Computational Study of the Clustering of a Cyclohexene

Article pubs.acs.org/JPCA

Computational Study of the Clustering of a Cyclohexene Autoxidation Product C6H8O7 with Itself and Sulfuric Acid Jonas Elm,*,† Nanna Myllys,† Noora Hyttinen,‡ and Theo Kurtén‡ †

Department of Physics and ‡Department of Chemistry, University of Helsinki, FIN-00014 Helsinki, Finland S Supporting Information *

ABSTRACT: We investigate the molecular interactions between sulfuric acid and a recently reported C6H8O7 ketodiperoxy acid formed through autoxidation from cyclohexene and ozone. Structurally similar but larger ELVOC (extremely low volatility organic compound) products formed from autoxidation of monoterpenes are believed to play a major role in the formation and early growth of atmospheric aerosol particles. Utilizing density functional theory geometries, with a DLPNOCCSD(T)/def2-QZVPP single point energy correction, the stepwise Gibbs free energies of formation have been calculated, and the stabilities of the molecular clusters have been evaluated. C6H8O7 interacts weakly with both itself and sulfuric acid, with standard free energies of formation (ΔG at 298 K and 1 atm) around or above 0 kcal/mol. This is due to the presence of strong intramolecular hydrogen bonds in the peroxyacid groups of C6H8O7. These stabilize the isolated molecule with respect to its clusters, and lead to unfavorable interaction energies. The addition of sulfuric acid to clusters containing C6H8O7 is somewhat more favorable, but the formed clusters are still far more likely to evaporate than to grow further in atmospheric conditions. These findings indicate that the O/C ratio cannot exclusively be used as a proxy for volatility in atmospheric new particle formation involving organic compounds. The specific molecular structure, and especially the number of strong hydrogen binding moieties, are equally important. The interaction between the C6H8O7 compound and aqueous phase sulfate ions indicates that ELVOC-type compounds can contribute to aerosol mass by effectively partitioning into the condensed phase. sulfuric acid molecules are needed to reach stable clusters.19 It has recently been inferred that extremely low volatile organic compounds (ELVOCs) participate in the initial steps in new particle formation.20,21 These are likely formed through a sequence of unimolecular peroxy radical hydrogen shift reactions and O2 addition reactions, eventually followed by uni- or bimolecular termination steps leading to closed-shell products.22,23This autoxidation mechanism rapidly leads to highly oxidized compounds with oxygen-to-carbon ratios (O/ C) around or even above 1. Very little is known about the specific structure of individual ELVOCs, but due to the nature of the autoxidation process, the compounds are believed to involve various carbonyl and hydrogen peroxide groups.20,24 Very recently, the hydroperoxyalkyl radical product of the peroxyradical hydrogen shift was directly experimentally detected in the oxidation of 1,3-cycloheptadiene in the work by Savee and Papajak.25 The most widely used precursor for studying biogenic secondary organic aerosols is the monoterpene α-pinene, a volatile organic compound emitted by pine trees (Figure 1a). Currently, there is no specific structural information about ELVOCs produced from monoterpenes, but recently, Rissanen

1. INTRODUCTION The formation of atmospheric aerosols is still one of the least understood processes in global climate models. New particle formation highly influences the concentration of cloud condensation nuclei (CCN) and have been estimated to account for roughly half the global budget of CCN.1 New particle formation is believed to occur through a clustering mechanism, involving sulfuric acid coupled with a stabilizing component such as ammonia, amines, or organic compounds.2 Recently, amines have been shown to efficiently enhance the new particle formation rate 1000-fold compared to ammonia.3 The underlying mechanisms have been shown to involve clusters containing two sulfuric acid and one or two dimethylamine molecules, which are stable against evaporation.4 Although ammonia and amines have been extensively studied,5−15 little is still known about the direct involvement of organic compounds in new particle formation. In 2004 Zhang et al. identified an enhanced new particle formation of sulfuric acid in the presence of organic acids.16 The work in 2009 by Zhang et al. indicated that a single cis-pinonic acid and three to five sulfuric acid molecules are required to reach a critical nucleus for new particle formation.17 In 2010 Metzger et al. suggested that only one organic compound and one sulfuric acid molecule was involved in the rate limiting step in new particle formation.18 The recent work by Schobesberger et al. indicates that one to four oxidized organics and one to three © 2015 American Chemical Society

Received: April 28, 2015 Revised: June 16, 2015 Published: July 8, 2015 8414

DOI: 10.1021/acs.jpca.5b04040 J. Phys. Chem. A 2015, 119, 8414−8421

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The Journal of Physical Chemistry A

Figure 1. (a) α-Pinene. (b) α-Pinene with its cyclohexene structure marked in red. (c) C6H8O7 oxidation product from cyclohexene ozonolysis.

Figure 2. Diagram for potential cluster formation steps in the sulfuric acid−C6H8O7 system.

et al. reported the formation of diperoxy acid compounds with additional keto and/or hydroperoxy substituents from cyclohexene autoxidation using both experimental and computational methods.26 Highly oxidized C6H8O7, C6H8O8, and C6H8O9 compounds were identified from the mass spectra, and connected to specific molecular structures formed through hydrogen shift, O2 addition, and termination reactions. Due to the structural resemblance between monoterpenes and cyclohexene (exemplified with α-pinene in Figure 1), we here wish to investigate the formation of molecular clusters between sulfuric acid and the C6H8O7 ketodiperoxy acid, using it as a proxy for oxidized monoterpene products with an O/C ratio above 1. Information about the C6H8O7−H2SO4 molecular interaction can further illuminate the direct involvement of monoterpene oxidation products in atmospheric new particle formation.

C6H8O7) are randomly distributed around the target molecule/cluster. 2. The structures are initially optimized using the semiempirical PM6 method. 3. For the converged structures a single point M06-2X/631+G(d) energy is calculated. 4. The structures are sorted and characterized by the total energy/dipole moment, and different conformations are identified. 5. Conformations within 15 kcal/mol of the lowest identified conformation are geometry optimized, and frequencies are calculated at the M06-2X/6-31+G(d) level. 6. Remaining identified conformations within 3 kcal/mol of the lowest conformation are subsequently used for the next cluster formation step, and the process is repeated from step 1. Using this cluster formation approach, a large portion of the congurational space is sampled, and this approach should yield a good guess for the global minimum. In each cluster formation step, extensive manual sampling has also been included. Once the entire potential energy surface has been searched at the M06-2X/6-31+G(d) level of theory the identified molecular clusters are further refined using the M06-2X, PW91, and ωB97X-D functionals with the 6-31++G(d,p) and 6-311+ +G(3df,3pd) basis sets. From recent benchmarks it has been established that the M06-2X, PW91, and ωB97X-D functionals are among some of the most reliable density functionals for obtaining the structure,32 electronic energy33,34 and Gibbs free energies32,35,36 of atmospheric molecular clusters. We recently identified that the reduction from the 6-311++G(3df,3pd) to the 6-31++G(d,p) basis set only introduced low errors in the thermal contribution to the Gibbs free energy at a significant gain in computational efficiency.37 To present the final Gibbs free energies of formation, we average over all six obtained values and estimate the scatter as one standard deviation (σ).

2. METHODS 2.1. Computational Details. All density functional theory geometry optimizations and frequency calculations have been performed in GAUSSIAN 09.27 Explicitly correlated coupled cluster calculations have been run using Molpro 2012.28 To modify the single point energy, we utilize a domain based local pair natural orbital coupled cluster method DLPNO-CCSD(T) with a def2-QZVPP basis set as implemented in ORCA.29 To identify the lowest free energy structure of the C6H8O7 molecule, it was initially scanned using a systematic rotor approach as carried out in Rissanen et al.26,31 Subsequently, the number of conformers was narrowed down using the M06-2X functional. This led to 12 unique conformations within 3 kcal/ mol of the lowest identified structure. Each of these conformations are then used as the starting point for forming the molecular clusters using the following semiempirically guided technique: 1. In each cluster formation step 1000 randomly oriented nucleate molecules (lowest free energy H2SO4 or 8415


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The Journal of Physical Chemistry A The σ-value thereby illustrates the sensitivity of the computed Gibbs free energy to the quantum chemical method. The calculations using different functionals and basis set are available as Supporting Information. 2.2. Cluster Formation Steps. Cluster formation steps involve the successive addition of monomer units to map the potential energy surface of cluster growth. In the case of cluster formation between sulfuric acid (H2SO4) and the (C6H8O7) ketodiperoxy acid, the following formation reaction yields the simplest complex: H 2SO4 + C6H8O7 ⇋ (H 2SO4 )(C6H8O7 )

Figure 3. (a) Molecular structure of the C3H4O6 diperoxy acid and (b) (C3H4O7)(H2SO4) complex used for benchmarking. The structures are presented at the M06-2X/6-311++G(3df,3pd) level of theory. Color coding: green = carbon, yellow = sulfur, red = oxygen, and white = hydrogen.

The formed (H2SO4)(C6H8O7) complex can then further form clusters by collision with either another H2SO4 or C6H8O7 molecule. This yields an array of possible cluster formation steps as depicted in Figure 2. From a computational point of view the C6H8O7 compound is relatively large and thereby we will focus on the interaction between up to two sulfuric acid molecules and two C6H8O7 compounds in this study. We will not go into further detail with the gray formation paths shown in Figure 2. Here we focus on the following cluster formation steps: C6H8O7 + C6H8O7 ⇋ (C6H8O7 )2

(1)

C6H8O7 + H 2SO4 ⇋ (C6H8O7 )(H 2SO4 )

(2)

presented at the M06-2X/6-311++G(3df,3pd) level of theory. The structures have been calculated using all three functionals (M06-2X, PW91, and ωB97X-D) with both the 6-31++G(d,p) and 6-311++G(3df,3pd) basis sets. All the functionals identified the structures in Figure 3 to be lowest in Gibbs free energy. The corresponding electronic binding energies are calculated on top of the DFT geometries and shown in Table 1. The variation in the calculated CCSD(T)-F12a/VDZ-F12 and DLPNO-CCSD(T)/def2-QZVPP single point energies thereby originate from the slightly different geometries of the same cluster. There is observed very little scatter in the CCSD(T)-F12a/ VDZ-F12 binding energy with a range from −16.94 to −17.61 kcal/mol. The DFT functionals yield highly varying binding energies that range from −14.80 to −21.74 kcal/mol for PW91/6-311++G(3df,3pd) and M06-2X/6-31++G(d,p), respectively. It is generally seen that M06-2X significantly overbinds and PW91 significantly underbinds the binding energies. The ωB97X-D functional using the 6-311++G(3df,3pd) basis set matches the coupled cluster single point energy well, with a deviation as low as 0.96 kcal/mol. Although there is a large scatter in the DFT binding energies, the thermal contribution to the Gibbs free energy (ΔGTherm,DFT) varies significantly less, with values from 13.29 to 15.39 kcal/mol. A negligible variation in the thermal contribution is seen when changing the basis set from 6 to 311++G(3df,3pd) to 6-31+ +G(d,p). This indicates that the electronic binding energy is the largest source of error when using DFT for these systems. Using the DLPNO variation of coupled cluster also reduces the scatter in the binding energy with a range from −14.95 to −16.26 kcal/mol. The binding energies significantly underbind compared to a regular coupled cluster by 1.21−2.66 kcal/mol, corresponding to an average underbinding of 1.59 kcal/mol. The ratio between the computed coupled cluster results is found to vary from 1.07 to 1.18 with an average value of 1.10. This is relatively consistent with previous results using local coupled cluster (DF-LCCSD(T)-F12/VDZ-F12), where a scaling factor of 1.07 was identified over a test set of 38 atmospherically relevant clusters.37 This implies that the DLPNO-CCSD(T)/def2-QZVPP calculations presented herein can be used as lower bound for the binding energy values. The calculated Gibbs free energy for each applied level of theory for the clusters formed in reactions 1−7 is available as Supporting Information. Similarly to the benchmark case, we observe significant variations in the predicted Gibbs free energies at the DFT level. The predicted formation free energy

(C6H8O7 )(H 2SO4 ) + C6H8O7 ⇋ (C6H8O7 )2 (H 2SO4 ) (3)

(C6H8O7 )(H 2SO4 ) + H 2SO4 ⇋ (C6H8O7 )(H 2SO4 )2

(4)

(C6H8O7 )(H 2SO4 )2 + C6H8O7 ⇋ (C6H8O7 )2 (H 2SO4 )2 (5)

(C6H8O7 )2 (H 2SO4 ) + H 2SO4 ⇋ (C6H8O7 )2 (H 2SO4 )2 (6)

(C6H8O7 )(H 2SO4 ) + (C6H8O7 )(H 2SO4 ) ⇋ (C6H8O7 )2 (H 2SO4 )2 H 2SO4 + H 2SO4 ⇋ (H 2SO4 )2

(7) (8)

The formation of the sulfuric acid dimer in (8) is included for comparison. Using the systematic sampling technique outlined above, we identified numerous conformations for each cluster. This indicates that the potential energy surface is rather complex for the sulfuric acid−C6H8O7 system, which is caused by the various flexible peroxy groups, where several orientations are possible.

3. RESULTS AND DISCUSSION 3.1. Sensitivity of the Applied DFT Methods. To evaluate the sensitivity of the applied DFT methods and the accuracy of the DLPNO-CCSD(T)/def2-QZVPP single point energy, the calculations are compared to a high level canonical CCSD(T)-F12a/VDZ-F12 calculation. Due to the memory scaling of the CCSD(T)-F12a/VDZ-F12 method, it cannot be applied to any of the clusters investigated herein, but it was possible to apply it to a C3H4O6 diperoxy acid, which is structurally similar to the larger C6H8O7 compound. The lowest identified Gibbs free energy molecular structure of both the C3H4O6 diperoxy acid compound and the (C3H4O6)(H2SO4) complex used for benchmarking are shown in Figure 3 8416


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Table 1. Calculated Single Point Energies (ΔE), Thermal Contribution to the Free Energy (ΔGTherm, DFT), and Resulting Gibbs Free Energies (ΔG) for the (C3H4O6)(H2SO4) Complexa method 6-31++G(d,p) M06-2X PW91 ωB97X-D 6-311++G(3df,3pd) M06-2X PW91 ωB97X-D a

ΔEDFT

ΔEF12

ΔEDLPNO

ΔGtherm, DFT

ΔΔEF12/DFT

ΔΔEF12/DLPNO

−21.74 −15.61 −19.49

−16.94 −17.61 −17.52

−15.47 −14.95 −16.18

14.94 14.22 13.42

−4.80 2.00 −1.97

1.47 2.66 1.34

−20.36 −14.80 −18.43

−17.37 −17.31 −17.47

−16.14 −15.70 −16.26

15.39 14.40 13.29

−2.99 2.51 −0.96

1.23 1.61 1.21

F12 refers to CCSD(T)-F12a/VDZ-F12 and DLPNO refers to DLPNO-CCSD(T)/def2-QZVPP calculations. All values are in kcal/mol.

Figure 4. Lowest identified Gibbs free energy structures calculated at the M06-2X/6-311++G(3df,3pd) level of theory: (a) C6H8O7, (b) (C6H8O7)2, (c) (C6H8O7)(H2SO4), (d) (C6H8O7)2(H2SO4), (e) (C6H8O7)(H2SO4)2, and (f) (C6H8O7)2(H2SO4)2.

contribution to the Gibbs free energy is relatively well reproduced at all the applied levels of theory, and indicates that an ab initio correction of the single point energy is essential for calculating the formation free energies for these systems. Calculated binding energies can be prone to basis set superposition errors (BSSE), but using a quadruple-ζ basis set should yield results close to the basis set limit. To quantify the magnitude of the BSSE, it was estimated for the (C6H8O7)(H2SO4) complex using the counterpoise correction scheme.30 The BSSE was found to be 1.1 kcal/mol, indicating that it is smaller than the corresponding underbinding of the DLPNO method. Furthermore, the BSSE is also smaller than the variation in coupled cluster binding energies depending on which DFT method is used for geometry optimization. 3.2. Cluster Formation. The lowest identified Gibbs free energy structures of clusters consisting of up to two sulfuric acid and two C6H8O7 compounds are shown in Figure 4. The corresponding averaged Gibbs free energies are shown in Table 2. The formation of (C6H8O7)2 dimers (1) is unfavorable with a positive ΔG value of 3.1 kcal/mol. As shown in Figure 4a, the isolated C6H8O7 compound has intramolecular hydrogen bonds from the −OOH group to the carbonyl group in the peroxy acid moiety. The interaction for forming the dimer involves breaking four intramolecular hydrogen bonds and forming four weaker intermolecular interactions (Figure 4b).

values vary significantly between the functionals, with values from +2.6 to −8.8 kcal/mol for PW91/6-31++G(d,p) and M06-2X/6-31++G(d,p), respectively, in the case of the (C6H8O7)(H2SO4) complex formation (2). There is only seen slight variations in the thermal contribution with a deviation around 1 kcal/mol between the different functionals in reaction 2. Using the smaller 6-31++G(d,p) basis set for obtaining the geometry in (2) has little effect on the thermal contribution, for M06-2X and PW91. For ωB97X-D there is seen a difference of 1.61 kcal/mol when changing from a 6-31+ +G(d,p) to a 6-311++G(3df,3pd) basis set. Although there are only slight variations in the thermal contributions, there is (similarly to the benchmark case above) seen a large scatter in the electronic binding energy with differences of up to 10.75 kcal/mol between M06-2X/6-311++G(3df,3pd) and PW91/6311++G(3df,3pd) for reaction 2. This indicates that the highest uncertainty in the calculated formation free energies originate from the DFT electronic binding energy. By applying a DLPNO-CCSD(T)/def2-QZVPP calculation to correct the single point energy, the scatter in the electronic binding energy is reduced significantly. This is consistent for the formation of all the clusters with very little difference in the binding energy depending on which functional has been used to obtain the geometry. A maximum variation of 2 kcal/mol is observed for the DLPNO coupled cluster binding energies for the (C6H8O7)2(H2SO4)2 cluster. This shows that the thermal 8417


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reactions 5−7. The addition of a C6H8O7 to the (C6H8O7)(H2SO4)2 cluster in reaction 5 is unfavorable with a Gibbs free energy of 1.3 kcal/mol. Taking the variation between the different functionals into account, this interaction is of very similar magnitude to the addition of C6H8O7 to the (C6H8O7)(H2SO4) complex in reaction 3. The addition of a sulfuric acid molecule to the (C6H8O7)2(H2SO4) cluster is thermodynamically favorable with a value of −3.9 kcal/mol, as shown in reaction 6. Similarly is seen for the collision between (C6H8O7)(H2SO4) pairs with a Gibbs free energy value of −3.7 kcal/mol. Clusters with two C6H8O7 compounds have highly entangled structures due to a large number of different hydrogen bonds. These structures are observed to have sulfuric acid molecules concentrated in the core and the C6H8O7 compounds enclosing them. This type of enclosing core− shell interaction could indicate one of the reasons for the weak interaction between the C6H8O7 compound and sulfuric acid. The short chain of the C6H8O7 compound implies that there will be an increased strain in the carbon backbone to interact with the sulfuric acid. This strain will presumably be reduced in larger monoterpene-based ELVOC compounds. As the above-reported interactions between sulfuric acid and the C6H8O7 compound using the DLPNO energies are underbinding, the values can be assumed to be a lower bound. Even shifting all formation free energies by −2.66 kcal/ mol, the maximum difference between local and regular coupled cluster results in section 3.1, would not influence the conclusion that the C6H8O7 compound forms quite weakly bound clusters with itself and with sulfuric acid. We recently demonstrated using pinic acid that has more than two strong hydrogen binding moieties (i.e., strong interaction between two acceptors and two donors) are required to yield stable clusters.38 The C6H8O7 compound studied here is shown to exhibit weak hydrogen bonding from the lack of strong hydrogen bond acceptors and thereby cannot be assumed to be relevant in the initial steps of atmospheric new particle formation. It is thereby evident that the O/C ratio is not an exclusive factor in atmospheric new particle formation involving organic compounds, but the number of strong hydrogen bonding groups is equally important. In larger ELVOCs there is the possibility of having three or more donor−acceptor pairs, which could potentially lead to the formation of a stable cluster. This stresses the further need to evaluate larger monoterpene oxidation products, once they become available. 3.3. Enrichment in Sulfate Aerosols. Besides being important for atmospheric new particle formation, organic compounds can also interact with existing aerosol particles. We have recently investigated the interaction between aqueous sulfate (SO42−) and glyoxal, an important precursor for secondary organic aerosol (SOA).39 It was found that glyoxal in its native form only interacted weakly with sulfate. Contrarily, the hydrated forms of glyoxal were found to form strong complexes with sulfate via its OH groups, by displacing water molecules from the solvation shell leading to a “salting-in effect”. Although the gas phase cluster formation between sulfuric acid and the C6H8O7 compound is very weak, the hydrogen peroxide (−O−OH) groups could interact strongly with aqueous sulfate ions in a manner similar to that found for glyoxal hydrates. Using a water polarizable continuum model (PCM) to describe the aqueous phase, the molecular interaction can be modeled using water displacement reactions:

Table 2. Average Gibbs Free Energy (ΔG) for the Formation of the Clusters via Reactions 1−8, Calculated Using DFT Geometries (with Three Different Functionals and Two Basis Sets) and DLPNO-CCSD(T)/def2-QZVPP Energy Correctionsa reaction

ΔG

σ

(1) C6H8O7 + C6H8O7 ⇋ (C6H8O7)2 (2) C6H8O7 + H2SO4 ⇋ (C6H8O7)(H2SO4) (3) (C6H8O7)(H2SO4) + C6H8O7 ⇋ (C6H8O7)2(H2SO4) (4) (C6H8O7)(H2SO4) + H2SO4 ⇋ (C6H8O7)(H2SO4)2 (5) (C6H8O7)(H2SO4)2 + C6H8O7 ⇋ (C6H8O7)2(H2SO4)2 (6) (C6H8O7)2(H2SO4) + H2SO4 ⇋ (C6H8O7)2(H2SO4)2 (7) (C6H8O7)(H2SO4) + (C6H8O7)(H2SO4) ⇋ (C6H8O7)2(H2SO4)2 (8) H2SO4 + H2SO4 ⇋ (H2SO4)2

3.1 −0.2 0.0 −5.1 1.3 −3.9 −3.7

0.9 0.6 1.4 0.5 1.6 0.7 1.4

−5.4

0.4

The uncertainty σ corresponds to one standard deviation, illustrating the sensitivity of the Gibbs free energy to the quantum chemical method used in the geometry optimizations. All values are in kcal/mol. a

This indicates that C6H8O7 compounds are certainly not capable of forming clusters on their own, and other participating vapors are necessary. The interaction between the C6H8O7 compound and sulfuric acid (2) is also seen to be weak. The formation free energy is found to be −0.2 kcal/mol. This low value is also due to the C6H8O7 compound being thermodynamically stable in its isolated form, which will hinder the interaction with sulfuric acid. For forming the cluster two intermolecular hydrogen bonds are broken, but three hydrogen bonds are formed in the cluster, which indicates the higher stability compared to the C6H8O7 dimer in (1). As seen in Figure 4c, the lowest identified complex shows that sulfuric acid interacts with the C6H8O7 compound through hydrogen bond formation to the carbonyl group and the peroxy groups. Curiously, there is seen no direct peroxy acid−sulfuric acid interaction in the form of a H bond from SOH to the carbonyl oxygen in the O C(OOH) group. This could indicate that the reason for the weak hydrogen bonding of the peroxy acid group is due to the lack of strong hydrogen bond acceptors. The reaction free energy of the addition of a C6H8O7 compound to the (C6H8O7)(H2SO4) complex in reaction 3 is 0.0 kcal/mol. This indicates that the further addition of C6H8O7 to a sulfuric acid molecule is more or less as unfavorable as the first addition step (Figure 4d). The addition of a sulfuric acid molecule to the (C6H8O7)(H2SO4) complex (4) is thermodynamically favorable with a predicted reaction free energy of −5.1 kcal/mol. The formation of the cluster involves the formation of additional hydrogen bonds, which increase the stability, Figure 4e. The increased stability compared to the other clusters is due to the sulfuric acid−sulfuric acid interaction, which is able to bridge from one peroxy acid moiety to the other. The Gibbs free energy value is thereby close to the formation of the sulfuric acid dimer (8) with a value of −5.4 kcal/mol. Though thermodynamically favorable, it does not imply that the clusters are stable against evaporation. For vapors such as H2SO4 or ELVOCs with pptlevel or subppt-level concentrations, Gibbs free energies of cluster formation of −12 kcal/mol or below are required for the clusters to be “stable” in the sense that they would collide with vapor molecules faster than they evaporate.38 The formation of the (C6H8O7)2(H2SO4)2 cluster (Figure 4f) can occur through three different routes as shown in 8418


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noted that the large absolute differences between the reaction energy in a vacuum and in solution are due to the relative instability of the sulfate dianion in vacuum. As the vacuum reaction energies are only used to compute the DFT-CCSD(T) energy difference; this issue does not affect the final results. The pure nonelectrostatic contributions (ΔEnonelec) have been calculated using the SMD parametrization.40 The Gibbs free energy of the water displacement reaction (9) is found to be +1.5 to −11.9 kcal/mol, depending on the functional utilized. Even though the number of separate molecules does not change in reaction 9, the reaction is entropically unfavorable, resulting in a large positive thermal contribution to the free energy. This is likely due to the loss of torsional flexibility of the C6H8O7 molecule in the clustering reaction. Unfortunately, coupled cluster calculations in conjunction with a solvent continuum model are not available, so to get a better estimate of the ΔG value for the water displacement reaction, several approximations are necessary. We estimate the approximate DLPNO-CCSD(T) binding free energy in a water solvent as the following:

organic + (SO4 2 −)(H 2O)6 ⇋ (organic)(SO4 2 −)(H 2O)5 + H 2O

(9)

For glyoxal the free energy for the water displacement reaction was found to be −5.44 kcal/mol. To test the interaction between the C6H8O7 compound and sulfate, the water displacement reaction (9) has been calculated using PW91, M06-2X and ωB97X-D with the 6-31++G(d,p) basis set in PCM(water). The (C6H8O7)(SO42−)(H2O)5 cluster was initially manually constructed by adding the five water molecules in various different positions. The lowest conformation was further sampled performing a semiempirical (PM6) molecular dynamic simulation up to 1 ns. Along the trajectory several cluster structures were extracted, the geometry was optimized, and frequencies were calculated. The lowest identified molecular structure of the (C6H8O7)(SO42−)(H2O)5 cluster is shown in Figure 5 calculated using the M06-2X functional.

ΔGsolv,DLPNO = ΔEvac,DLPNO + ΔGtherm,DFT + ΔΔEsolv,DFT

Here ΔGtherm,DFT is the thermal contribution to the free energy calculated at the DFT level in a water solvent. The shift in the binding energy due to solvation (ΔΔEsolv,DFT) is calculated as the difference between the vacuum (ΔEvac,DFT) and solvent (ΔEwater,DFT) binding energies. This yields a ΔGsolv,DLPNO value in the range −5.7 to −8.2 kcal/mol. Despite the entropic penalty, the clustering of C6H8O7 with sulfate is thus likely at least as strong as that of hydrated glyoxal (ΔG = −5.44 kcal/ mol), which implies that the solubility of C6H8O7 into aerosol particles may be enhanced several orders of magnitude by the presence of sulfate ions. This indicates that polyperoxyacid compounds such as C6H8O7 are not participating directly in the initial steps in new particle formation but could potentially contribute to aerosol mass, by partitioning into the particle phase. It should be noted that neither the hydration reaction of the carbonyl groups of the C6H8O7 compound nor other aqueous phase reactions are considered here.

4. CONCLUSIONS We have investigated the molecular interaction between a recently reported cyclohexene autoxidation product and sulfuric acid. We find that DFT does not describe the binding energy of the investigated C6H8O7 compounds well and that a higher level correlated method is essential for obtaining accurate binding energies. This further emphasizes the risk of using only a single DFT functional for modeling atmospheric cluster formation and implies that more than one functional should routinely be applied to determine potential errors. We found a weak interaction between C6H8O7 and H2SO4, which indicates that not only the O/C ratio but also the

Figure 5. Lowest identified molecular structure of the (C6H8O7)(SO42−)(H2O)5 cluster, calculated at the M06-2X/6-31++G(d,p) level of theory.

The C6H8O7 compound forms multiple hydrogen bonds both with the sulfate ion and with the water molecules. The electronic reaction energies are calculated on top of the DFT geometries and shown in Table 3. The variation in the calculated single point energies thereby originate from the slightly different geometries of the same cluster. It should be

Table 3. Calculated Reaction Energies (ΔE) for the Water Displacement Reaction (9) Using DFT/6-31++G(d,p) and DLPNOCCSD(T)/def2-QZVPPa method

ΔEwater,DFT

ΔEnonelec

ΔEvac,DFT

ΔΔEsolv

ΔGtherm,DFT

ΔEvac,DLPNO

ΔEsolv,DLPNO

ΔGsolv,DLPNO

M06-2X PW91 ωB97X-D

−19.7 −4.6 −15.1

−1.5 −0.9 −1.3

−28.0 −10.4 −23.7

8.4 5.8 8.6

7.8 6.1 6.2

−21.9 −20.0 −23.0

−13.5 −14.2 −14.4

−5.7 −8.1 −8.2

a

The thermal contribution to the Gibbs free energy (ΔGTherm,DFT) is calculated using the PCM(water) optimized structure. All values are in kcal/ mol. 8419


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absolute number of strong hydrogen binding groups are important for determining the clustering ability of an organic molecule. This merits the further need to study large monoterpene oxidation products, when their precise molecular structures are resolved. The observed weak hydrogen bonding between the peroxy acid moieties and sulfuric acid indicates that for these types of diperoxy acid compounds to be directly involved in atmospheric new particle formation, larger clusters might be necessary. Alternatively, it could also indicate that another stabilizing component (such as water, bases, etc.) is required to reach a stable cluster. The further need to identify the molecular interaction between diperoxy acids and water/ ammonia is thereby crucial to gain a better understanding of the importance of ELVOC compounds in multicomponent new particle formation. We furthermore investigate the potential for the C6H8O7 compound to interact with aqueous sulfate ions, which indicates that short chained diperoxy acid compounds can potentially contribute to aerosol growth, by partitioning into the aqueous aerosol phase.

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ASSOCIATED CONTENT

S Supporting Information *

All identified minimum structures and the electronic energies (ΔE), thermal contributions to the Gibbs free energy (ΔGcorr) and Gibbs free energies (ΔG) for each functional and basis set are available as Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b04040.

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AUTHOR INFORMATION

Corresponding Author

*J. Elm. E-mail: jonas.elm@helsinki.fi. Phone: +4528938085. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Jonas Elm thanks the Danish centre for scientific computing for computational resources and the Carlsberg foundation for financial support. Theo Kurtén and Noora Hyttinen thank the Academy of Finland for funding. We thank CSC-IT Center for Science in Espoo, Finland, for computing time.

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Computational Study of the Clustering of a Cyclohexene

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