.6 -5.2 18.2 18.8 -10.5 -7.7 -2.5 0.8 5.0 6.7 -15.6 -11.9 -12.4 -11.0 -4.5 -1.7 -3.5 -2.0 -17.8 -14.7 -10.7 -9.4 -3.4 -0.6 9.6 10.1 -1.1 1.0 -1.9 -1.9 -15.5 -11.1 -8.2 -5.3 -17.8 -14.2 -12.6 -11.3 -2.5 0.8 5.0 6.7 -15.6 -11.9 -12.4 -11.0 -4.5 -1.7 -3.5 -2.0 -17.8 -14.7 -10.7 -9.4 -15.5 -11.1 -8.2 -5.3 -17.8 -14.2 -12.6 -11.3


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Table 2: Rate coefficients (cm3 molecule−1 s−1 ) for hydrolysis and ammonolysis of SO3 at different temperatures calculated by transition state theory T (K) 213 230 259 280 290 298 300 310 320

UN-cat Channel A kWM 5.7×10−24 4.5×10−24 5.2×10−24 8.0×10−24 1.1×10−23 1.4×10−23 1.4×10−23 2.0×10−23 3.0×10−23

Hydrolysis WM-cat Channel C Channel G kWM+WM kWM−WM 1.9×10−10 6.9×10−8 7.1×10−11 1.3×10−8 1.7×10−11 1.2×10−9 −12 7.6×10 3.0×10−10 −12 5.3×10 1.6×10−10 4.1×10−12 1.0×10−10 3.8×10−12 9.4×10−11 2.8×10−12 5.6×10−11 2.1×10−12 3.4×10−11

AM-cat Channel D Channel H kWM+AM kWM−AM 5.2×10−1 5.8 4.8×10−2 3.3×10−1 1.7×10−3 5.9×10−3 −4 2.4×10 5.3×10−4 −4 1.0×10 1.9×10−4 5.4×10−5 8.9×10−5 −5 4.7×10 7.4×10−5 −5 2.2×10 3.1×10−5 1.1×10−5 1.3×10−5

UN-cat Channel B kAM 2.9×10−16 5.4×10−17 8.3×10−18 3.9×10−18 3.1×10−18 2.7×10−18 2.6×10−18 2.4×10−18 2.3×10−18

Ammonolysis WM-cat AM-cat Channel E Channel F Channel I kAM+WM kAM+AM kAM−AM 6.7×10−13 1.2×10−6 9.4×106 3.5×10−13 3.0×10−7 1.4×105 1.6×10−13 4.2×10−8 3.9×102 −13 −8 1.1×10 1.3×10 1.2×101 −14 −9 9.2×10 8.1×10 2.6 8.1×10−14 5.6×10−9 8.6×10−1 7.9×10−14 5.1×10−9 6.5×10−1 6.9×10−14 3.3×10−9 1.8×10−1 6.1×10−14 2.2×10−9 5.3×10−2

Table 3: Rate coefficients (cm3 molecule−1 s−1 ) for hydrolysis and ammonolysis of SO3 at different temperatures calculated by master equation T (K) 213 230 259 280 290 298 300 310 320

Uncat Channel A kWM 4.8×10−24 4.8×10−24 6.3×10−24 9.5×10−24 1.2×10−23 1.5×10−23 1.6×10−23 2.3×10−23 3.2×10−23

Hydrolysis WM-cat Channel C Channel G kWM+WM kWM−WM 8.1×10−12 3.6×10−12 5.8×10−12 2.8×10−12 3.1×10−12 1.8×10−12 2.0×10−12 1.3×10−12 1.6×10−12 1.1×10−12 1.4×10−12 9.7×10−13 1.3×10−12 9.4×10−13 1.1×10−12 8.0×10−13 8.7×10−13 6.8×10−13

AM-cat Channel D Channel H kWM+AM kWM−AM 7.8×10−10 4.5×10−8 4.1×10−10 6.5×10−9 −10 2.2×10 2.7×10−11 −10 5.3×10 7.4×10−12 6.3×10−10 5.7×10−12 7.2×10−10 4.7×10−12 7.1×10−10 4.2×10−12 8.0×10−10 2.9×10−12 8.3×10−10 1.7×10−12

28

Uncat Channel B kAM 3.1×10−18 2.5×10−18 2.0×10−18 1.8×10−18 1.8×10−18 1.8×10−18 1.8×10−18 1.9×10−18 2.0×10−18


Ammonolysis WM-cat AM-cat Channel E Channel F Channel I kAM+WM kAM+AM kAM−AM 1.6×10−13 1.9×10−9 6.1×10−8 1.2×10−13 1.4×10−9 3.8×10−8 8.0×10−14 8.3×10−10 1.9×10−8 6.2×10−14 5.9×10−10 1.2×10−8 5.7×10−14 4.8×10−10 9.3×10−9 5.4×10−14 4.1×10−10 7.7×10−9 5.3×10−14 4.0×10−10 7.4×10−9 4.9×10−14 3.3×10−10 5.9×10−9 4.5×10−14 2.7×10−10 4.7×10−9

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Figure 1: Molecular geometries of species involve in (a) uncatalyzed, (b) water catalyzed and (c) ammonia catalyzed hydrolysis of SO3 optimized at the B3LYP/cc-pV(T+d)Z level of theory

29



Potential energy (kcal mol−1 )

TSSO −WM 3 16.0

10

0

SO3 +WM 0.0

SO3 -WM -7.6

−10

SA -19.5

−20

(a)


0 −5

SO3 +WM-WM 0.0

SO3 -WM + WM -3.7

TSSO −WM−WM 3 -7.8

−10 −15

SA+WM -15.7

SO3 -WM-WM -13.7

−20 −25 SA-WM -27.4

−30

(b) 0 Potential energy (kcal mol−1 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 38

−5

SO3 +WM-AM 0.0

SO3 -WM + AM

−10 −15

-2.8

SA+AM -14.6

TSSO −WM−AM 3 -15.8 SO3 -WM-AM -15.8

−20 −25 −30

SA-AM -29.9

(c)

Figure 2: ZPE corrected potential energy profiles for (a) uncatalyzed (violet), (b) water catalyzed (green) and (c) ammonia catalyzed (magenta) hydrolysis of SO3 calculated at the CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory 30


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TSSO −WM 3 25.7

Gibbs free energy (kcal mol−1 )

25 20 15 10 5 0

SO3 -WM 2.0 SO3 +WM 0.0

−5

SA -7.1

(a) TSSO −WM−WM 3 6.7


5 SO3 + WM-WM

0

0.0

SO3 -WM-WM 0.8

SO3 -WM+WM -1.8

−5

SA+WM

−10

-11.0

SA-WM -11.9

(b) 0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


−2

SO3 +WM-AM 0.0

TSSO −WM−AM SO3 -WM 3 + -2.0 AM SO3 -WM-AM -0.2 -1.7

−4 −6 −8

SA+AM -9.4

−10 −12 −14 −16

SA-AM -14.7

(c)

Figure 3: ZPE corrected Gibbs free energy profiles for (a) uncatalyzed (violet), (b) water catalyzed (green) and (c) ammonia catalyzed (magenta) hydrolysis of SO3 calculated at the CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory 31



Figure 4: Molecular geometries of species involve in (a) uncatalyzed, (b) water catalyzed and (c) ammonia catalyzed ammonolysis of SO3 optimized at the B3LYP/cc-pV(T+d)Z level of theory

32


Page 32 of 38

Page 33 of 38

TSSO −AM 3 9.0


10 5 0

SO3 +AM 0.0

−5 −10 −15

SO3 -AM -17.6

−20

SMA -18.9

(a)


2 0

SO3 -AM+WM 0.0

TSSO −AM−WM 3 -0.1 SMA+WM -1.3

−2 −4 −6 −8 SMA-WM -9.1

−10 −12

SO3 -AM-WM -11.7

(b) 0 Potential energy (kcal mol−1 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


SO3 +AM-AM 0.0

−5 −10 −15

SO3 -AM + AM -15.3

SMA+AM -16.6

TSSO −AM−AM 3

−20

-22.3

−25 −30

SO3 -AM-AM SMA-AM

-27.9

-30.5

(c)

Figure 5: ZPE corrected potential energy profiles for (a) uncatalyzed (teal), (b) water catalyzed (blue) and (c) ammonia catalyzed (red)ammonolysis of SO3 calculated at the CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory 33




TSSO −AM 3 18.8

15

10

5 SO3 +AM 0.0

0 SO3 -AM -5.2

−5

SMA -7.7

(a) 12 TSSO −AM−WM 3 10.1


10 8 6 4 2 SO3 -AM+WM 0.0

SMA-WM 1.0

0

SMA+WM

SO3 -AM-WM

0

-1.9

-0.6

−2


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 38

(b) SO3 +AM-AM 0.0

−2 −4 −6 −8

TSSO −AM−AM 3 -5.3

SO3 -AM + AM -8.8

−10 −12

SMA+AM -11.3 SO3 -AM-AM -11.1

−14

SMA-AM -14.2

(c)

Figure 6: ZPE corrected Gibbs free energy profiles for (a) uncatalyzed (teal), (b) water catalyzed (blue) and (c) ammonia catalyzed (red)ammonolysis of SO3 calculated at the CCSD(T)/cc-pV(T+d)Z//B3LYP/cc-pV(T+d)Z level of theory 34


Page 35 of 38

T (K) 312.5

294.1

277.8

263.2

250

238.1

227.3

217.4

kAM-AM

10

kWM-AM 0 kWM+AM

ln(k)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-10

kAM+AM

-20

kWM-WM kWM+WM

-30

kAM+WM

-40

kAM

-50

kWM 3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

-1

1000/T (K )

Figure 7: Temperature dependence of rate coefficients for hydrolysis and ammonolysis of SO3 within 213 to 320 K calculated by transition state theory

35



T (K) 312.5

294.1

277.8

263.2

250

238.1

-15

227.3

217.4

kAM-AM kAM+AM

-20

kWM+AM kWM+WM

kWM-AM

-25

kWM-WM -30 ln(k)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 38

kAM+WM

-35 kAM

-40

-45

-50 kWM -55 3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

-1

1000/T (K )

Figure 8: Temperature dependence of rate coefficients for hydrolysis and ammonolysis of SO3 within 213 to 320 K calculated by master equation

36


Page 37 of 38

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Influence of Ammonia and Water on the Fate of Sulfur Trioxide in the

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