Influence of Nucleation Precursors on the Reaction Kinetics of

Article pubs.acs.org/JPCA

Influence of Nucleation Precursors on the Reaction Kinetics of Methanol with the OH Radical Jonas Elm,*,† Merete Bilde,‡ and Kurt V. Mikkelsen† †

Department of Chemistry, H. C. Ørsted Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Århus C, Denmark

‡

S Supporting Information *

ABSTRACT: The mechanism and kinetics of the reaction of methanol with the OH radical in the absence and presence of common atmospheric nucleation precursors (H2O, NH3, and H2SO4) have been investigated using different computational methods. The statistical Gibb’s free energy of formation has been calculated using M06-2X/6-311++G(3df,3pd) in order to assess cluster stability. Methanol is found to have an unfavorable interaction with water and ammonia but form stable complexes with sulfuric acid. The reaction kinetics with the OH radical and methanol with or without the presence of nucleation precursors has been studied using a CCSD(T)F12a/VDZ-F12//BH&HLYP/aug-cc-pVTZ∥Eckart methodology, and it is found that the presence of water is unlikely to change the overall reaction rate and mechanism of hydrogen abstraction from methanol. Ammonia is able to both enhance the reaction rate and change the reaction mechanism, but due to a very weak interaction with methanol, this process is unlikely to occur under atmospheric conditions. Sulfuric acid is, in contrast, found to be able to act as a stabilizing factor for methanol and is able to change the reaction mechanism. These findings show the first indications that nucleation precursors such as ammonia and sulfuric acid are able to alter the reaction mechanism of an atmospherically relevant organic compound.

1. INTRODUCTION Methanol is emitted to the atmosphere in significant amounts with global emissions estimated to be up to 240 Tg C/year.1 This can be compared with total global emissions of nonmethane volatile organic compounds (VOCs) to the atmosphere, which are estimated to be in the range of 1300− 1350 Tg C/year.2 The main source of methanol to the atmosphere is plant growth, and measurements from the leaves of a number of plant species have shown that the methanol flux is comparable to that of other major biogenic volatile compounds such as isoprene.2,3 Other sources of methanol in the atmosphere are atmospheric reactions, plant decay, biomass burning, biofuels, vehicles, and industry.3 Because large quantities of methanol are annually emitted into the atmosphere from various sources, it is important to know the atmospheric fate of the compound and its potential impact on processes such as nucleation. During the daytime, the major sink of atmospheric organics (including methanol) is hydrogen abstraction by the OH radical. Laboratory studies have estimated the atmospheric lifetime of methanol to be on the order of 2 weeks.4 Due to this relatively long residence time, we hypothesize that it is possible for methanol to interact with nucleation precursors such as H2O, NH3, and H2SO4 and that methanol thereby could be incorporated into aerosols through the initial steps of nucleation. The exact mechanism for new particle formation still remains elusive. Generally, it has © 2013 American Chemical Society

been established that it is multicomponent in nature, and the mechanism can be described through a H2SO4−H2O−X process, where X acts as a stabilizer. Several species have been proposed to be the principal stabilizer, and numerous computational studies involving prenucleation cluster formation have been performed with different compounds such as NH3,5−9 amines,10−15 organics,16−28 and ionic species.29−37 The effect of the most abundant nucleation precursor (H2O) has been the subject of several recent computational studies such as the reactivity of hydrated sulfur compounds,38−41 and the interaction with water has shown to exhibit a significant catalytic effect in the formation of H2SO4.42,43 Recently, sulfuric acid has been shown to act as a catalyst in the hydrolysis of SO3 and formaldehyde.44,45 Organic molecules have shown no net catalytic effect by forming complexes with water due to a relatively weak intermolecular interaction.46−49 In this work, we computationally investigate the interaction of methanol with a series of atmospheric nucleation precursors (H2O, NH3, and H2SO4). We then proceed to investigate the effect of each of these nucleation precursors on the reaction kinetics and mechanism of hydrogen abstraction from methanol in the gas Received: May 24, 2013 Revised: July 9, 2013 Published: July 9, 2013 6695

dx.doi.org/10.1021/jp4051269 | J. Phys. Chem. A 2013, 117, 6695−6701

The Journal of Physical Chemistry A

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2.2. Reaction Kinetics. The calculations of the rate constants and branching ratios have been performed using the BH&HLYP/aug-cc-pVTZ optimized geometries. The importance of an additional tight d-function to the aug-ccpVTZ was tested but found to be negligible with regard to the structure and partition functions of the sulfuric acid transition states (TSs). The nature of each stationary point was confirmed by a frequency analysis, and in the case of TS structures, the imaginary frequency was visually inspected and the intrinsic reaction coordinate (IRC) was followed at the same level of theory to ensure that the TS connects the correct reactants and products. The single-point energies have been corrected with a high-level explicitly correlated coupled cluster singles and doubles with perturbative triples CCSD(T)-F12a54,55 calculation using the VDZ-F12 basis set.56 For evaluation of the tunnelling contribution, an asymmetrical Eckart tunnelling correction was used. This methodology has recently been shown to yield accurate ambient rate constants and branching ratios for the hydrogen abstraction reaction by the OH radical for atmospherically relevant oxygenated organics.57 To evaluate the total rate constant, conventional TS theory was applied58

phase by the OH radical. The results are discussed in the context of atmospheric chemistry.

2. COMPUTATIONAL METHODOLOGY 2.1. Cluster Formation. All density functional theory calculations have been performed in Gaussian 09,50 and all explicitly correlated coupled cluster calculations have been performed in Molpro version 2010.1.51 Geometry optimization and frequency calculations of prenucleation cluster formation have been calculated with the M06-2X functional using the 6311++(3df,3pd) basis set. Our recent benchmark studies have shown that M06-2X/6-311++G(3df,3pd) yields reasonable equilibrium structures and thermochemistry of prenucleation clusters with good correlation with experimental results.52 In a more recent benchmark study, the M06-2X functional was shown to yield binding energies in good correlation (MUD = 0.96 kcal/mol) with CCSD(T)-F12/jun-cc-pV(T+d)Z results of (H2SO4)((CH3)2NH) and (H2SO4)2(NH3) clusters.53 The performance of the M06-2X functional was only transcended by the PW6B95-D3 functional using the MG3S basis set. Currently, an analysis of the frequencies is not available; therefore, as an estimate of the thermochemistry, we utilized the M06-2X functional. A large challenge in calculating cluster formation is the ability to systematically scan the configurational space such that most possible conformations are taken into account when calculating the overall Gibb’s free energy of formation. Usually, a stepwise procedure is performed by adding one nucleate in different chosen positions to the previous minimum structure using chemical intuition. Here, we perform each nucleation step by adding 1000 randomly oriented nucleate molecules (H2O, NH3, and H2SO4) randomly distributed around the target molecule/complex. The 1000 generated structures are initially geometry optimized using the semiempirical PM6 method with tight convergence criteria to generate the initial guess conformations. The identified conformations are then optimized with M06-2X/6311++(3df,3pd) to yield the final structures. The population of a given conformation 1 is calculated as P(1) =

ΔG

(

exp − RT1

(

∑s exp

k total =

i

)

∑ P(s)ΔGs s

(3)

3. RESULTS AND DISCUSSION 3.1. Interaction between Methanol and Nucleation Precursors (H2O, NH3, H2SO4). Due to the long atmospheric residence time of methanol, we hypothesize that it is possible for methanol to interact with nucleation precursors. In Figure 1, the identified lowest-energy conformations of (CH3OH)(H2SO4) complexes with water and ammonia can be seen calculated at the M06-2X/6-311++G(3df,3pd) level of theory. In Table 1, the calculated number of identified stable conformations, the minimum/statistical Gibb’s free energies of formation, and the population of the lowest identified minimum can be seen. The interaction between methanol and water/ammonia (R1 and R2) is observed to be highly unfavorable with positive ΔGmin values of +3.36 and +2.27 kcal/mol, respectively. It is observed that the uptake of methanol by sulfuric acid (R3) is slightly more favorable than the corresponding uptake of a water molecule to form the monohydrate (R4) with ΔGmin of −3.82 and −3.09 kcal/mol, respectively. The subsequent interaction between the (CH3OH)(H2SO4) complex and a water molecule (R9) is similar to the second hydration of sulfuric acid (R5), which indicates that the complex formation between methanol and sulfuric acid does not hinder the further uptake of water

(1)

where s denotes the different conformations. By taking all identified conformations into account, the thermally averaged expectation value of the free energy of reaction can be calculated as ⟨ΔG⟩ =

⎡ ΔE ‡ ⎤ kBT QTS, i exp⎢ − i ⎥ ⎢⎣ kBT ⎥⎦ h Q R Q OH

Here, the total rate constant is expressed as the sum of the individual ith reaction paths, with Q denoting the molecular partition functions evaluated as the product of the individual contributions from translation, rotation, vibration, and electronic for the TS, the reactant (R), and the OH radical (OH). The OH radical has two low-lying electronic states (2Π3/2 and 2Π1/2) separated by 140 cm−1.59 The electronic partition function for the OH radical is thereby evaluated as qe = 2 + 2e−140/kBT = 3.019. κi(T) is the quantum mechanical tunnelling correction, and σi is the symmetry factor that denotes the reaction path degeneracy. In the case of methanol, the O−H hydrogen abstraction pathway has a symmetry factor of σO−H = 1, while the C−H hydrogen abstraction pathway has σC−H = 3

)

ΔG − RTs

∑ σi κi(T )

(2)

Using eq 2, it is possible to incorporate statistics into the analysis of the free energies by including all of the identified stable conformations. A conformation is considered stable as long as it is within 3 kcal/mol of the lowest identified energy minimum. The following nucleation step then uses all previous stable conformations as initial guess structures. The conformation with lowest free energy is then subjected to 1000 new randomly oriented nucleates, while higher-energy conformations are subjected to 300. By utilizing this procedure, it is possible in an ad hoc fashion to include nuclear effects by systematically scanning the configurational space and thereby obtain reliable “global” minimum structures and statistical thermochemistry. 6696



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found to be placed at the opposite site instead of participating in a larger hydrogen- bonded network at the same site. This indicates that the incorporation of methanol in small molecular clusters does not hinder the further interaction with nucleation precursors and that methanol shows properties similar to those of a single water molecule. 3.2. Assessment of the TS Structure. The TS structure of the methanol C−H hydrogen abstraction reaction using different DFT functionals and coupled cluster results are presented in Table 2. Recently, it has been pointed out that Table 2. Structural Parameters of the C−H Hydrogen Abstraction Reaction of Methanol Using Various DFT Functionals and Coupled Cluster Theory Figure 1. Molecular structure of the complexes between methanol and nucleation precursors (H2O, NH3, and H2SO4) identified. (a) Complex formed in reaction R3, (b) complex formed in reaction R9, (c) complex formed in reaction R11, and (d) complex formed in reaction R10.

Table 1. Calculated Gibb’s Free Energy of Formation for the Methanol Complex with Either Water, Ammonia, or Sulfuric Acida reaction R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11

CH3OH + H2O ⇌ (CH3OH)(H2O) CH3OH + NH3 ⇌ (CH3OH)(NH3) CH3OH + H2SO4 ⇌ (CH3OH)(H2SO4) (H2SO4) + H2O ⇌ (H2SO4)(H2O) (H2SO4)(H2O) + H2O ⇌ (H2SO4)(H2O)2 (H2SO4)(H2O)2 + H2O ⇌ (H2SO4)(H2O)3 H2SO4 + NH3 ⇌ (H2SO4)(NH3) (H2SO4)(NH3) + H2O ⇌ (H2SO4)(NH3)(H2O) (CH3OH)(H2SO4) + H2O ⇌ (CH3OH)(H2SO4)(H2O) (CH3OH)(H2SO4)(H2O) + H2O ⇌ (CH3OH)(H2SO4) (H2O)2 (CH3OH)(H2SO4) + NH3 ⇌ (CH3OH)(H2SO4)(NH3)

# confs

ΔGmin

5

+3.36

+4.12

5

+2.27

+2.77

4

−3.82

0.61

−3.53

3

−3.09

0.73

−2.87

5

−2.77

0.55

−2.46

17

−2.25

0.39

−1.67

2

−7.91

0.97

−7.84

15

−1.80

0.80

−1.36

14

−2.66

0.22

−2.35

18

−2.31

0.30

−1.64

7

−5.50

0.46

−5.26

P(min)

⟨ΔG⟩

method

‡ νC−H

RC···H

RH···O

∠C···H···O

B3LYP BH&HLYP M06 M06-2X M06-HX MP2 CCSD/6-311+G(d,p) CCSD/VTZ CCSD-F12a/VDZ-F12

171i 1220i 391i 784i 2035i 1366i 1127i 1256i 1030i

1.111 1.193 1.175 1.150 1.155 1.167 1.187 1.191 1.180

1.853 1.357 1.436 1.499 1.464 1.402 1.381 1.362 1.396

142.4 175.6 169.0 157.2 150.0 163.6 168.3 166.3 168.7

DFT functionals that show a good performance for barrier heights usually predict accurate TS structures.60 Very little change in structure is seen when increasing the CCSD basis set from the medium-sized 6-311+G(d,p) to the larger cc-pVTZ basis set. By comparing the coupled cluster results with the DFT functionals, it is observed that the BH&HLYP functional shows excellent correlation in describing the bonding distances of the C−H TS. The bond angle at the TS is also seen to be relatively well reproduced with a 9° discrepancy between BH&HLYP and the coupled cluster result. More importantly, the BH&HLYP functional shows a representative estimate of the imaginary frequency of the nuclear motion at the TS, which is utterly important when estimating tunnelling corrections. This further encourages the use of the BH&HLYP functional. 3.3. Single-Point Energy Convergence. Because the rate constant depends exponentially on the energy, it is very important to obtain the corrected energy at a high accuracy. In Table 3, the convergence of both regular CCSD(T) and CCSD(T)-F12a using different basis sets and extrapolation to the complete basis set (CBS) limit can be seen. CCSD(T)/ CBS and CCSD(T)-F12a/CBS yield identical rate constants using the default L3 extrapolation functional in Molpro. The differences of the results from CCSD(T)/CBS and CCSD(T)F12a/CBS are within 0.02 and 0.05 kcal/mol for the C−H and O−H hydrogen abstraction pathways, respectively. A very slow basis set convergence is observed with regular CCSD(T), where a quadruple-ζ basis set (VQZ) is required to even obtain the correct sign of the C−H hydrogen abstraction channel. Even when using a quintuple basis set (V5Z), the limit is not reached. Using explicitly correlated coupled cluster, the energy convergence to the CBS limit occurs more rapidly due to the correct treatment of the wave function cusp as r12 → 0. Using the VTZ-F12 basis set yield results in good agreement with the CBS limit. It is seen that the VDZ-F12 basis set yields results close to the basis set limit with errors only of 0.11 and 0.16 kcal/mol for the C−H and O−H hydrogen abstraction channels, respectively. The rate constants (without tunnelling

a

For comparison, the calculated Gibb’s free energies for selected complexes with methanol are also shown.

compared to sulfuric acid hydrates. In the (CH3OH)(H2SO4)(H2O) complex, it is observed that the water and methanol molecules are residing at the same site of sulfuric acid to participate in a larger hydrogen-bonded network. The complex with the addition of the water at the opposite site is found to be 0.23 kcal/mol higher in energy than the identified lowestenergy conformation. When adding ammonia to the (CH3OH)(H2SO4) complex (as in R11), the lowest-energy identified structure has methanol and ammonia residing at opposite sites of the sulfuric acid, where the conformation with the ammonia molecule at the same site is found to be 0.52 kcal/ mol higher in energy. When adding the second water to the (CH3OH)(H2SO4)(H2O) cluster (R10), the water is similarly 6697



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Table 3. Coupled Cluster Energies (kcal/mol) of the C−H and O−H Reaction Pathways of Methanol Relative to the Isolated Reactants Using the BH&HLYP/aug-cc-pvtz Geometrya

a

CCSD(T)

ΔEC−H

ΔEO−H

VDZ VTZ VQZ V5Z CBS(D:T:Q:5)

2.70 0.63 −0.02 −0.26 −0.40

3.37 2.35 2.40 2.48 2.40

CCSD(T)-F12

ΔEC−H

ΔEO−H

VDZ-F12 VTZ-F12 VQZ-F12 CBS(D-F12:T-F12:Q-F12)

−0.31 −0.36 −0.42 −0.42

2.57 2.39 2.41 2.35

ktot 9.5 2.9 8.9 1.3 1.7

× × × × ×

10−16 10−14 10−14 10−13 10−13

ktot 1.4 1.6 1.7 1.7

× × × ×

10−13 10−13 10−13 10−13

ktot is the total rate constant calculated in cm3 s−1 molecule−1 without tunnelling. The CBS limit is calculated using the L3 functional.

seen to be greatly stabilized if the three isolated reactants are used as reference energies. This would, however, imply that the mechanism would occur through a three-body collision and is highly unlikely. A more likely scenario is that two of the molecules of CH3OH, OH, and H2O initially form a complex and then collide with the third molecule. In the case of (H2O)(OH) + CH3OH, an energy lowering of both reaction pathways is observed, but the overall reaction rate is slightly lower than that for the reaction without water. We observe a similar result for the (CH3OH)(OH) + H2O mechanism. In the case of the (CH3OH)(H2O) + OH mechanism, two different (CH3OH)(H2O) complexes with almost identical energy (0.26 kcal/mol difference) were identified. The overall rate constant has was calculated as the thermally averaged rate constant of the two conformations. Both conformations lead to a stabilization of the TS and overall yield a larger rate constant, which thereby catalyzes the reaction of methanol by the OH radical. In order for water-assisted hydrogen abstraction from methanol to have atmospheric implications, the two-body complexes must exist in the gas phase. In the case of all of the reactions in Table 4, the Gibb’s free energy of formation calculated at the CCSD(T)-F12a/VDZ//BH&HLYP/aug-ccpVTZ level of theory was found to be positive (between 1.13 and 2.73 kcal/mol) and thereby favors the isolated reactants. In a recent study, it was reported that due to the positive ΔG, the relative abundance at 50% relative humidity of the (CH3OH)(H2O) complex was lower than 0.02%.49 We thereby infer that water is not capable of catalyzing the reaction of methanol with the OH radical in the atmosphere. 3.5. Ammonia-Assisted Hydrogen Abstraction. Ammonia is the most common base encountered in the atmosphere, with atmospheric concentrations on the order of ppbs.61 To our knowledge, the effect of ammonia on atmospheric oxidation by OH has never been investigated before and is thereby worth studying, especially because trace amounts of ammonia have been shown to be present as a contaminant even in extremely clean environments such as in the Cern CLOUD chamber.62 In Figure 3, the identified RC, TS, and PC of the ammonia-assisted hydrogen abstraction reaction can be seen. In Table 5, the reaction kinetics of the individual reaction pathways with and without an ammonia molecule can be seen. Similarly to water, it is very unlikely for the three-body collision to occur. The formation of the (NH3)(OH) complex is observed only to have a slightly positive ΔG value, and only a negligible amount of this complex is thus expected to be present in the atmosphere. However, this complex only slightly stabilizes the TS, and the rate constant is only a factor of ∼2 larger than the one for the reaction without ammonia present. Similar to the water-assisted reaction, two conformations of the (CH3OH)(NH3) complex were identified. The lowest-energy conformation was 1.49 kcal/mol lower in energy, and this

corrections) are seen to give a value of the same magnitude in the case of explicitly correlated coupled cluster, whereas regular coupled cluster needs at least a quintuple basis set to be relatively converged and agree with the CBS limit. This indicates that CCSD(T)-F12a/VDZ-F12 represents a good compromise between accuracy and computational effort when calculating the single-point energy correction and will therefore be used in this work. 3.4. Water-Assisted Hydrogen Abstraction. Because water catalysis plays an important role in several atmospheric reactions, the effect of water on the methanol hydrogen abstraction was investigated. In Figure 2, the identified reactant complex (RC), TS, and product complex (PC) of the waterassisted hydrogen abstraction reaction can be seen.

Figure 2. Molecular structure of the identified RC, TS, and PC in water-assisted hydrogen abstraction from methanol by OH. The O−H hydrogen abstraction pathway (top) and C−H hydrogen abstraction pathway (bottom).

In Table 4, the reaction kinetics of the individual reaction pathways with or without a water molecule can be seen using different mechanisms. The energy barriers of both pathways are Table 4. CCSD(T)-F12a/VDZ-F12//BH&HLYP/aug-ccpVTZ∥Eckart Calculated Energies (ΔE in kcal/mol) of the Individual Reaction Pathways and Total Rate Constants (cm3 s−1 molecule−1) with and without a Water Molecule Present reaction mechanism CH3OH + OH CH3OH + H2O + OH (H2O)(OH) + CH3OH (CH3OH)(OH) + H2O (CH3OH)(H2O) + OH

ΔGcomplex

ΔEC−H

ΔEO−H

1.53 1.13 2.57

−0.31 −6.42 −2.65 −1.78 −2.83

2.57 −2.85 0.92 1.79 0.74

ktot 6.0 1.9 2.5 1.3 1.8

× × × × ×

10−13 10−14 10−13 10−13 10−12 6698



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Figure 3. Molecular structure of the identified RC, TS, and PC of ammonia-assisted hydrogen abstraction from methanol. The O−H hydrogen abstraction pathway (top) and C−H hydrogen abstraction pathway (bottom).

Figure 4. Molecular structure of the identified RC, TS, and PC of sulfuric-acid-assisted hydrogen abstraction from methanol. The O−H hydrogen abstraction pathway (top) and C−H hydrogen abstraction pathway (bottom).

Table 5. CCSD(T)-F12a/VDZ-F12//BH&HLYP/aug-ccpVTZ∥Eckart Calculated Energies (ΔE in kcal/mol) of the Individual Reaction Pathways and Total Rate Constants (cm3 s−1 molecule−1) with and without an Ammonia Molecule Present

Table 6. CCSD(T)-F12a/VDZ-F12//BH&HLYP/aug-ccpVTZ∥Eckart Calculated Energies (ΔE in kcal/mol) of the Individual Reaction Pathways and Total Rate Constants (cm3 s−1 molecule−1) with and without a Sulfuric Acid Molecule Present

reaction mechanism CH3OH + OH CH3OH + NH3 + OH (NH3)(OH) + CH3OH (CH3OH)(OH) + NH3 (CH3OH)(NH3) + OH

ΔGcomplex

ΔEC−H

ΔEO−H

0.57 1.13 2.49

−0.31 −6.56 −1.29 −1.92 −1.55

2.57 −3.76 1.50 0.88 1.25

ktot 6.0 4.4 1.1 2.9 2.9

× × × × ×

reaction mechanism

10−13 10−13 10−12 10−12 10−11

CH3OH + OH CH3OH + H2SO4 + OH (H2SO4)(OH) + CH3OH (CH3OH)(OH) + H2SO4 (CH3OH)(H2SO4) + OH

ΔGcomplex

ΔEC−H

ΔEO−H

−0.25 1.13 −2.91

−0.31 −15.11 −7.07 −10.47 −2.79

2.57 −11.14 −3.11 −6.50 1.18

ktot 6.0 7.3 4.8 4.9 5.4

× × × × ×

10−13 10−11 10−11 10−10 10−13

collision schemes. Besides the catalytic effect, it is also important to know whether the reaction mechanism is altered due to the presence of nucleation precursors. In Table 7, the

conformation is presented in Table 5. If the (CH3OH)(NH3) complex collided with the OH radical, it would have a high impact on reaction kinetics, but the complex formation is very unlikely due to the high positive ΔG value when forming the complex. Similar to the case of water, this indicates that ammonia is not able to enhance the reaction of methanol under atmospheric conditions. 3.6. Sulfuric-Acid-Assisted Hydrogen Abstraction. Above, it was inferred that neither water nor ammonia is able to catalyze the chemical reaction due to a too weak intermolecular interaction that would lead to very low atmospheric concentrations of the complexes. From the calculated statistical ΔG values, it suggests that sulfuric acid might form a strong complex with methanol. In Figure 4, RC, TS, and PC of the sulfuric-acid-assisted reaction can be seen. Only a single RC was identified, which indicates that both the C−H and O−H hydrogen abstractions occur from this global complex. In Table 6, the reaction kinetics of the sulfuric-acidassisted hydrogen abstraction reactions can be seen. It is observed that both the (H2SO4)(OH) and (CH3OH)(H2SO4) complexes are stable with ΔG values of −0.25 and −2.91 kcal/ mol, respectively. From the (H2SO4)(OH) + CH3OH mechanism, a rate constant 2 orders of magnitude larger than the one for the unassisted reaction is obtained. The (CH3OH)(H2SO4) + OH mechanism involves the most stable complex, but the reaction rate is seen to be unaffected. 3.7. Reaction Mechanism of Nucleation-PrecursorAssisted Hydrogen Abstraction. In the three previous sections, the total reaction rate constants of the water-, ammonia-, and sulfuric-acid-assisted hydrogen abstraction reactions from methanol were investigated considering different

Table 7. Characteristics of the TSs of Isolated Methanol and with Either H2O, NH3, or H2SO4 as a Stabilizer stabilizer

‡ νC−H

ΔEC−H,fwd

none H2O NH3 H2SO4 stabilizer

1220i 1821i 1789i 666i ν‡O−H

4.35 3.47 5.37 5.47

none H2O NH3 H2SO4

2443i 2636i 2630i 2686i

ΔEC−H,rev

ΔEO−H,fwd

26.97 27.67 31.18 26.02 ΔEO−H,rev

7.22 8.37 11.78 9.43

19.17 19.76 19.28 17.32

κC−H

ΓC−H

4 9 17 2 κO−H

0.94 0.94 0.16 0.32 ΓO−H

171 500 2908 1024

0.06 0.06 0.84 0.68

characteristics of the O−H and C−H TSs can be seen. It is observed that in the case of the C−H hydrogen abstraction, the calculated forward barriers (ΔEC−H,fwd) only differ by ∼1 kcal/ mol, whereas the reverse barriers (ΔEC−H,rev) differ up to ∼5 kcal/mol. The presence of either a water or ammonia molecule increases the imaginary frequency (ν‡) of the TS by 50%, which corresponds to increased tunnelling correction (κ) by factors of 2 and 4, respectively. In the case of sulfuric acid, the imaginary frequency is damped by a factor of 2, which leads to the same damping in the tunnelling correction. In the O−H hydrogen abstractions, the imaginary frequencies are in all cases relatively identical (2443i−2686i), whereas the barriers vary slightly more (up to 3.5 kcal/mol for the forward and 2 kcal/mol for the 6699



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Notes

reverse reaction barriers, respectively). The high barrier in the ammonia reaction gives a correspondingly high tunnelling correction. These variations in the TS characteristics yield a high difference in the corresponding branching ratios (Γ) of the individual reaction paths. The water-assisted reaction is found to be unaffected, with only a 6% contribution from the O−H abstraction channel. The ammonia-assisted reaction is found to alter the reaction mechanism such that the hydrogen abstraction predominantly occurs from the O−H pathway (84%). This is mainly due to the very high tunnelling coefficient and is an intriguing result that indicates that nucleation precursors are able to change the reaction mechanism even of a simple reaction. Sulfuric acid is seen to have the same, but less profound, effect where 68% of the hydrogen abstraction occurs at the O−H group. Combined with the favorable complex formation between methanol and sulfuric acid, this could indicate that it is possible to change the resulting oxidation products.

The authors declare no competing financial interest.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

All structures are available. This material is available free of charge via the Internet at http://pubs.acs.org.

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ACKNOWLEDGMENTS

The authors thank the Danish Center for Scientific Computing for providing computer resources, the Danish Natural Science Research Counsil/The Danish Councils for Independent Research, and the Villum Kann Rasmussen Foundation for financial support

4. CONCLUSION We have investigated the effect of nucleation precursors on the reaction rate and mechanism of the hydrogen abstraction reactions from methanol. The statistical Gibb’s free energy of formation has been calculated, and it was found that methanol is able to form hydrogen-bonded complexes with sulfuric acid with the same strength as the corresponding hydrate. The uptake of methanol by sulfuric acid is found not to hinder the further interaction of sulfuric acid with nucleation precursors, though methanol will likely be in competition with other clustering partners with higher concentrations such as water or with larger binding energies, for example, strong bases or organic acids. From both the statistical analysis and the reaction kinetics, it was found that the interaction between methanol and water/ammonia is very weak, and thereby, it is highly unlikely that these complexes exist in the atmosphere. Consequently, it is not likely that neither water- nor ammonia-assisted reactions have a catalytic effect. No catalytic effect is observed in the case of the (CH3OH)(H2SO4) + OH reaction, but sulfuric acid is found to be able to alter the reaction mechanism. Due to the strong complex formation, this indicates that the presence of sulfuric acid with organics might lead to oxidation products not initially anticipated, and reaction kinetics involving the complex formation of sulfuric acid with common atmospheric organics that bind strongly needs further study. Though ammonia is not able to catalyze the reaction of methanol and OH on its own, it was found that ammonia highly enhanced the tunnelling contribution. This could indicate that ammonia-assisted reactions might play an important role if combined with another stabilizer such as sulfuric acid. Further investigation of the reactivity of small clusters of (H2SO4)(NH3)(organic) with the OH radical could be of interest.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 6700



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Influence of Nucleation Precursors on the Reaction Kinetics of

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