Configurational Sampling of Noncovalent (Atmospheric) Molecular Clusters: Sulfuric Acid and Guanidine

Iodine Clusters in the Atmosphere I: Computational Benchmark and Dimer Formation of Oxyacids and Oxides

The contribution of iodine-containing compounds to atmospheric new particle formation is still not fully understood, but iodic acid and iodous acid are thought to be significant contributors. While several quantum chemical studies have been carried out on clusters containing iodine, there is no comprehensive benchmark study quantifying the accuracy of the applied methods. Here, we present the first study in a series that investigate the role of iodine species in atmospheric cluster formation. In this work, we have studied the iodic acid, iodous acid, iodine tetroxide, and iodine pentoxide monomers and their dimers formed with common atmospheric precursors. We have tested the accuracy of commonly applied methods for calculating the geometry of the monomers, thermal corrections of monomers and dimers, the contribution of spin-orbit coupling to monomers and dimers, and finally, the accuracy of the electronic energy correction calculated at different levels of theory. We find that optimizing the structures either at the ωB97X-D3BJ/aug-cc-pVTZ-PP or the M06-2X/aug-cc-pVTZ-PP level achieves the best thermal contribution to the binding free energy. The electronic energy correction can then be calculated at the ZORA-DLPNO-CCSD(T0) level with the SARC-ZORA-TZVPP basis for iodine and ma-ZORA-def2-TZVPP for non-iodine atoms. We applied this methodology to calculate the binding free energies of iodine-containing dimer clusters, where we confirm the qualitative trends observed in previous studies. However, we identify that previous studies overestimate the stability of the clusters by several kcal/mol due to the neglect of relativistic effects. This means that their contributions to the currently studied nucleation pathways of new particle formation are likely overestimated.

Photochemical Mechanisms in Atmospherically Relevant Iodine Oxide Clusters

Atmospheric new particle formation events can be driven by iodine oxides or oxoacids via both neutral and ionic mechanisms. Photolysis of new particles likely plays a significant role in their growth mechanisms, but their spectra and photolysis mechanisms remain difficult to characterize. We recorded ultraviolet (UV) photodissociation spectra of (I2O5)0-3(IO3-) clusters, observing loss of an O atom, I2O4, and (I2O5)1,2 in the atmospherically relevant range of 300-340 nm. With increasing cluster size, the intensity of absorption red shifts and generally increases, suggesting particles photolyze more frequently as they grow. Estimates of the rates indicate that even relatively small clusters are likely to undergo photolysis under high-UV conditions. Vibrational spectra identify the covalent moiety I3O8- as the likely chromophore, not IO3-. The I2O5 loss pathway competes with particle growth, while the slower O loss pathway likely produces 3O + 3(cluster) products that could drive subsequent intraparticle chemistry, particularly with co-adsorbed organic or amine species.

Reparameterization of GFN1-xTB for atmospheric molecular clusters: applications to multi-acid-multi-base systems

Atmospheric molecular clusters, the onset of secondary aerosol formation, are a major part of the current uncertainty in modern climate models. Quantum chemical (QC) methods are usually employed in a funneling approach to identify the lowest free energy cluster structures. However, the funneling approach highly depends on the accuracy of low-cost methods to ensure that important low-lying minima are not missed. Here we present a reparameterized GFN1-xTB model based on the clusteromics I-V datasets for studying atmospheric molecular clusters (AMC), denoted AMC-xTB. The AMC-xTB model reduces the mean of electronic binding energy errors from 7-11.8 kcal mol-1 to roughly 0 kcal mol-1 and the root mean square deviation from 7.6-12.3 kcal mol-1 to 0.81-1.45 kcal mol-1. In addition, the minimum structures obtained with AMC-xTB are closer to the ωB97X-D/6-31++G(d,p) level of theory compared to GFN1-xTB. We employ the new parameterization in two new configurational sampling workflows that include an additional meta-dynamics sampling step using CREST with the AMC-xTB model. The first workflow, denoted the "independent workflow", is a commonly used funneling approach with an additional CREST step, and the second, the "improvement workflow", is where the best configuration currently known in the literature is improved with a CREST + AMC-xTB step. Testing the new workflow we find configurations lower in free energy for all the literature clusters with the largest improvement being up to 21 kcal mol-1. Lastly, by employing the improvement workflow we massively screened 288 new multi-acid-multi-base clusters containing up to 8 different species. For these new multi-acid-multi-base cluster systems we observe that the improvement workflow finds configurations lower in free energy for 245 out of 288 (85.1%) cluster structures. Most of the improvements are within 2 kcal mol-1, but we see improvements up to 8.3 kcal mol-1. Hence, we can recommend this new workflow based on the AMC-xTB model for future studies on atmospheric molecular clusters.

Cost-effective approach for atmospheric accretion reactions: a case of peroxy radical addition to isoprene

We present an accurate and cost-effective method for investigating the accretion reactions between unsaturated hydrocarbons and oxidized organic radicals. We use accretion between isoprene and primary, secondary and tertiary alkyl peroxy radicals as model reactions. We show that a systematic semiempirical transition state search can lead to better transition state structures than relaxed scanning with density functional theory with a significant gain in computational efficiency. Additionally, we suggest accurate and effective quantum chemical methods to study accretion reactions between large unsaturated hydrocarbons and oxidized organic radicals. Furthermore, we examine the atmospheric relevance of these types of reactions by calculating the bimolecular reaction rate coefficients and formation rates under atmospheric conditions from the quantum chemical reaction energy barriers.

Evidence of nitrate-based nighttime atmospheric nucleation driven by marine microorganisms in the South Pacific

Our understanding of ocean-cloud interactions and their effect on climate lacks insight into a key pathway: do biogenic marine emissions form new particles in the open ocean atmosphere? Using measurements collected in ship-borne air-sea interface tanks deployed in the Southwestern Pacific Ocean, we identified new particle formation (NPF) during nighttime that was related to plankton community composition. We show that nitrate ions are the only species for which abundance could support NPF rates in our semicontrolled experiments. Nitrate ions also prevailed in the natural pristine marine atmosphere and were elevated under higher sub-10 nm particle concentrations. We hypothesize that these nucleation events were fueled by complex, short-term biogeochemical cycling involving the microbial loop. These findings suggest a new perspective with a previously unidentified role of nitrate of marine biogeochemical origin in aerosol nucleation.

Computational Tools for Handling Molecular Clusters: Configurational Sampling, Storage, Analysis, and Machine Learning

Computational modeling of atmospheric molecular clusters requires a comprehensive understanding of their complex configurational spaces, interaction patterns, stabilities against fragmentation, and even dynamic behaviors. To address these needs, we introduce the Jammy Key framework, a collection of automated scripts that facilitate and streamline molecular cluster modeling workflows. Jammy Key handles file manipulations between varieties of integrated third-party programs. The framework is divided into three main functionalities: (1) Jammy Key for configurational sampling (JKCS) to perform systematic configurational sampling of molecular clusters, (2) Jammy Key for quantum chemistry (JKQC) to analyze commonly used quantum chemistry output files and facilitate database construction, handling, and analysis, and (3) Jammy Key for machine learning (JKML) to manage machine learning methods in optimizing molecular cluster modeling. This automation and machine learning utilization significantly reduces manual labor, greatly speeds up the search for molecular cluster configurations, and thus increases the number of systems that can be studied. Following the example of the Atmospheric Cluster Database (ACDB) of Elm (ACS Omega, 4, 10965-10984, 2019), the molecular clusters modeled in our group using the Jammy Key framework have been stored in an improved online GitHub repository named ACDB 2.0. In this work, we present the Jammy Key package alongside its assorted applications, which underline its versatility. Using several illustrative examples, we discuss how to choose appropriate combinations of methodologies for treating particular cluster types, including reactive, multicomponent, charged, or radical clusters, as well as clusters containing flexible or multiconformer monomers or heavy atoms. Finally, we present a detailed example of using the tools for atmospheric acid-base clusters.

Toward Modeling the Growth of Large Atmospheric Sulfuric Acid-Ammonia Clusters

Studying large atmospheric molecular clusters is needed to understand the transition between clusters and aerosol particles. In this work, we studied the (SA)n(AM)n clusters with n up to 30 and the (SA)m(AM)m±2 clusters, with m = 6-20. The cluster configurations are sampled using the ABCluster program, and the cluster geometries and thermochemical parameters are calculated using GFN1-xTB. The cluster binding energies are calculated using B97-3c. We find that the addition of sulfuric acid is preferred to the addition of ammonia. The addition free energies were found to have large uncertainties, which could potentially be attributed to errors in the applied level of theory. Based on DLPNO-CCSD(T0)/aug-cc-pVTZ benchmarks of the binding energies of the large (SA)8-9(AM)10 and (SA)10(AM)10-11 clusters, we find that ωB97X-D3BJ with a large basis set is required to yield accurate binding and addition energies. However, based on recalculations of the single-point energy at r2SCAN-3c and ωB97X-D3BJ/6-311++G(3df,3pd), we show that the single-point energy contribution is not the primary source of error. We hypothesize that a larger source of error might be present in the form of insufficient configurational sampling. Finally, we train Δ machine learning model on (SA)n(AM)n clusters with n up to 5 and show that we can predict the binding energies of clusters up to sizes of (SA)30(AM)30 with a binding energy error below 0.6 %. This is an encouraging approach for accurately modeling the binding energies of large acid-base clusters in the future.

Nitric Acid and Organic Acids Suppress the Role of Methanesulfonic Acid in Atmospheric New Particle Formation

Multicomponent atmospheric molecular clusters, typically comprising a combination of acids and bases, play a pivotal role in our climate system and contribute to the perplexing uncertainties embedded in modern climate models. Our understanding of cluster formation is limited by the lack of studies on complex mixed-acid-mixed-base systems. Here, we investigate multicomponent clusters consisting of mixtures of several acid and base molecules: sulfuric acid (SA), methanesulfonic acid (MSA), nitric acid (NA), formic acid (FA), along with methylamine (MA), dimethylamine (DMA), and trimethylamine (TMA). We calculated the binding free energies of a comprehensive set of 252 mixed-acid-mixed-base clusters at the DLPNO-CCSD(T0)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory. Combined with the existing datasets, we simulated the new particle formation (NPF) rates using the Atmospheric Cluster Dynamics Code (ACDC). We find that the presence of NA and FA had a substantial impact, increasing the NPF rate by 60% at realistic conditions. Intriguingly, we find that NA and FA suppress the role of MSA in NPF. These findings suggest that even high concentration of MSA has a limited impact on NPF in polluted regions with high FA and NA. We outline a method for generating a lookup table that could potentially be used in climate models that sufficiently incorporates all the required chemistry. By unraveling the molecular mechanisms of mixed-acid-mixed-base clusters, we get one step closer to comprehending their implications for our global climate system.

Current and future machine learning approaches for modeling atmospheric cluster formation

The formation of strongly bound atmospheric molecular clusters is the first step towards forming new aerosol particles. Recent advances in the application of machine learning models open an enormous opportunity for complementing expensive quantum chemical calculations with efficient machine learning predictions. In this Perspective, we present how data-driven approaches can be applied to accelerate cluster configurational sampling, thereby greatly increasing the number of chemically relevant systems that can be covered.

Heterogeneous Ion-Induced Nucleation of Water and Butanol Vapors Studied via Computational Quantum Chemistry beyond Prenucleation and Critical Cluster Sizes

Water and butanol are used as working fluids in condensation particle counters, and condensation of a single vapor onto an ion can be used as a simple model system for the study of ion-induced nucleation in the atmosphere. Motivated by this, we examine heterogeneous nucleation of water (H₂O) and n-butanol (BuOH) vapors onto three positively (Li⁺, Na⁺, K⁺) and three negatively charged (F^-, Cl^-, Br^-) ions using classical nucleation theory and computational quantum chemistry methods. We study phenomena that cannot be captured by Kelvin-Thomson equation for small nucleation ion cores. Our quantum chemistry calculations reveal the molecular mechanism behind ion-induced nucleation for each studied system. Typically, ions become solvated from all sides after several vapor molecules condense onto the ion. However, we show that the clusters of water and large negatively charged ions (Cl^- and Br^-) thermodynamically prefer the ion being migrated to the cluster surface. Although our methods generally do not show clear sign-preference for ion-water nucleation, we identified positive sign-preference for ion-butanol nucleation caused by the possibility to form stabilizing hydrogen bonds between butanol molecules condensed onto a positively charged ion. These bonds cannot form when butanol condenses onto a negatively charged ion. Therefore, we show that ion charge, its sign, as well as vapor properties have effects on the prenucleation and critical cluster/droplet sizes and also on the molecular mechanism of ion-induced nucleation.

Clusteromics V: Organic Enhanced Atmospheric Cluster Formation

Formic acid (FA) is a prominent candidate for organic enhanced nucleation due to its high abundance and stabilizing effect on smaller clusters. Its role in new particle formation is studied through the use of state-of-the-art quantum chemical methods on the cluster systems (acid)_1-2(FA)₁(base)_1-2 with the acids being sulfuric acid (SA)/methanesulfonic acid (MSA) and the bases consisting of ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). A funneling approach is used to determine the cluster structures with initial configurations generated through the ABCluster program, followed by semiempirical PM7 and ωB97X-D/6-31++G(d,p) calculations. The final binding free energy is calculated at the DLPNO-CCSD(T₀)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory using the quasi-harmonic approximation. Cluster dynamics simulations show that FA has a minuscule or negligible effect on the MSA-FA-base systems as well as most of the SA-FA-base systems. The SA-FA-DMA cluster system shows the highest influence from FA with an enhancement of 21%, compared to its non-FA counterpart.

Atmospheric Sulfuric Acid-Multi-Base New Particle Formation Revealed through Quantum Chemistry Enhanced by Machine Learning

The formation of molecular clusters and secondary aerosols in the atmosphere has a significant impact on the climate. Studies typically focus on the new particle formation (NPF) of sulfuric acid (SA) with a single base molecule (e.g., dimethylamine or ammonia). In this work, we examine the combinations and synergy of several bases. Specifically, we used computational quantum chemistry to perform configurational sampling (CS) of (SA)_0-4(base)_0-4 clusters with five different types of bases: ammonia (AM), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). Overall, we studied 316 different clusters. We used a traditional multilevel funnelling sampling approach augmented by a machine-learning (ML) step. The ML made the CS of these clusters possible by significantly enhancing the speed and quality of the search for the lowest free energy configurations. Subsequently, the cluster thermodynamics properties were evaluated at the DLPNO-CCSD(T₀)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory. The calculated binding free energies were used to evaluate the cluster stabilities for population dynamics simulations. The resultant SA-driven NPF rates and synergies of the studied bases are presented to show that DMA and EDA act as nucleators (although EDA becomes weak in large clusters), TMA acts as a catalyzer, and AM/MA is often overshadowed by strong bases.

The role of hydration in atmospheric salt particle formation

New-particle formation from condensable acid and base molecules is a ubiquitous phenomenon in the atmosphere. The role of water in salt particle formation is not fully understood as it can stabilize or destabilize cluster structures, which leads to non-linear effects on cluster formation dynamics. In the studied systems, increased relative humidity can enhance the particle formation for up to four orders of magnitude in the case of nitric acid, but it can also slightly reduce the particle formation in the cases of sulfuric acid and methanesulfonic acid. As the effect of relative humidity in salt particle formation varies many orders of magnitude depending on the acid and base molecules, neglecting hydration or using the same value for different systems may introduce remarkable inaccuracies in large-scale models.

Massive Assessment of the Binding Energies of Atmospheric Molecular Clusters

Quantum chemical studies of the formation and growth of atmospheric molecular clusters are important for understanding aerosol particle formation. However, the search for the lowest free-energy cluster configuration is extremely time consuming. This makes high-level benchmark data sets extremely valuable in the quest for the global minimum as it allows the identification of cost-efficient computational methodologies, as well as the development of high-level machine learning (ML) models. Herein, we present a highly versatile quantum chemical data set comprising a total of 11 749 (acid)_1-2(base)_1-2 cluster configurations, containing up to 44 atoms. Utilizing the LUMI supercomputer, we calculated highly accurate PNO-CCSD(F12*)(T)/cc-pVDZ-F12 binding energies of the full set of cluster configurations leading to an unprecedented data set both in regard to sheer size and with respect to the level of theory. We employ the constructed benchmark set to assess the performance of various semiempirical and density functional theory methods. In particular, we find that the r²-SCAN-3c method shows excellent performance across the data set related to both accuracy and CPU time, making it a promising method to employ during cluster configurational sampling. Furthermore, applying the data sets, we construct ML models based on Δ-learning and provide recommendations for future application of ML in cluster configurational sampling.

Computational chemistry of cluster: Understanding the mechanism of atmospheric new particle formation at the molecular level

New particle formation (NPF), which exerts significant influence over human health and global climate, has been a hot topic and rapidly expands field of research in the environmental and atmospheric chemistry recent years. Generally, NPF contains two processes: formation of critical nucleus and further growth of the nucleus. However, due to the complexity of the atmospheric nucleation, which is a multicomponent process, formation of critical clusters as well as their growth is still connected to large uncertainties. Detection limits of instruments in measuring specific gaseous aerosol precursors and chemical compositions at the molecular level call for computational studies. Computational chemistry could effectively compensate the deficiency of laboratory experiments as well as observations and predict the nucleation mechanisms. We review the present theoretical literatures that discuss nucleation mechanism of atmospheric clusters. Focus of this review is on different nucleation systems involving sulfur-containing species, nitrogen-containing species and iodine-containing species. We hope this review will provide a deep insight for the molecular interaction of nucleation precursors and reveal nucleation mechanism at the molecular level.

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.

Clusteromics IV: The Role of Nitric Acid in Atmospheric Cluster Formation

Nitric acid (NA) has previously been shown to affect atmospheric new particle formation; however, its role still remains highly uncertain. Through the employment of state-of-the-art quantum chemical methods, we study the (acid)_1-2(base)_1-2 and (acid)₃(base)₂ clusters containing at least one nitric acid (NA) and sulfuric acid (SA) or methanesulfonic acid (MSA) with bases ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). The initial cluster configurations are generated using the ABCluster program. PM7 and ωB97X-D/6-31++G(d,p) calculations are used to reduce the number of relevant configurations. The thermochemical parameters are calculated at the ωB97X-D/6-31++G(d,p) level of theory with the quasi-harmonic approximation, and the final single-point energies are calculated with high-level DLPNO-CCSD(T₀)/aug-cc-pVTZ calculations. The enhancing effect from the presence of nitric acid on cluster formation is studied using the calculated thermochemical data and cluster dynamics simulations. We find that when NA is in excess compared with the other acids, it has a substantial enhancing effect on the cluster formation potential.

Experimental and Theoretical Study on the Enhancement of Alkanolamines on Sulfuric Acid Nucleation

Alkanolamines such as monoethanolamine (MEA), diethanolamine (DEA), and triethanolamine (TEA) are extensively used for CO₂ capture and consumer products. Despite their prevalence in industrial applications, the fate of alkanolamines in the atmosphere remains relatively unknown. One likely reaction pathway for these chemicals in the atmosphere is new particle formation with sulfuric acid. Here, we present the first experimental results showing the formation of sulfuric acid dimers enhanced by MEA, DEA, and TEA from the measurement of molecular clusters. This study examines the nucleation reactions of MEA, DEA, and TEA with sulfuric acid in a clean, laminar flow reactor. The chemical compositions and concentrations of the freshly nucleated clusters were analyzed using a custom-built atmospheric pressure chemical ionization long time-of-flight mass spectrometer known as the Pittsburgh Cluster CIMS. Quantum chemical calculations and kinetic modeling of sulfuric acid-MEA/DEA/TEA clusters were also performed to determine relative cluster stabilities between these sulfuric acid-base systems. Experimental results indicate that MEA, DEA, and TEA at the part per trillion by volume (pptv) concentrations can enhance sulfuric acid dimer formation rates but to a lesser extent than dimethylamine (DMA). Thus, MEA, DEA, and TEA will potentially play an important role in new particle formation in industrial cities where these alkanolamines are emitted.

Clusteromics III: Acid Synergy in Sulfuric Acid-Methanesulfonic Acid-Base Cluster Formation

Acid-base molecular clusters are an important stage in atmospheric new particle formation. While such clusters are most likely multicomponent in nature, there are very few reports on clusters consisting of multiple acid molecules and multiple base molecules. By applying state-of-the-art quantum chemical methods, we herein study electrically neutral (SA)₁(MSA)₁(base)_0-2 clusters with base = ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA) and ethylenediamine (EDA). The cluster structures are obtained using a funneling approach employing the ABCluster program, semiempirical PM7 calculations and ωB97X-D/6-31++G(d,p) calculations. The final binding free energies are calculated at the DLPNO-CCSD(T₀)/aug-cc-pVTZ//ωB97X-D/6-31++G(d,p) level of theory using the quasi-harmonic approximation. Based on the calculated cluster geometries and thermochemistry (at 298.15 K and 1 atm), we find that the mixed (SA)₁(MSA)₁(base)_1-2 clusters more resemble the (SA)₂(base)_1-2 clusters compared to the (MSA)₂(base)_1-2 clusters. Hence, some of the steric hindrance and lack of hydrogen bond capacity previously observed in the (MSA)₂(base)_1-2 clusters is diminished in the corresponding (SA)₁(MSA)₁(base)_1-2 clusters. Cluster kinetics simulations reveal that the presence of an MSA molecule in the clusters enhances the cluster formation potential by up to a factor of 20. We find that the SA-MSA-DMA clusters have the highest cluster formation potential, and thus, this system should be further extended to larger sizes in future studies.

Real-time monitoring of aerosol particle formation from sulfuric acid vapor at elevated concentrations and temperatures

In the present study, time-resolved aerosol particle formation from sulfuric acid vapor is examined with special attention to the stabilization of molecular clusters in the early phase of unary nucleation. An important factor governing this process is the amount of condensable acid vapor. Here it is produced from fast gas-phase reactions in a batch-type reaction cell for which we introduce modifications enabling real-time monitoring. The key component for size- and time-resolved detection of ultrafine particles is a new 1 nm-SMPS. With this new tool at hand, the effect of varying the precursor concentration over two orders of magnitude is investigated. We demonstrate the ability to tune between different growth scenarios as indicated by the size-resolved particle traces which exhibit a transition from sigmoidal over quasi-stationary to peak-like shape. The second key parameter relevant for nucleation studies is the temperature-dependent cluster evaporation. Due to a temperature rise during the mixing stage of the experiment, evaporation is strongly promoted in the early phase. Therefore, the present study extends the T-range used in, e.g., smog chambers. We investigate this temperature effect in a kinetic simulation and can successfully combine simulated and measured data for validating theoretical evaporation rates obtained from DLPNO-CCSD(T₀)-calculations.

Computational Investigation of the Formation of Peroxide (ROOR) Accretion Products in the OH- and NO3-Initiated Oxidation of α-Pinene

The formation of accretion products (“dimers”) from recombination reactions of peroxyl radicals (RO₂) is a key step in the gas-phase generation of low-volatility vapors, leading to atmospheric aerosol particles. We have recently demonstrated that this recombination reaction very likely proceeds via an intermediate complex of two alkoxy radicals (RO···OR′) and that the accretion product pathway involves an intersystem crossing (ISC) of this complex from the triplet to the singlet surface. However, ISC rates have hitherto not been computed for large and chemically complex RO···OR′ systems actually relevant to atmospheric aerosol formation. Here, we carry out systematic conformational sampling and ISC rate calculations on ³(RO···OR′) clusters formed in the recombination reactions of different diastereomers of the first-generation peroxyl radicals originating in both OH- and NO₃-initiated reactions of α-pinene, a key biogenic hydrocarbon for atmospheric aerosol formation. While we find large differences between the ISC rates of different diastereomer pairs, all systems have ISC rates of at least 10⁶ s^–1, and many have rates exceeding 10¹⁰ s^–1. Especially the latter value demonstrates that accretion product formation via the suggested pathway is a competitive process also for α-pinene-derived RO₂ and likely explains the experimentally observed gas-phase formation of C₂₀ compounds in α-pinene oxidation.

Tri-Base Synergy in Sulfuric Acid-Base Clusters

Synergistic effects between different bases can greatly enhance atmospheric sulfuric acid (SA)-base cluster formation. However, only the synergy between two base components has previously been investigated. Here, we extend this concept to three bases by studying large atmospherically relevant (SA)3(base)3 clusters, with the bases ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA) and ethylenediamine (EDA). Using density functional theory—ωB97X-D/6-31++G(d,p)—we calculate the cluster structures and vibrational frequencies. The thermochemical parameters are calculated at 29,815 K and 1 atm, using the quasi-harmonic approximation. The binding energies of the clusters are calculated using high level DLPNO-CCSD(T0)/aug-cc-pVTZ. We find that the cluster stability in general depends on the basicity of the constituent bases, with some noteworthy additional guidelines: DMA enhances the cluster stability, TMA decreases the cluster stability and there is high synergy between DMA and EDA. Based on our calculations, we find it highly likely that three, or potentially more, different bases, are involved in the growth pathways of sulfuric acid-base clusters.

Clusteromics II: Methanesulfonic Acid-Base Cluster Formation

The role of methanesulfonic acid (MSA) in atmospheric new particle formation remains highly uncertain. Using state-of-the-art computational methods, we study the electrically neutral (MSA)0-2(base)0-2 clusters, with base = ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA). The cluster configurations are obtained using the ABCluster program and the number of initial cluster configurations is reduced based on PM7 calculations. Thermochemical parameters are calculated using the quasi-harmonic approximation based on the ωB97X-D/6-31++G(d,p) cluster structures and vibrational frequencies. The single point energies are calculated at the DLPNO-CCSD(T0)/aug-cc-pVTZ level of theory. We find that MSA shows a different interaction pattern with the bases compared to sulfuric acid and does not simply follow the basicity of the bases for these small clusters. In all cases, we find that the MSA-base clusters show very low cluster formation potential, indicating that electrically neutral clusters consisting solely of MSA as the clustering acid are most likely not capable of forming and growing under realistic atmospheric conditions.

Molecular properties affecting the hydration of acid-base clusters

In the atmosphere, water in all phases is ubiquitous and plays important roles in catalyzing atmospheric chemical reactions, participating in cluster formation and affecting the composition of aerosol particles. Direct measurements of water-containing clusters are limited because water is likely to evaporate before detection, and therefore, theoretical tools are needed to study hydration in the atmosphere. We have studied thermodynamics and population dynamics of the hydration of different atmospherically relevant base monomers as well as sulfuric acid-base pairs. The hydration ability of a base seems to follow in the order of gas-phase base strength whereas hydration ability of acid-base pairs, and thus clusters, is related to the number of hydrogen binding sites. Proton transfer reactions at water-air interfaces are important in many environmental and biological systems, but a deeper understanding of their mechanisms remain elusive. By studying thermodynamics of proton transfer reactions in clusters containing up to 20 water molecules and a base molecule, we found that that the ability of a base to accept a proton in a water cluster is related to the aqueous-phase basicity. We also studied the second deprotonation reaction of a sulfuric acid in hydrated acid-base clusters and found that sulfate formation is most favorable in the presence of dimethylamine. Molecular properties related to the proton transfer ability in water clusters are discussed.

New Particle Formation from the Vapor Phase: From Barrier-Controlled Nucleation to the Collisional Limit

Studies of vapor phase nucleation have largely been restricted to one of two limiting cases-nucleation controlled by a substantial free energy barrier or the collisional limit where the barrier is negligible. For weakly bound systems, exploring the transition between these regimes has been an experimental challenge, and how nucleation evolves in this transition remains an open question. We overcome these limitations by combining complementary Laval expansion experiments, providing new particle formation data for carbon dioxide over a uniquely broad range of conditions. Our experimental data together with a kinetic model using rate constants from high-level quantum chemical calculations provide a comprehensive picture of new particle formation as nucleation transitions from a barrier-dominated process to the collisional limit.

Calculating Reliable Gibbs Free Energies for Formation of Gas-Phase Clusters that Are Critical for Atmospheric Chemistry: (H2SO4)3

The effects of atmospheric aerosols on our climate are one of the biggest uncertainties in global climate models. Calculating the pathway for the formation of pre-nucleation clusters that become aerosols is challenging, requiring a comprehensive analysis of configurational space and highly accurate Gibbs free energy calculations. We identified a large set of minimum energy configurations of (H₂SO₄)₃ using a sampling technique based on a genetic algorithm and a stepwise density functional theory (DFT) approach and computed the thermodynamics of formation of these configurations with more accurate wavefunction-based electronic energies computed on the DFT geometries. The DLPNO-CCSD(T) methods always return more positive energies compared to the DFT energies. Within the DLPNO-CCSD(T) methods, extrapolating to the complete basis set limit gives more positive free energies compared to explicitly correlated single-point energies. The CBS extrapolation was shown to be robust as both the 4-5 inverse polynomial and Riemann zeta function schemes were within chemical accuracy of one another.

New Particle Formation and Growth from Dimethyl Sulfide Oxidation by Hydroxyl Radicals

Dimethyl sulfide (DMS) is produced by plankton in oceans and constitutes the largest natural emission of sulfur to the atmosphere. In this work, we examine new particle formation from the primary pathway of oxidation of gas-phase DMS by OH radicals. We particularly focus on particle growth and mass yield as studied experimentally under dry conditions using the atmospheric simulation chamber AURA. Experimentally, we show that aerosol mass yields from oxidation of 50-200 ppb of DMS are low (2-7%) and that particle growth rates (8.2-24.4 nm/h) are comparable with ambient observations. An HR-ToF-AMS was calibrated using methanesulfonic acid (MSA) to account for fragments distributed across both the organic and sulfate fragmentation table. AMS-derived chemical compositions revealed that MSA was always more dominant than sulfate in the secondary aerosols formed. Modeling using the Aerosol Dynamics, gas- and particle-phase chemistry kinetic multilayer model for laboratory CHAMber studies (ADCHAM) indicates that the Master Chemical Mechanism gas-phase chemistry alone underestimates experimentally observed particle formation and that DMS multiphase and autoxidation chemistry is needed to explain observations. Based on quantum chemical calculations, we conclude that particle formation from DMS oxidation in the ambient atmosphere will most likely be driven by mixed sulfuric acid/MSA clusters clustering with both amines and ammonia.

Heterogeneous Nucleation of Butanol on NaCl: A Computational Study of Temperature, Humidity, Seed Charge, and Seed Size Effects

Using a combination of quantum chemistry and cluster size distribution dynamics, we study the heterogeneous nucleation of n-butanol and water onto sodium chloride (NaCl)₁₀ seeds at different butanol saturation ratios and relative humidities. We also investigate how the heterogeneous nucleation of butanol is affected by the seed size through comparing (NaCl)₅, (NaCl)₁₀, and (NaCl)₂₅ seeds and by seed electrical charge through comparing (Na₁₀Cl₉)⁺, (NaCl)₁₀, and (Na₉Cl₁₀)⁻ seeds. Butanol is a common working fluid for condensation particle counters used in atmospheric aerosol studies, and NaCl seeds are frequently used for calibration purposes and as model systems, for example, sea spray aerosol. In general, our simulations reproduce the experimentally observed trends for the NaCl–BuOH–H₂O system, such as the increase of nucleation rate with relative humidity and with temperature (at constant supersaturation of butanol). Our results also provide molecular-level insights into the vapor–seed interactions driving the first steps of the heterogeneous nucleation process. The main purpose of this work is to show that theoretical studies can provide molecular understanding of initial steps of heterogeneous nucleation and that it is possible to find cost-effective yet accurate-enough combinations of methods for configurational sampling and energy evaluation to successfully model heterogeneous nucleation of multicomponent systems. In the future, we anticipate that such simulations can also be extended to chemically more complex seeds.

Clusteromics I: Principles, Protocols, and Applications to Sulfuric Acid-Base Cluster Formation

We recently coined the term clusteromics as a holistic approach for obtaining insight into the chemical complexity of atmospheric molecular cluster formation and at the same time providing the foundation for thermochemical databases that can be utilized for developing machine learning models. Here, we present the first paper in the series that applies state-of-the-art computational methods to study multicomponent (SA)0-2(base)0-2 clusters, with SA = sulfuric acid and base = [ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA)] with all combinations of the five bases. The initial cluster configurations are obtained using the ABCluster program and the number of relevant configurations are reduced based on PM7 and ωB97X-D/6-31++G(d,p) calculations. Thermochemical parameters are calculated based on the ωB97X-D/6-31++G(d,p) cluster structures and vibrational frequencies using the quasi-harmonic approximation. The single-point energies are refined with a high-level DLPNO-CCSD(T0)/aug-cc-pVTZ calculation. Using the calculated thermochemical data, we perform kinetics simulations to evaluate the potential of these small (SA)0-2(base)0-2 clusters to grow into larger cluster sizes. In all cases we find that having more than one type of base molecule present in the cluster will increase the potential for forming larger clusters primarily due to the increased available vapor concentration.

Toward a Holistic Understanding of the Formation and Growth of Atmospheric Molecular Clusters: A Quantum Machine Learning Perspective

The formation of atmospheric molecular clusters is an important stage in forming new particles in the atmosphere. Despite being a highly focused research area, the exact chemical species involved in the initial steps in new particle formation remain elusive. In this Perspective the main challenges and recent progression in the field are outlined with a special emphasis on the chemical complexity of the puzzle and prospect of modeling larger clusters. In general, there is a high demand for accurate and more complete quantum chemical data sets that can be applied in cluster distribution dynamics models and coupled to atmospheric chemical transport models. A view on how the community could reach this goal by applying data-driven machine learning approaches for more efficient exploration of cluster configurations is presented. A path toward larger clusters and direct molecular dynamics simulations of cluster formation and growth using machine learning models is discussed.

Hydration motifs of ammonium bisulfate clusters show complex temperature dependence

The role of water in the formation of particles from atmospheric trace gases is not well understood, in large part due to difficulties in detecting its presence under atmospheric conditions and the variety of possible structures that must be screened computationally. Here, we use infrared spectroscopy and variable-temperature ion trap mass spectrometry to investigate the structural motifs adopted by water bound to ammonium bisulfate clusters and their temperature dependence. For clusters featuring only acid-base linkages, water adopts a bridging arrangement spanning an adjacent ammonium and bisulfate. For larger clusters, water can also insert into a bisulfate-bisulfate hydrogen bond, yielding hydration isomers with very similar binding energies. The population of these isomers shows a complex temperature evolution, as an apparent third isomer appears with a temperature dependence that is difficult to explain using simple thermodynamic arguments. These observations suggest that the thermodynamics of water binding to atmospheric clusters such as these may not be straightforward.

Molecular level insights into the direct health impacts of some organic aerosol components

Quantum chemistry and biomodeling indicate that the studied organic aerosol components cannot directly cause oxidative stress or mutagenicity/carcinogenicity.

Seed-Adsorbate Interactions as the Key of Heterogeneous Butanol and Diethylene Glycol Nucleation on Ammonium Bisulfate and Tetramethylammonium Bromide

Condensation particle counter (CPC) instruments are commonly used to detect atmospheric nanoparticles. They operate on the basis of condensing an organic working fluid on the nanoparticle seeds to grow the particles to a detectable size, and at the size of few nanometers, their efficiency depends on how well the working fluid interacts with the seeds under the measurement conditions. This study models the first steps of heterogeneous nucleation of two working fluids commonly used in CPCs (diethylene glycol (DEG) and n-butanol) onto two positively charged seeds, ammonium bisulfate and tetramethylammonium bromide. The nucleation process is modeled on a molecular level using a combination of systematic configurational sampling and density functional theory (DFT). We take into account the conformational flexibility of DEG and n-butanol and determine the key factors that can improve the efficiency of nanoparticle measurements by CPCs. The results show that hydrogen bonding between the seed and the working fluid molecules is central to the adsorption of the first DEG/n-butanol molecules onto the seeds. However, intermolecular hydrogen bonding between the adsorbed molecules can also enhance the nucleation process for the weakly adsorbing vapor molecules. Accordingly, the heterogeneous nucleation probability is higher for working fluid-nanoparticle combinations with a higher potential for hydrogen bonding; in this case, DEG and ammonium bisulfate. Moreover, conformational analysis and methodology evaluations indicate that the consideration of adsorbate conformers and step-wise addition of the vapor molecules to the seeds is not essential for qualitative modeling of heterogeneous nucleation systems, at least for systems where the adsorbate and seed chemical properties are clearly different. This is the first molecular-level modeling study reporting detailed chemical reasons for experimentally observed seed and working fluid preferences in CPCs and reproducing the experimental observations. Our presented approach can be likely used for predicting preferences in similar nucleating systems.

Comparing Reaction Routes for 3(RO···OR') Intermediates Formed in Peroxy Radical Self- and Cross-Reactions

Organic peroxy radicals (RO₂) are key intermediates in the chemistry of the atmosphere. One of the main sink reactions of RO₂ is the recombination reaction RO₂ + R'O₂, which has three main channels (all with O₂ as a coproduct): (1) R_-H═O + R'OH, (2) RO + R'O, and (3) ROOR'. The RO + R'O "alkoxy" channel promotes radical and oxidant recycling, while the ROOR' "dimer" channel leads to low-volatility products relevant to aerosol processes. The ROOR' channel has only recently been discovered to play a role in the gas phase. Recent computational studies indicate that all of these channels first go through an intermediate complex ¹(RO···³O₂···OR'). Here, ³O₂ is very weakly bound and will likely evaporate from the system, giving a triplet cluster of two alkoxy radicals: ³(RO···OR'). In this study, we systematically investigate the three reaction channels for an atmospherically representative set of RO + R'O radicals formed in the corresponding RO₂ + R'O₂ reaction. First, we systematically sample the possible conformations of the RO···OR' clusters on the triplet potential energy surface. Next, we compute energetic parameters and attempt to estimate reaction rate coefficients for the three channels: evaporation/dissociation to RO + R'O, a hydrogen shift leading to the formation of R'_-H═O + ROH, and "spin-flip" (intersystem crossing) leading to, or at least allowing, the formation of ROOR' dimers. While large uncertainties in the computed energetics prevent a quantitative comparison of reaction rates, all three channels were found to be very fast (with typical rates greater than 10⁶ s^-1). This qualitatively demonstrates that the computationally proposed novel RO₂ + R'O₂ reaction mechanism is compatible with experimental data showing non-negligible branching ratios for all three channels, at least for sufficiently complex RO₂.

Establishing the structural motifs present in small ammonium and aminium bisulfate clusters of relevance to atmospheric new particle formation

Atmospheric new particle formation is the process by which atmospheric trace gases, typically acids and bases, cluster and grow into potentially climatically relevant particles. Here, we evaluate the structures and structural motifs present in small cationic ammonium and aminium bisulfate clusters that have been studied both experimentally and computationally as seeds for new particles. For several previously studied clusters, multiple different minimum-energy structures have been predicted. Vibrational spectra of mass-selected clusters and quantum chemical calculations allow us to assign the minimum-energy structure for the smallest cationic cluster of two ammonium ions and one bisulfate ion to a C_S-symmetry structure that is persistent under amine substitution. We derive phenomenological vibrational frequency scaling factors for key bisulfate vibrations to aid in the comparison of experimental and computed spectra of larger clusters. Finally, we identify a previously unassigned spectral marker for intermolecular bisulfate-bisulfate hydrogen bonds and show that it is present in a class of structures that are all lower in energy than any previously reported structure. Tracking this marker suggests that this motif is prominent in larger clusters as well as ∼180 nm ammonium bisulfate particles. Taken together, these results establish a set of structural motifs responsible for binding of gases at the surface of growing clusters that fully explain the spectrum of large particles and provide benchmarks for efforts to improve structure predictions, which are critical for the accurate theoretical treatment of this process.

Impact of Quantum Chemistry Parameter Choices and Cluster Distribution Model Settings on Modeled Atmospheric Particle Formation Rates

We tested the influence of various parameters on the new particle formation rate predicted for the sulfuric acid-ammonia system using quantum chemistry and cluster distribution dynamics simulations, in our case, Atmospheric Cluster Dynamics Code (ACDC). We found that consistent consideration of the rotational symmetry number of monomers (sulfuric acid and ammonia molecules, and bisulfate and ammonium ions) leads to a significant rise in the predicted particle formation rate, whereas inclusion of the rotational symmetry number of the clusters only changes the results slightly, and only in conditions where charged clusters dominate the particle formation rate. This is because most of the clusters stable enough to participate in new particle formation have a rotational symmetry number of 1, and few exceptions to this rule are positively charged clusters. In contrast, the application of the quasi-harmonic correction for low-frequency vibrational modes tends to generally decrease predicted new particle formation rates and also significantly alters the slope of the formation rate curve plotted against the sulfuric acid concentration, which is a typical convention in atmospheric aerosol science. The impact of the maximum size of the clusters explicitly included in the simulations depends on the simulated conditions. The errors arising from a limited set of clusters are higher for higher evaporation rates, and thus tend to increase with temperature. Similarly, the errors tend to be higher for lower vapor concentrations. The boundary conditions for outgrowing clusters (that are counted as formed particles) have only a small influence on the results, provided that the definition is chemically reasonable and that the set of simulated clusters is sufficiently large. A comparison with data from the Cosmics Leaving OUtdoor Droplets (CLOUD) chamber and a cluster distribution dynamics model using older quantum chemistry input data shows improved agreement when using our new input data and the proposed combination of symmetry and quasi-harmonic corrections.

Enhancing Potential of Trimethylamine Oxide on Atmospheric Particle Formation

The role of an oxidation product of trimethylamine, trimethylamine oxide, in atmospheric particle formation is studied using quantum chemical methods and cluster formation simulations. Molecular-level cluster formation mechanisms are resolved, and theoretical results on particle formation are confirmed with mass spectrometer measurements. Trimethylamine oxide is capable of forming only one hydrogen bond with sulfuric acid, but unlike amines, trimethylamine oxide can form stable clusters via ion–dipole interactions. That is because of its zwitterionic structure, which causes a high dipole moment. Cluster growth occurs close to the acid:base ratio of 1:1, which is the same as for other monoprotic bases. Enhancement potential of trimethylamine oxide in particle formation is much higher than that of dimethylamine, but lower compared to guanidine. Therefore, at relatively low concentrations and high temperatures, guanidine and trimethylamine oxide may dominate particle formation events over amines.