Molecular Interaction of Pinic Acid with Sulfuric Acid: Exploring the

Article pubs.acs.org/JPCA

Molecular Interaction of Pinic Acid with Sulfuric Acid: Exploring the Thermodynamic Landscape of Cluster Growth Jonas Elm,*,† Theo Kurtén,‡ 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, University of Helsinki, FIN-00014 Helsinki, Finland ¶ Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Århus C, Denmark ‡

S Supporting Information *

ABSTRACT: We investigate the molecular interactions between the semivolatile α-pinene oxidation product pinic acid and sulfuric acid using computational methods. The stepwise Gibbs free energies of formation have been calculated utilizing the M06-2X functional, and the stability of the clusters is evaluated from the corresponding ΔG values. The first two additions of sulfuric acid to pinic acid are found to be favorable with ΔG values of −9.06 and −10.41 kcal/mol. Addition of a third sulfuric acid molecule is less favorable and leads to a structural rearrangement forming a bridged sulfuric acid−pinic acid cluster. The involvement of more than one pinic acid molecule in a single cluster is observed to lead to the formation of favorable (pinic acid)2(H2SO4) and (pinic acid)2(H2SO4)2 clusters. The identified most favorable growth paths starting from a single pinic acid molecule lead to closed structures without the further possibility for attachment of either sulfuric acid or pinic acid. This suggests that pinic acid cannot be a key species in the first steps in nucleation, but the favorable interactions between sulfuric acid and pinic acid imply that pinic acid can contribute to the subsequent growth of an existing nucleus by condensation.

1. INTRODUCTION New particle formation via nucleation is a significant source of atmospheric aerosols.1 Nucleated particles can subsequently grow up to the size of cloud condensation nuclei (CCN), which can affect the properties and lifetime of clouds.2 Atmospheric nucleation is believed to provide up to half of the global CCN budget3 and depending on location can more than double the concentration of CCN over the course of a day.4,5 New particle formation in the atmosphere is a complex process involving multiple components, and knowledge about the exact mechanism and compounds involved at the molecular level is limited. Recently, the direct implication of amines has been established in the work by Almeida et al.6 It was shown that ppt levels of dimethylamine enhanced new particle formation rates more than 1000-fold compared to ammonia, which is sufficient to account for the new particle formation events observed in the atmosphere. The involvement of nonbasic organic compounds in nucleation is less clear and has only been elucidated in the past few years.7−9 The first indications of the participation of organic vapors in nucleation was the study by Zhang et al., who showed an enhanced nucleation of sulfuric acid in the presence of organic acids.10 Subsequent work has supported the involvement of organic compounds and suggested that a single organic compound is sufficient to reach the critical nucleus.11,12 The recent work by Schobesberger et al.13 indicates that 1−4 oxidized organics and 1−3 sulfuric acid molecules are needed in order to reach a critical nucleus. It is, however, uncertain if the concept of a critical nucleus applies to atmospherically relevant systems,14 as in the case of the dimethylamine/sulfuric acid cluster systems, and a barrierless formation has been shown.15 © 2014 American Chemical Society

A large challenge in resolving the possible participation of organic compounds in nucleation is the large number of oxidized compounds present in the atmosphere. Very recently, it has been established that extremely low volatile organic compounds (ELVOCs) can be directly linked to organic enhanced nucleation.16,17 The mechanism for the formation of ELVOCs is believed to occur by means of an autoxidation scheme through a consecutive internal hydrogen shift reaction by peroxy radicals.18 The phrase ELVOCs covers a large range of highly oxidized organic compounds, with a high oxygen to carbon (O/C) ratio of around 1 or even above. There is, however, limited knowledge about the specific molecular structure of individual ELVOCs. Most studies of the role of organic compounds have involved α-pinene, a volatile organic compound (VOC) emitted from pine trees. Several distinct oxidation products of α-pinene have been identified, and a good candidate for involvement in organic nucleation is pinic acid.19−22 Pinic acid is classified as a semivolatile organic compound (SVOC),23 with a O/C ratio of (4:9), and with its two acid moieties, it could potentially form clusters with several sulfuric acid molecules. Zhao et al. have earlier addressed the formation and stability of small pinonic acid−sulfuric acid clusters using computational methods.24 Pinonic acid and pinic acid have similar carbon skeletons but differ in that pinic acid has two carboxylic acid groups, while pinonic acid has a single carboxylic acid group and a carbonyl group. Received: April 16, 2014 Revised: June 20, 2014 Published: July 2, 2014 7892

dx.doi.org/10.1021/jp503736s | J. Phys. Chem. A 2014, 118, 7892−7900

The Journal of Physical Chemistry A

Article

(1pa)(1sa) and (1pa)(2sa) clusters were identified in the sampling. A mean absolute deviation (MAD) of 1.01 kcal/mol was found in the Gibbs free energy when lowering the basis set from 6-311++G(3df,3pd) to 6-31+G(d). Thereby, the truncation of the basis set in the sampling routine does not seem to induce severe errors. The largest structures studied here, such as the (1pa)(4sa) and (2pa)(2sa) clusters, were manually sampled using both a combinatorial approach by defining different hydrogen bonding sites for clustering and simulated annealing techniques using a MMFF94 force field. Unless otherwise noted, tabulated values are presented at the M06-2X/6-31+G(d) level of theory.

Here, we wish to establish the molecular interaction between pinic acid and sulfuric acid in order to identify the role of pinic acid in atmospheric nucleation and growth. We study large clusters involving 1−2 pinic acids and 1−4 sulfuric acid molecules. In particular, we wish to investigate the cluster morphology to see how several sulfuric acid molecules attach to the pinic acid molecule at the molecular level.

2. COMPUTATIONAL METHODOLOGY All DFT geometry optimizations and frequency calculations have been performed in Gaussian 09.25 We employ a systematic sampling technique where a large number of randomly generated conformations are initially optimized using PM6. Identified different conformations (up to a cutoff of 8 kcal/mol or a maximum of 150 conformations) are subsequently refined using density functional theory. For a detailed description, we refer to our previous investigations.26,27 We utilize the M062X28 functional on the basis of recent benchmarks, which show its adequate performance in calculating binding energies and Gibbs free energies of formation for clusters of atmospheric relevance.29−32 The applied semiempirically guided sampling technique should, for this system, supply equal functionality as more extensive sampling methods such as Replica Exchange Molecular Dynamics.33 Pinic acid has several internal rotational degrees of freedom of the carboxylic acid moieties, leading to different conformations. Ten different rotamers were scanned, and the lowest identified Gibbs free energy conformation at the M062X/6-311++G(3df,3pd) level of theory can be seen in Figure 1.

3. CLUSTER STABILITIES The formation free energy of clusters can be converted into cluster evaporation rates (kevap) via detailed balance.34 However, this requires an estimate of the cluster formation rate (kform), that is, the bimolecular rate coefficient for the reaction forming the cluster. Often, this is assumed to equal the hard-sphere (molecule−molecule or molecule−cluster) collision rate. However, this may cause large errors for more complex molecules such as pinic acid, which might form Hbonded clusters only for some particular collision geometries. A more robust measure of cluster stability can be obtained by computing the cluster formation free energy for which the evaporation rate (kevap) of a vapor molecule from a cluster is equal to the rate at which the same vapor condenses to form that cluster, which at a given vapor concentration c is simply equal to (kform·c). The formation rate cancels out of this expression, and we obtain ⎡ c ⎤ ΔG = RT ·ln⎢ ⎥ ⎣ cref ⎦ where cref is the reference pressure at which ΔG is calculated (typically 1 atm) and c is the vapor concentration. Thus, at a vapor concentration of 1 ppt, a ΔG of −16.3 kcal/mol is required for evaporation and condensation to match that at 298 K. For a vapor concentration of 10 ppt, this is reduced to −15.0 kcal/mol, and for a vapor concentration of 10 ppb, it is reduced to −10.9 kcal/mol.

Figure 1. Lowest identified Gibbs free energy conformation of pinic acid calculated at the M06-2X/6-311++G(3df,3pd) level of theory. The left carboxylic acid moiety will be denoted as acid group 1, while the right carboxylic acid moiety will be denoted as acid group 2.

4. RESULTS AND DISCUSSION 4.1. (Pinic Acid)(H2SO4) Clusters. Figure 2 depicts the lowest identified Gibbs free energy conformations of one sulfuric acid residing at either the carboxylic acid moiety 1 or 2 of pinic acid. To assess the performance of the M06-2X functional, the first addition of sulfuric acid to pinic acid was also calculated using the PW91 and ωB97X-D functionals, both with the 6-31+G(d) and 6-311++G(3df,3pd) basis sets. The PW91 functional has previously been used extensively for atmospheric applications,35−40 and both the PW91 and ωB97X-D functionals have shown similar performance as M06-2X in yielding binding energies in good agreement with coupled cluster calculations on atmospherically relevant clusters.30 The electronic energy (ΔE), enthalpy (ΔH), entropy (ΔS), and Gibbs free energy of formation (ΔG) are presented in Table 1. The ΔG values have been calculated at three different temperature (258, 278, and 298 K), which represent typical atmospheric values. The 278 K corresponds to a springtime day at a boreal forest site in Hyytiälä and is a typical temperature employed in the CLOUD chamber experiments to simulate the atmosphere.6,13 It is

This conformation was used as the starting point for a systematical sampling of configurational space. The two acid moieties will be denoted as 1 and 2, respectively, referring to the left and right acid groups in Figure 1. Clusters will be denoted as (npax−y)(msa), where n and m refers to the number of pinic acid molecules (pa) and sulfuric acid molecules (sa) in the cluster and x−y refers to how many sulfuric acid molecules reside at acid moiety 1 and 2, respectively. The potential rotations of the acid groups complicate the potential energy surface, and extensive manual sampling was included at each cluster formation step in order to thoroughly sample the configurational space. We found that utilizing the M06-2X/6-311++G(3df,3pd) methodology beyond (1pa)(2sa) clusters became computationally demanding while still maintaining a systematic scan of the configurational space. In order to preserve a reliable configurational search, we lowered the basis set to 6-31+G(d) in the scanning. To assess the potential error introduced by lowering the basis set, the (1pa)(1sa) and (1pa)(2sa) clusters were initially sampled with the full M06-2X/6-311++G(3df,3pd) methodology and compared to the truncated basis set approach. A total of 118 7893



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formic acid (ΔG = −6.44) and acetic acid (ΔG = −7.46).35 For other dicarboxylic acids (malonic, phthalic, and succinic acid) ΔG values from −4.23 to −4.93 kcal/mol have been reported using a PW91/6-311++G(3df,3pd)//B3LYP/6-311++G(2d,2p) methodology.41 The stronger binding of sulfuric acid to pinic acid further validates its potential importance in atmospheric particle growth. 4.2. (Pinic Acid)(H2SO4)2 Clusters. While the first addition of sulfuric acid to pinic acid leads to two different conformations that are close in Gibbs free energy, the addition of a second sulfuric acid can potentially yield three different cluster morphologies. Figure 3 contains the lowest identified Gibbs free energy structures of the three different conformations for the second addition of sulfuric acid to pinic acid, (1pa2−0)(2sa), (1pa1−1)(2sa), and (1pa0−2)(2sa). Table 2 contains the calculated electronic energy, enthalpy, entropy, and Gibbs free energy of formation, using the most stable (1pa)(1sa) cluster as a reference. The second addition of sulfuric acid will primarily occur at acid group 1, leading to the (1pa2−0)(2sa) cluster, with a Gibbs free energy of formation of −10.41 kcal/mol at 298 K. This slightly more favorable value than the first addition (−9.06 kcal/mol) is due to the formation of an additional hydrogen bond. The addition of one sulfuric acid molecule at each moiety in the (1pa1−1)(2sa) cluster is found to be less favorable by 3 kcal/mol. Both sulfuric acid molecules residing at the acid group 2 as in the (1pa0−2)(2sa) cluster are below 1 kcal/mol less stable. Besides the (1pa2−0)(2sa), (1pa1−1)(2sa), and (1pa0−2)(2sa) cluster conformations, the rotation of acid group 2 to pointing upward can lead to the bridging of the two sulfuric acid molecules, between the two sulfuric acid moieties. This cluster, termed (1pabridged)(2sa), can be seen in Figure 4. This bridged structure is the lowest conformation regarding electronic energy and enthalpy, but due to a more negative entropy contribution, it is not the lowest Gibbs free energy structure. This implies that this conformation becomes more favorable at lower temperatures, but a temperature as low as

Figure 2. Two lowest identified Gibbs free energy structures of the pinic acid−sulfuric acid complex. (Left) The sulfuric acid molecule attached to the acid moiety 1 on pinic acid, denoted (1pa1−0)(1sa). (Right) The sulfuric acid molecule attached to the acid moiety 2 on pinic acid, denoted (1pa0−1)(1sa). The atoms are color coded as following: carbon = dark gray, hydrogen = light gray, oxygen = red, and sulfur = yellow.

observed that all functionals agree well on the Gibbs free energy of formation (298 K) using the large basis set 6-311+ +G(3df,3pd) for the addition to both the acid moiety 1 and 2. All of the functionals show that sulfuric acid addition to the acid group 1 forming the (1pa1−0)(1sa) complex is most favorable. The values are within 1 kcal/mol of each other and range from −9.30 to −8.50 kcal/mol for M06-2X/6-311++G(3df,3pd) and PW91/6-311++G(3df,3pd), respectively. ωB97X-D/6-311+ +G(3df,3pd) depicts a value of −9.16 kcal/mol. Truncating the basis set to 6-31+G(d) still predicts that acid moiety 1 is the most acidic, with values in good agreement with the larger basis set 6-311++G(3df,3pd), having deviations of less than 1 kcal/ mol. All of the functionals are observed to yield similar thermodynamic parameters, and these results are rather independent of basis set. The predicted values of the Gibbs free energy of formation between sulfuric acid and pinic acid are slightly more favorable than the values computationally predicted for other atmospherically relevant acids. Oxalic acid has been shown to exhibit a very weak binding (ΔG = −3.24) at the PW91/6-311++G(3df,3pd) level of theory.37 Slightly more negative values are predicted for

Table 1. Electronic Energy (ΔE), Enthalpy (ΔH), Entropy (ΔS), and Gibbs Free Energy (ΔG) for the Formation of the Pinic Acid−Sulfuric Acid Complexa reaction M06-2X/6-311++G(3df,3pd) pa + sa ⇌ (1pa1−0)(1sa) pa + sa ⇌ (1pa0−1)(1sa) M06-2X/6-31+G(d) pa + sa ⇌ (1pa1−0)(1sa) pa + sa ⇌ (1pa0−1)(1sa) PW91/6-311++G(3df,3pd) pa + sa ⇌ (1pa1−0)(1sa) pa + sa ⇌ (1pa0−1)(1sa) PW91/6-31+G(d) pa + sa ⇌ (1pa1−0)(1sa) pa + sa ⇌ (1pa0−1)(1sa) ωB97X-D/6-311++G(3df,3pd) pa + sa ⇌ (1pa1−0)(1sa) pa + sa ⇌ (1pa0−1)(1sa) ωB97X-D/6-31+G(d) pa + sa ⇌ (1pa1−0)(1sa) pa + sa ⇌ (1pa0−1)(1sa) a

ΔE

ΔH

ΔS

ΔG258K

ΔG278K

ΔG298K

−20.46 −19.81

−19.87 −19.43

−35.46 −34.37

−10.72 −10.57

−10.01 −9.88

−9.30 −9.19

−20.83 −20.28

−19.94 −19.26

−36.49 −36.94

−10.53 −9.73

−9.80 −8.99

−9.06 −8.24

−19.98 −19.46

−19.70 −18.89

−37.55 −37.16

−10.01 −9.30

−9.26 −8.56

−8.50 −7.81

−19.66 −19.24

−18.89 −18.27

−36.93 −36.88

−9.37 −8.76

−8.63 −8.02

−7.89 −7.28

−20.15 −19.72

−19.47 −18.82

−34.56 −36.24

−10.55 −9.47

−9.86 −8.74

−9.16 −8.01

−20.17 −19.77

−19.05 −18.60

−35.12 −36.40

−9.99 −9.20

−9.29 −8.48

−8.58 −7.74

The ΔE, ΔH, and ΔG values are in kcal/mol, and ΔS is in cal/K·mol. 7894



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Figure 3. Three lowest identified Gibbs free energy structures of the (1pa)(2sa) clusters. (Left) Both sulfuric acid molecules attached to the acid moiety 1 on pinic acid, denoted (1pa2−0)(2sa). (Middle) One sulfuric acid molecule attached to each site at pinic acid, denoted (1pa1−1)(1sa). (Right) Both sulfuric acid molecules attached to the acid moiety 2 on pinic acid, denoted (1pa0−2)(2sa).

Table 2. Electronic Energy (ΔE), Enthalpy (ΔH), Entropy (ΔS), and Gibbs Free Energy (ΔG) for the Formation of the (1pa)(2sa) Clustera (1pa)(1sa) (1pa)(1sa) (1pa)(1sa) (1pa)(1sa) a

+ + + +

reaction

ΔE

ΔH

ΔS

ΔG258K

ΔG278K

ΔG298K

⇌ ⇌ ⇌ ⇌

−23.81 −19.43 −22.95 −27.29

−22.87 −18.27 −21.76 −26.03

−41.81 −36.91 −41.10 −59.02

−12.92 −9.49 −11.98 −11.98

−12.08 −8.75 −11.16 −10.80

−10.41 −7.27 −9.51 −8.43

sa sa sa sa

(1pa2−0)(2sa) (1pa1−1)(2sa) (1pa0−2)(2sa) (1pabridged)(2sa)

The ΔE, ΔH, and ΔG values are in kcal/mol, and ΔS is in cal/K·mol.

acid molcecules are residing at the same acid moiety, the Gibbs free energy of formation is relatively low, with a ΔG298K of −3.04 and −4.16 kcal/mol in the case of the (1pa0−3)(3sa) and (1pa3−0)(3sa) clusters, respectively. As the bridged structure is found to be the lowest Gibbs free energy conformation, the third addition of a sulfuric acid molecule must lead to a significant structural rearrangement to get from the (1pa2−0)(2sa) cluster to the bridged (1pabridged)(3sa) cluster. 4.4. (Pinic Acid)(H2SO4)4 Clusters. The cluster formation between four sulfuric acid molecules and one pinic acid molecule can lead to several different conformations. As stated in the Computational Methodology section, the configurational sampling was limited slightly for these large structures, but from the findings in the previous sections, there exist a few logical choices to investigate. As the conformations with all sulfuric acids residing at the same acid group were significantly less favorable than the conformations with sulfuric acid molecules at both pinic acid acid groups structures, the (1pa4−0)(3sa) and (1pa0−4)(3sa) clusters were not considered. In Figure 7, the lowest identified Gibbs free energy conformations of the (1pa2−2)(4sa) and (1pabridged)(4sa) clusters can be seen. In Table 4, the stepwise Gibbs free energy of formation for the (1pa)(4sa) clusters can be seen using the most stable (1pa)(3sa) as a reference. It is seen that the formation of the bridged cluster with four sulfuric acid molecules is highly favorable. This is due to the (1pabridged)(4sa) cluster being less strained than the (1pabridged)(3sa) cluster, which leads to a lowering in the entropy contribution. The stepwise Gibbs free energy is seen to be high, with a ΔG value of −9.46 kcal/mol at 298 K. The formation of the (1pa3−1)(4sa) and (1pa1−3)(4sa) clusters is observed to be significantly less favorable with Gibbs free energies of formation of −4.99 and −4.10 kcal/mol, respectively. While the formation of the (1pabridged)(4sa) cluster is highly favorable, it leads to a “closed” structure, which prevents further clustering without the next sulfuric acid addition entering the bridging chain. A similar bridged

Figure 4. Lowest identified Gibbs free energy conformation of the (1pabridged)(2sa) cluster, with bridging between the two acid moieties.

183 K would be required for it to become more favorable than the (1pa2−0)(2sa) cluster. 4.3. (Pinic Acid)(H2SO4)3 Clusters. The cluster formation between three sulfuric acids and one pinic acid can lead to four different combinations, (1pa3−0)(3sa), (1pa2−1)(3sa), (1pa1−2)(3sa), and (1pa0−3)(3sa). The lowest identified Gibbs free energy structures are shown in Figure 5. Besides these structures, a bridged structure (1pabridged)(3sa) similar to the cluster with two sulfuric acid molecules was identified, as shown in Figure 6. The associated enthalpy, entropy, and Gibbs free energy of formation for all of the (1pa)(3sa) cluster conformations can be seen in Table 3. It is observed that the lowest identified conformation (at 298 K) is the (1pabridged)(3sa) cluster with three sulfuric acid molecules bridged between pinic acid moiety 1 and 2. This structure is significantly lower in both electronic energy and enthalpy and thereby capable of overcoming the entropy contribution that made the (1pabridged)(2sa) less favorable. The third addition of sulfuric acid to pinic acid is observed to be significantly less favorable than the first two additions of sulfuric acid, with a Gibbs free energy of formation of −6.82 kcal/mol at 298 K. It is seen that the (1pa2−1)(3sa) cluster is the second most favorable, with ΔG298K = −5.96 kcal/mol, with (1pa1−2)(3sa) close behind, ΔG298K = −5.80 kcal/mol. When all three sulfuric 7895



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Figure 5. Four lowest identified Gibbs free energy structures of the (1pa)(3sa) clusters. (Top left) The (1pa3−0)(3sa) cluster. (Top right) The (1pa2−1)(3sa) cluster. (Lower left) The (1pa1−2)(3sa) cluster. (Lower right) The (1pa0−3)(3sa) cluster.

Figure 7. Lowest identified Gibbs free energy conformations of the (1pa2−2)(4sa) and (1pabridged)(4sa) clusters.

Figure 6. Lowest identified Gibbs free energy conformation of the (1pabridged)(3sa) cluster, with bridging between the two pinic acid moieties.

growth, clusters involving two pinic acid molecules are investigated. The simplest cluster with two pinic acids is the pinic acid dimer. The lowest identified structure is found to be the bridged dimer structure with the two pinic acids interaction via both acid groups. This structure is found to have a high entropy contribution of −58.53 cal/K·mol, similar to the (1pabridged)(2sa) cluster, due to the strained structure, which severely limits the Gibbs free energy. Several other structures are close in Gibbs free energy and involve the interaction between a single acid moiety from each pinic acid. The lowest identified pinic

(1pabridged)(5sa) cluster was identified, with a slightly lower Gibbs free energy of formation of −7.36 kcal/mol. This value is in line with the sulfuric acid dimer formation with a reported value of −7.10 kcal/mol at the G4MP2 level of theory,34 which could indicate that the sulfuric acid addition to pinic acid beyond the (1pabridged)(4sa) cluster is negligible. 4.5. Clusters Involving Two Pinic Acid Molecules. In the above sections, only a single pinic acid molecule was present in each cluster. To further investigate the cluster

Table 3. Electronic Energy (ΔE), Enthalpy (ΔH), Entropy (ΔS), and Gibbs Free Energy (ΔG) for the Formation of the Different (1pa)(3sa) Clustersa (1pa)(2sa) (1pa)(2sa) (1pa)(2sa) (1pa)(2sa) (1pa)(2sa) a

+ + + + +

reaction

ΔE

ΔH

ΔS

ΔG258K

ΔG278K

ΔG298K

⇌ ⇌ ⇌ ⇌ ⇌

−15.24 −19.23 −18.23 −13.90 −25.58

−13.79 −17.55 −16.87 −12.26 −23.62

−32.32 −38.87 −37.14 −30.95 −56.36

−6.10 −8.30 −8.03 −4.90 −10.21

−5.45 −7.52 −7.29 −4.28 −9.08

−4.16 −5.96 −5.80 −3.04 −6.82

sa sa sa sa sa

(1pa3−0)(3sa) (1pa2−1)(3sa) (1pa1−2)(3sa) (1pa0−3)(3sa) (1pabridged)(3sa)




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Table 4. Electronic Energy (ΔE), Enthalpy (ΔH), Entropy (ΔS), and Gibbs Free Energy (ΔG) for the Formation of the (1pa)(4sa) Clustera (1pa)(3sa) (1pa)(3sa) (1pa)(3sa) (1pa)(3sa) a

+ + + +

reaction

ΔE

ΔH

ΔS

ΔG258K

ΔG278K

ΔG298K

⇌ ⇌ ⇌ ⇌

−10.29 −16.04 −10.26 −21.18

−9.36 −15.09 −8.91 −19.76

−14.64 −27.97 −16.11 −34.55

−5.58 −8.43 −4.75 −11.53

−5.29 −7.87 −4.43 −10.84

−4.99 −6.75 −4.10 −9.46

sa sa sa sa

(1pa3−1)(4sa) (1pa2−2)(4sa) (1pa1−3)(4sa) (1pabridged)(4sa)

The ΔE, ΔH, and ΔG values are in kcal/mol, and ΔS is in cal/K·mol.

acid dimer (2pa) is shown in Figure 8. The associated Gibbs free energy of formation for the dimer is shown in Table 5 and

Figure 9. Lowest identified Gibbs free energy conformation of the (2pa)(1sa) cluster. Figure 8. Lowest identified Gibbs free energy structure of the pinic acid dimer.

is found to be −7.05 kcal/mol at 298 K. This value is slightly more negative than the value previously reported for the dimer formation of formic acid (ΔG = −5.69 kcal/mol) or acetic acid (ΔG = −6.27 kcal/mol)35 at the PW91/6-311++G(3df,3pd) level of theory. The addition of a sulfuric acid molecule to the pinic acid dimer can lead to several different conformations. A single conformation was identified to be significantly (ΔG > 3 kcal/ mol) more stable than the rest of the identified stable conformations. The molecular structure of the lowest identified Gibbs free energy (2pa)(1sa) cluster is shown in Figure 9. In Table 5, the calculated electronic energy, enthalpy, entropy, and Gibbs free energy of formation can be seen, using the most stable pinic acid dimer as a reference. It is observed that the addition of a sulfuric acid to the pinic acid dimer highly stabilizes the cluster with a Gibbs free energy of formation of ΔG = −12.16 kcal/mol at 298 K. This is due to a significant lowering in the entropy contribution leading to a less strained structure. The addition of a second sulfuric acid molecule leading to the (2pa)(2sa) cluster yielded a single structure that is significantly lower in energy than the others. The lowest identified conformation can be seen in Figure 10, and the associated Gibbs free energy of formation is shown in Table 5. Similar to the previous structures, it is observed that the bridged structure is the most stable, and the formation of the cluster has a Gibbs free energy value of −9.10 kcal/mol at 298

Figure 10. Lowest identified Gibbs free energy conformation of the (2pa)(2sa) cluster.

K. This indicates that pinic acid and sulfuric acid form 2:1 and 2:2 clusters with relatively high formation free energies. 4.6. Cluster Growth Mechanism. From the above sections, it is seen that the Gibbs free energy of formation associated with addition to a single pinic acid molecule as well as the additional addition of a sulfuric acid is 9 kcal/mol or above (up to four added sulfuric acid molecules), except in the formation of the (1sa)(3sa) cluster. Stabilization when the fourth sulfuric acid molecule is added is due to the formation of a hydrogen-bonded ring structure. The Gibbs free energy has been calculated using the most stable cluster as the starting point. This will in several cases imply that there needs to be significant molecular rearrangement in order to go from one minimum structure to the next one. By defining the acid groups 1 and 2 of pinic acid as distinct sites for attaching the sulfuric acid molecules, an analysis of the cluster formation pathways can be carried out. In addition to cluster stability, the relative concentrations of pinic acid and sulfuric acids molecules in the gas phase are important for the reaction path. In the following,

Table 5. Electronic Energy (ΔE), Enthalpy (ΔH), Entropy (ΔS), and Gibbs Free Energy (ΔG) for the Formation of the Pinic Acid Dimer (2pa) and the Formation of the (2pa)(1sa) and (2pa)(2sa) Clustersa

a

reaction

ΔE

ΔH

ΔS

ΔG258K

ΔG278K

ΔG298K

pa + pa ⇌ (2pa) 2pa + sa ⇌ (2pa)(1sa) (2ps)(1sa) + sa ⇌ (2pa)(2sa)

−25.94 −23.15 −24.26

−24.50 −22.60 −22.59

−58.53 −35.01 −45.24

−9.40 −13.56 −10.92

−8.23 −12.86 −10.01

−7.05 −12.16 −9.10




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we consider only cluster stability. Figure 11 presents the thermodynamic landscape (i.e identified local minima on the

Figure 12. Stability diagram for attaching sulfuric acid to two pinic acids. The color is coded according to Gibbs free energy of formation as follows: yellow, 8−9 kcal/mol; green, >9 kcal/mol. Calculations were performed at 278 K.

formation free energies are relatively high, they are still significantly lower than the reported values for sulfuric acid clusters stabilized by dimethylamine (∼−15 kcal/mol), and the pinic acid clusters might be susceptible to evaporation of both sulfuric and pinic acid, depending on their relative concentrations. Additionally, the identified clusters between pinic acid and sulfuric acid lead to “dead end” closed structures with no polar side chains available for further clustering. Thereby, pinic acid appears to be unable to be involved in the first step of nucleation but could potentially be involved in the further growth by condensation on an existing nucleus. These findings are consistent with the recent suggestion by Donahue et al. that pinic acid is outside of the potential “nucleator” region.42 This indicates that in order for an organic species to be involved in the initial steps in nucleation, more than two strong binding moieties are certainly required, which would imply a much higher O/C ratio than pinic acid.

Figure 11. Stability diagram for attaching sulfuric acid to pinic acid. The color is coded according to the Gibbs free energy of formation as follows: red, 9 kcal/mol. Calculations were performed at 278 K.

potential energy surface) of the pinic acid−sulfuric acid cluster growth at 278 K in the form of a stability diagram. The different pathways have been color coded after the stability such that red paths have a Gibbs free energy of formation less than 7 kcal/mol, orange and yellow are in the range 7−9 kcal/mol, and green has formation Gibbs free energies above 9 kcal/mol. The colors have been chosen such that the sulfuric acid dimer falls into the orange/yellow category with reported values of −7.10 kcal/mol using the G4MP2 method and with a value of −8.37 at the M06-2X/6311++G(3df,3pd) level of theory. In order to be an efficient stabilizer for nucleation, the pinic acid pathway has to be significantly more favorable than the formation of the sulfuric acid dimer. It is observed that there exists several pathways for which the next addition of a sulfuric acid molecule is at least 9 kcal/mol or higher. The first two additions of sulfuric acid will mainly lead to the (1pa2−0)(2sa) and (1pa0−2)(2sa) clusters and only a very limited amount of the (1pa1−1)(2sa) cluster. The third addition occurs through either the formation of a (1pa2−1)(3sa) or (1pa1−2)(3sa) cluster, which through a structural rearrangement can form the bridged (1pabridged)(3sa), which is slightly lower in Gibbs free energy. The addition of the fourth sulfuric acid should exclusively yield the (1pabridged)(4sa) cluster with no contributions to either of the rearranged (1pa3−1)(4sa), (1pa2−2)(4sa), or (1pa1−3)(4sa) clusters. The pathway analysis can be extended to include a second pinic acid molecule, as shown in Figure 12 as a stability diagram for the upper path. The formation of the pinic acid dimer is observed to progress with a ΔG of −8.23 kcal/mol at 278 K. Besides the pinic acid dimer, all other pathways leading to a cluster involving two pinic acid molecules are highly favorable, with a Gibbs free energy of formation of at least 10 kcal/mol. The growth of the pinic acid−sulfuric acid system yields clusters with a favorable Gibbs free energy of formation in the range of −10.01 to −12.86 kcal/mol for the clusters (pa)(2sa), (pa)(4sa), (2pa)(1sa), and (2pa)(2sa) at 278 K. While these

5. CONCLUSIONS We have investigated the molecular interaction between the semivolatile pinic acid molecule and sulfuric acid using density functional theory. We found that our usually employed methodology with the large 6-311++G(3df,3pd) basis set became computationally expensive even for the (1pa)(3sa) clusters. The truncation of the basis set from 6-311+ +G(3df,3pd) to 6-31+G(d) utilized in the geometry optimization only yielded a MAD of ∼1 kcal/mol in the Gibbs free energy of formation for 118 (1pa)(1sa) and (1pa)(2sa) clusters. The truncation of the basis set yields a large computational speed up compared to the error introduced. While this may be specific for the studied system at hand, it could be useful to further investigate this trend to allow routine calculations on larger systems while still maintaining a rigorous sampling technique. From the computed Gibbs free energies of formation, we have evaluated the cluster stabilities of a series of clusters containing one or two pinic acid molecules and up to four sulfuric acid molecules and found that pinic acid and sulfuric acid form strong hydrogen-bonded clusters. The involvement of more than one pinic acid molecule is observed to lead to highly stabilized (2pa)(sa) and (2pa)(2sa) clusters. While the clusters are indeed more stable than values previously reported for clusters of sulfuric acid with smaller organic acids, the Gibbs free energies of formation are mostly in the range of 9−12 kcal/ mol and thereby significantly lower than the interaction between sulfuric acid and dimethylamine. This suggests that pinic acid is not directly involved in the initial steps of atmospheric nucleation but could be capable of contributing to 7898



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the growth of an existing nucleus by condensation on the surface. In order to identify key compounds for the involvement in the initial steps of nucleation, further work involving the potential ELVOCs is required. The further modeling of larger nanoscale clusters consisting of pinic acid, sulfuric acid, and water using molecular dynamics simulations could yield important insight into the properties of these clusters for CCN activation and direct involvement in the global climate.43−46

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ASSOCIATED CONTENT

S Supporting Information *

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

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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