Elucidating the Limiting Steps in Sulfuric Acid–Base New Particle Formation

The molecular interactions between sulfuric acid (sa) and methylamine (ma) are investigated using computational methods. The molecular structures and vibrational frequencies of (sa)_<i>a</i>(ma)_<i>b</i> clusters, with <i>a</i>, <i>b</i> ≤ 4, were obtained with the ωB97X-D functional using a 6-31++G­(d,p) basis set. The single-point energies were corrected using the domain-based local pair natural orbital coupled cluster methodDLPNO–CCSD­(T)with an aug-cc-pVTZ basis set. The calculated Gibbs free energies (Δ<i><i>G</i></i>) of the clusters are used to calculate the evaporation rates of the (sa)_<i>a</i>(ma)_<i>b</i> cluster system and compare them to the corresponding ammonia clusters. With the atmospheric cluster dynamics code (ACDC), the new particle formation rates of the (sa)_<i>a</i>(ma)_<i>b</i> clusters were simulated and compared to the (sa)_<i>a</i>(dma)_<i>b</i> cluster system. It is found that methylamine is not capable of explaining observed new particle formation event in the ambient atmosphere. Looking into the calculated Gibbs free energy profiles it is found that the limiting steps in forming stable (sa)_3–4(base)_3–4 clusters depend strongly on the formation of the (sa)₁(base)₁ and (sa)₂(base)₂ clusters. These findings further support that compounds with high basicity are required to form the very initial cluster nucleus, which serves as the basis for forming new particles in the atmosphere

Elucidating the Limiting Steps in Sulfuric Acid–Base New Particle Formation

The molecular interactions between sulfuric acid (sa) and methylamine (ma) are investigated using computational methods. The molecular structures and vibrational frequencies of (sa)_<i>a</i>(ma)_<i>b</i> clusters, with <i>a</i>, <i>b</i> ≤ 4, were obtained with the ωB97X-D functional using a 6-31++G­(d,p) basis set. The single-point energies were corrected using the domain-based local pair natural orbital coupled cluster methodDLPNO–CCSD­(T)with an aug-cc-pVTZ basis set. The calculated Gibbs free energies (Δ<i><i>G</i></i>) of the clusters are used to calculate the evaporation rates of the (sa)_<i>a</i>(ma)_<i>b</i> cluster system and compare them to the corresponding ammonia clusters. With the atmospheric cluster dynamics code (ACDC), the new particle formation rates of the (sa)_<i>a</i>(ma)_<i>b</i> clusters were simulated and compared to the (sa)_<i>a</i>(dma)_<i>b</i> cluster system. It is found that methylamine is not capable of explaining observed new particle formation event in the ambient atmosphere. Looking into the calculated Gibbs free energy profiles it is found that the limiting steps in forming stable (sa)_3–4(base)_3–4 clusters depend strongly on the formation of the (sa)₁(base)₁ and (sa)₂(base)₂ clusters. These findings further support that compounds with high basicity are required to form the very initial cluster nucleus, which serves as the basis for forming new particles in the atmosphere

Contribution of Methanesulfonic Acid to the Formation of Molecular Clusters in the Marine Atmosphere

Because of the lack of long-term measurements, new particle formation (NPF) in the marine atmosphere remains puzzling. Using quantum chemical methods, this study elucidates the cluster formation and further growth of sulfuric acid–methane­sulfonic acid–dimethylamine (SA-MSA-DMA) clusters, relevant to NPF in the marine atmosphere. The cluster structures and thermochemical parameters of (SA)n(MSA)m(DMA)l (n + m ≤ 4 and l ≤ 4) systems are calculated using density functional theory at the ωB97X-D/6-31++G(d,p) level of theory, and the single-point energies are calculated using high-level DLPNO-CCSD(T0)/aug-cc-pVTZ calculations. The calculated thermochemistry is used as input to the Atmospheric Cluster Dynamics Code (ACDC) to gain insight into the cluster dynamics. At ambient conditions (298.15 K, 1 atm), we find that the distribution of outgrowing clusters primarily consists of SA and DMA, with a minor contribution from the mixed SA–MSA–DMA clusters. At lower temperature (278.15 K, 1 atm) the distribution broadens, and clusters containing one or more MSA molecules emerge. These findings show that in the cold marine atmosphere MSA likely participates in atmospheric NPF

Assessment of Density Functional Theory in Predicting Structures and Free Energies of Reaction of Atmospheric Prenucleation Clusters

This work assesses different computational strategies for predicting structures and Gibb’s free energies of reaction of atmospheric prenucleation clusters. The performance of 22 Density Functional Theory functionals in predicting equilibrium structures of molecules and water prenucleation clusters of atmospheric relevance is evaluated against experimental data using a test set of eight molecules and prenucleation clusters: SO₂, H₂SO₄, CO₂·H₂O, CS₂·H₂O, OCS·H₂O, SO₂·H₂O, SO₃·H₂O, and H₂SO₄·H₂O. Furthermore, the functionals are tested and compared for their ability to predict the free energy of reaction for the formation of five benchmark atmospheric prenucleation clusters: H₂SO₄·H₂O, H₂SO₄·(H₂O)₂, H₂SO₄·NH₃, HSO₄^–·H₂O, and HSO₄^–·(H₂O)₂. The performance is evaluated against experimental data, coupled cluster, and complete basis set extrapolation procedure methods. Our investigation shows that the utilization of the M06-2X functional with the 6-311++G­(3df,3pd) basis set represents an improved approach compared to the conventionally used PW91 functional, yielding mean absolute errors of 0.48 kcal/mol and maximum errors of 0.67 kcal/mol compared to experimental results

Influence of Nucleation Precursors on the Reaction Kinetics of Methanol with the OH Radical

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

Computational Study of the Clustering of a Cyclohexene Autoxidation Product C₆H₈O₇ with Itself and Sulfuric Acid

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 DLPNO-CCSD­(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 (<i>Δ<i>G</i></i> 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

Molecular Interaction of Pinic Acid with Sulfuric Acid: Exploring the Thermodynamic Landscape of Cluster Growth

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 Δ<i>G</i> values. The first two additions of sulfuric acid to pinic acid are found to be favorable with Δ<i>G</i> 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

Strong Hydrogen Bonded Molecular Interactions between Atmospheric Diamines and Sulfuric Acid

We investigate the molecular interaction between methyl-substituted <i>N</i>,<i>N</i>,<i>N</i>′,<i>N</i>′-ethylenediamines, propane-1,3-diamine, butane-1,4-diamine, and sulfuric acid using computational methods. Molecular structure of the diamines and their dimer clusters with sulfuric acid is studied using three density functional theory methods (PW91, M06-2X, and ωB97X-D) with the 6-31++G­(d,p) basis set. A high level explicitly correlated CCSD­(T)-F12a/VDZ-F12 method is used to obtain accurate binding energies. The reaction Gibbs free energies are evaluated and compared with values for reactions involving ammonia and atmospherically relevant monoamines (methylamine, dimethylamine, and trimethylamine). We find that the complex formation between sulfuric acid and the studied diamines provides similar or more favorable reaction free energies than dimethylamine. Diamines that contain one or more secondary amino groups are found to stabilize sulfuric acid complexes more efficiently. Elongating the carbon backbone from ethylenediamine to propane-1,3-diamine or butane-1,4-diamine further stabilizes the complex formation with sulfuric acid by up to 4.3 kcal/mol. Dimethyl-substituted butane-1,4-diamine yields a staggering formation free energy of −19.1 kcal/mol for the clustering with sulfuric acid, indicating that such diamines could potentially be a key species in the initial step in the formation of new particles. For studying larger clusters consisting of a diamine molecule with up to four sulfuric acid molecules, we benchmark and utilize a domain local pair natural orbital coupled cluster (DLPNO-CCSD­(T)) method. We find that a single diamine is capable of efficiently stabilizing sulfuric acid clusters with up to four acid molecules, whereas monoamines such as dimethylamine are capable of stabilizing at most 2–3 sulfuric acid molecules

Strong Hydrogen Bonded Molecular Interactions between Atmospheric Diamines and Sulfuric Acid

We investigate the molecular interaction between methyl-substituted <i>N</i>,<i>N</i>,<i>N</i>′,<i>N</i>′-ethylenediamines, propane-1,3-diamine, butane-1,4-diamine, and sulfuric acid using computational methods. Molecular structure of the diamines and their dimer clusters with sulfuric acid is studied using three density functional theory methods (PW91, M06-2X, and ωB97X-D) with the 6-31++G­(d,p) basis set. A high level explicitly correlated CCSD­(T)-F12a/VDZ-F12 method is used to obtain accurate binding energies. The reaction Gibbs free energies are evaluated and compared with values for reactions involving ammonia and atmospherically relevant monoamines (methylamine, dimethylamine, and trimethylamine). We find that the complex formation between sulfuric acid and the studied diamines provides similar or more favorable reaction free energies than dimethylamine. Diamines that contain one or more secondary amino groups are found to stabilize sulfuric acid complexes more efficiently. Elongating the carbon backbone from ethylenediamine to propane-1,3-diamine or butane-1,4-diamine further stabilizes the complex formation with sulfuric acid by up to 4.3 kcal/mol. Dimethyl-substituted butane-1,4-diamine yields a staggering formation free energy of −19.1 kcal/mol for the clustering with sulfuric acid, indicating that such diamines could potentially be a key species in the initial step in the formation of new particles. For studying larger clusters consisting of a diamine molecule with up to four sulfuric acid molecules, we benchmark and utilize a domain local pair natural orbital coupled cluster (DLPNO-CCSD­(T)) method. We find that a single diamine is capable of efficiently stabilizing sulfuric acid clusters with up to four acid molecules, whereas monoamines such as dimethylamine are capable of stabilizing at most 2–3 sulfuric acid molecules

Hydration of Atmospheric Molecular Clusters: A New Method for Systematic Configurational Sampling

We present a new systematic configurational sampling algorithm for investigating the potential energy surface of hydrated atmospheric molecular clusters. The algorithm is based on creating a Fibonacci sphere around each atom in the cluster and adding water molecules to each point in nine different orientations. For the sampling of water molecules to existing hydrogen bonds, the cluster is displaced along the hydrogen bond, and a water molecule is placed in between in three different orientations. Generated redundant structures are eliminated based on minimizing the root-mean-square distance of different conformers. Initially, the clusters are sampled using the semiempirical PM6 method and subsequently using density functional theory (M06-2X and ωB97X-D) with the 6-31++G­(d,p) basis set. Applying the developed algorithm, we study the hydration of sulfuric acid with up to 15 water molecules. We find that the addition of the first four water molecules “saturate” the sulfuric acid molecule and that they are more thermodynamically favorable than the addition of water molecules 5–15. Using the large generated set of conformers, we assess the performance of approximate methods (ωB97X-D, M06-2X, PW91, and PW6B95-D3) in calculating the binding energies and assigning the global minimum conformation compared to high level CCSD­(T)-F12a/VDZ-F12 reference calculations. The tested DFT functionals systematically overestimate the binding energies compared to coupled cluster calculations, and we find that this deficiency can be corrected by a simple scaling factor