Atmospheric Molecular Clusters Research Articles

Massive Assessment of the Geometries of Atmospheric Molecular Clusters.

Atmospheric molecular clusters are important for the formation of new aerosol particles in the air. However, current experimental techniques are not able to yield direct insight into the cluster geometries. This implies that to date there is limited information about how accurately the applied computational methods depict the cluster structures. Here we massively benchmark the molecular geometries of atmospheric molecular clusters. We initially assessed how well different DF-MP2 approaches reproduce the geometries of 45 dimer clusters obtained at a high DF-CCSD(T)-F12b/cc-pVDZ-F12 level of theory. Based on the results, we find that the DF-MP2/aug-cc-pVQZ level of theory best resembles the DF-CCSD(T)-F12b/cc-pVDZ-F12 reference level. We subsequently optimized 1283 acid-base cluster structures (up to tetramers) at the DF-MP2/aug-cc-pVQZ level of theory and assessed how more approximate methods reproduce the geometries. Out of the tested semiempirical methods, we find that the newly parametrized atmospheric molecular cluster extended tight binding method (AMC-xTB) is most reliable for locating the correct lowest energy configuration and yields the lowest root mean square deviation (RMSD) compared to the reference level. In addition, we find that the DFT-3c methods show similar performance as the usually employed ωB97X-D/6-31++G(d,p) level of theory at a potentially reduced computational cost. This suggests that these methods could prove to be valuable for large-scale screening of cluster structures in the future.

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.

Accurate modeling of the potential energy surface of atmospheric molecular clusters boosted by neural networks.

The computational cost of accurate quantum chemistry (QC) calculations of large molecular systems can often be unbearably high. Machine learning offers a lower computational cost compared to QC methods while maintaining their accuracy. In this study, we employ the polarizable atom interaction neural network (PaiNN) architecture to train and model the potential energy surface of molecular clusters relevant to atmospheric new particle formation, such as sulfuric acid-ammonia clusters. We compare the differences between PaiNN and previous kernel ridge regression modeling for the Clusteromics I-V data sets. We showcase three models capable of predicting electronic binding energies and interatomic forces with mean absolute errors of <0.3 kcal mol-1 and <0.2 kcal mol-1 Å-1, respectively. Furthermore, we demonstrate that the error of the modeled properties remains below the chemical accuracy of 1 kcal mol-1 even for clusters vastly larger than those in the training database (up to (H2SO4)15(NH3)15 clusters, containing 30 molecules). Consequently, we emphasize the potential applications of these models for faster and more thorough configurational sampling and for boosting molecular dynamics studies of large atmospheric molecular clusters.

Formation of atmospheric molecular clusters containing nitric acid with ammonia, methylamine, and dimethylamine.

This study investigates the formation of atmospheric molecular clusters containing ammonia (NH3, A), methylamine (CH3NH2, MA), or dimethylamine (CH3NHCH3, DMA) with nitric acid (HNO3, NA) using quantum mechanics. The Atmospheric Cluster Dynamic Code (ACDC) was employed to simulate the total evaporation rate, formation rate, and growth pathways of three types of clusters under dry and hydrated conditions. This study evaluates the enhancing potential of A/MA/DMA for NA-based new particle formation (NPF) at parts per trillion (ppt) levels. The results indicate that A/MA/DMA can enhance NA-based NPF at high nitric acid concentrations and low temperatures in the atmosphere. The enhancing potential of MA is weaker than that of DMA but stronger than that of A. Cluster growth predominantly follows the lowest free energy pathways on the acid-base grid, with the formation of initial acid-base dimers (NA)(A), (NA)(MA), and (NA)(DMA) being crucial. Hydration influences the evaporation rate and formation rate of clusters, especially for initial clusters. When the humidity is at 100%, the formation rate for NA-A, NA-MA, and NA-DMA clusters can increase by approximately 109, 107, and 104-fold compared to the corresponding unhydrated clusters, respectively. These results highlight the significance of nitric acid nucleation in NPF events in low-temperature, high-humidity atmospheres, particularly in regions like China with significant automobile exhaust pollution.

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.

Improved Configurational Sampling Protocol for Large Atmospheric Molecular Clusters.

The nucleation process leading to the formation of new atmospheric particles plays a crucial role in aerosol research. Quantum chemical (QC) calculations can be used to model the early stages of aerosol formation, where atmospheric vapor molecules interact and form stable molecular clusters. However, QC calculations heavily depend on the chosen computational method, and when dealing with large systems, striking a balance between accuracy and computational cost becomes essential. We benchmarked the binding energies and structures and found the B97-3c method to be a good compromise between the accuracy and computational cost for studying large cluster systems. Further, we carefully assessed configurational sampling procedures for targeting large atmospheric molecular clusters containing up to 30 molecules (approximately 2 nm in diameter) and proposed a funneling approach with highly improved accuracy. We find that several parallel ABCluster explorations lead to better guesses for the cluster global energy minimum structures than one long exploration. This methodology allows us to bridge computational studies of molecular clusters, which typically reach only around 1 nm, with experimental studies that often measure particles larger than 2 nm. By employing this workflow, we searched for low-energy configurations of large sulfuric acid-ammonia and sulfuric acid-dimethylamine clusters. We find that the binding free energies of clusters containing dimethylamine are unequivocally more stable than those of the ammonia-containing clusters. Our improved configurational sampling protocol can in the future be applied to study the growth and dynamics of large clusters of arbitrary compositions.

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.

Quantum chemical modeling of atmospheric molecular clusters involving inorganic acids and methanesulfonic acid

Atmospheric molecular cluster formation is the first stage toward aerosol particle formation. Despite intensive progress in recent years, the relative role of different vapors and the mechanisms for forming clusters is still not well-understood. Quantum chemical (QC) methods can give insight into the cluster formation mechanisms and thereby yield information about the potentially relevant compounds. Here, we summarize the QC literature on clustering involving species such as sulfuric acid, methanesulfonic acid, and nitric acid. The importance of iodine species such as iodous acid (HIO2) and iodic acid (HIO3) in atmospheric cluster formation is an emerging topic, and we critically review the recent literature and give our view on how to progress in the future. We outline how machine learning (ML) methods can be used to enhance cluster configurational sampling, leading to a massive increase in the cluster compositions that can be modeled. In the future, ML-boosted cluster formation could allow us to comprehensively understand complex cluster formation with multiple pathways, leading us one step closer to implementing accurate cluster formation mechanisms in atmospheric models.

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.

Clusterome: A Comprehensive Data Set of Atmospheric Molecular Clusters for Machine Learning Applications.

Formation and growth of atmospheric molecular clusters into aerosol particles impact the global climate and contribute to the high uncertainty in modern climate models. Cluster formation is usually studied using quantum chemical methods, which quickly becomes computationally expensive when system sizes grow. In this work, we present a large database of ∼250k atmospheric relevant cluster structures, which can be applied for developing machine learning (ML) models. The database is used to train the ML model kernel ridge regression (KRR) with the FCHL19 representation. We test the ability of the model to extrapolate from smaller clusters to larger clusters, between different molecules, between equilibrium structures and out-of-equilibrium structures, and the transferability onto systems with new interactions. We show that KRR models can extrapolate to larger sizes and transfer acid and base interactions with mean absolute errors below 1 kcal/mol. We suggest introducing an iterative ML step in configurational sampling processes, which can reduce the computational expense. Such an approach would allow us to study significantly more cluster systems at higher accuracy than previously possible and thereby allow us to cover a much larger part of relevant atmospheric compounds.

Recent advances in quantum fragmentation approaches to complex molecular and condensed‐phase systems

AbstractQuantum mechanical (QM) calculations are critical in quantitatively understanding the relationship between the structure and physicochemical properties of various chemical systems. However, the sharply increasing computational cost with the system size has severely hindered applying direct QM calculations on large‐sized systems. Hence, linear‐scaling and/or fragmentation QM methods have been proposed to overcome this difficulty. In this review, we focus on the recent development and applications of the electrostatically embedded generalized molecular fractionation with the conjugate caps (EE‐GMFCC) method in probing various properties of complex large molecules and condensed‐phase systems. The EE‐GMFCC method is now capable of describing the localized excited states of biomolecules and molecular crystals with a chromophore. The EE‐GMF method is also combined with anharmonic vibrational calculations for accurate simulation of the infrared spectrum of the magic number H+(H2O)21 cluster at the coupled cluster level. With an adaptive fragmentation scheme, the EE‐GMF‐based ab initio molecular dynamics is able to directly simulate chemical reactions occurred in atmospheric molecular clusters. Furthermore, by combining the EE‐GMF(CC) method and deep machine learning techniques, neural network potentials can be efficiently constructed for accurate simulations of complex systems with the accuracy of high‐level wave function methods. The EE‐GMF(CC) method is expected to become a practical tool for quantitative description of complex large molecules and condensed‐phase systems with high‐level ab initio theories or ab initio quality potentials.This article is categorized under: Electronic Structure Theory &gt; Ab Initio Electronic Structure Methods Structure and Mechanism &gt; Computational Biochemistry and Biophysics Structure and Mechanism &gt; Reaction Mechanisms and Catalysis

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.

Formation of atmospheric molecular clusters from organic waste products and sulfuric acid molecules: a DFT study

DFT calculations show that skatole oxidation products may likely initiate the formation of nucleation precursors in the atmosphere.

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.

Atmospherically Relevant Hydrogen-Bonded Interactions between Methanesulfonic Acid and H2SO4 Clusters: A Computational Study.

A detailed and systematic quantum-chemical calculation has been performed with high-level density functional theory (DFT) to analyze the electrostatic interaction of methanesulfonic acid (CH3SO3H), also known as MSA, with pre-formed clusters of sulfuric acid (H2SO4) molecules in ambient conditions. Both MSA and H2SO4 are considered as atmospheric molecules that might play active roles in aerosol formation. The interactions between MSA and H2SO4 clusters lead to the formation of MSA···(H2SO4)n (n = 2, 3) complexes stabilized by the formation of different types of intermolecular hydrogen bond networks. Analyses of cluster binding energies and free energy changes associated with their formation indicate that MSA could bring additional stability into the atmospheric molecular clusters responsible for aerosol formation. Variations of Gibbs free energy with temperature and pressure have been analyzed. The lower temperatures and pressures at the higher altitudes of the troposphere are found to play in favor of higher stability of the MSA···(H2SO4)n clusters. Effects of hydrogen bond formation on dipole moment, mean polarizability, and anisotropy of polarizability of the clusters have been analyzed. Rayleigh scattering intensities are found to increase many-fold when light interacts with the MSA···(H2SO4)n clusters.

Highly oxygenated organic molecule cluster decomposition in atmospheric pressure interface time-of-flight mass spectrometers

Abstract. Identification of atmospheric molecular clusters and measurement of their concentrations by atmospheric pressure interface time-of-flight (APi-TOF) mass spectrometers may be affected by systematic error due to possible decomposition of clusters inside the instrument. Here, we perform numerical simulations of decomposition in an APi-TOF mass spectrometers and formation in the atmosphere of a set of clusters which involve a representative kind of highly oxygenated organic molecule (HOM), with the molecular formula C10H16O8. This elemental composition corresponds to one of the most common mass peaks observed in experiments on ozone-initiated autoxidation of α-pinene. Our results show that decomposition is highly unlikely for the considered clusters, provided their bonding energy is large enough to allow formation in the atmosphere in the first place.

Modeling the formation and growth of atmospheric molecular clusters: A review

Molecular clusters are ubiquitous constituents of the ambient atmosphere, that can grow into larger sizes forming new aerosol particles. The formation and growth of small clusters into aerosol particles remain one of the largest uncertainties in global climate predictions. This has made the modeling of atmospheric molecular clustering into an active field of research, yielding direct molecular level information about the formation mechanism. We review the present state-of-the-art quantum chemical methods and cluster distribution dynamics models that are applied to study the formation and growth of atmospheric molecular clusters. We outline the current challenges in applying theoretical methods and the future directions to move the field forward.

Hydration of Atmospheric Molecular Clusters III: Procedure for Efficient Free Energy Surface Exploration of Large Hydrated Clusters.

Sampling the shallow free energy surface of hydrated atmospheric molecular clusters is a significant challenge. Using computational methods, we present an efficient approach to obtain minimum free energy structures for large hydrated clusters of atmospheric relevance. We study clusters consisting of two to four sulfuric acid (sa) molecules and hydrate them with up to five water (w) molecules. The structures of the "dry" clusters are obtained using the ABCluster program to yield a large pool of low-lying conformer minima with respect to free energy. The conformers (up to ten) lowest in free energy are then hydrated using our recently developed systematic hydrate sampling technique. Using this approach, we identify a total of 1145 unique (sa)2-4(w)1-5 cluster structures. The cluster geometries and thermochemical parameters are calculated at the ωB97X-D/6-31++G(d,p) level of theory, at 298.15 K and 1 atm. The single-point energy of the most stable clusters is calculated using a high-level DLPNO-CCSD(T0)/aug-cc-pVTZ method. Using the thermochemical data, we calculate the equilibrium hydrate distribution of the clusters under atmospheric conditions and find that the larger (sa)3 and (sa)4 clusters are significantly more hydrated than the smaller (sa)2 cluster or the sulfuric acid (sa)1 molecule. These findings indicate that more than five water molecules might be required to fully saturate the sulfuric acid clusters with water under atmospheric conditions. The presented methodology gives modelers a tool to take the effect of water explicitly into account in atmospheric particle formation models based on quantum chemistry.

Assessment of the DLPNO Binding Energies of Strongly Noncovalent Bonded Atmospheric Molecular Clusters.

This work assesses the performance of DLPNO-CCSD(T0), DLPNO-MP2, and density functional theory methods in calculating the binding energies of a representative test set of 45 atmospheric acid–acid, acid–base, and acid–water dimer clusters. The performance of the approximate methods is compared to high level explicitly correlated CCSD(F12*)(T)/complete basis set (CBS) reference calculations. Out of the tested density functionals, ωB97X-D3(BJ) shows the best performance with a mean deviation of 0.09 kcal/mol and a maximum deviation of 0.83 kcal/mol. The RI-CC2/aug-cc-pV(T+d)Z level of theory severely overpredicts the cluster binding energies with a mean deviation of −1.31 kcal/mol and a maximum deviation up to −3.00 kcal/mol. Hence, RI-CC2/aug-cc-pV(T+d)Z should not be utilized for studying atmospheric molecular clusters. The DLPNO variants are tested both with and without the inclusion of explicit correlation (F12) in the wavefunction, with different pair natural orbital (PNO) settings (loosePNO, normalPNO, and tightPNO) and using both double and triple zeta basis sets. The performance of the DLPNO-MP2 methods is found to be independent of PNO settings and yield low mean deviations of −0.84 kcal/mol or below. However, DLPNO-MP2 requires explicitly correlated wavefunctions to yield maximum deviations below 1.40 kcal/mol. For obtaining high accuracy, with maximum deviation below ∼1.0 kcal/mol, either DLPNO-CCSD(T0)/aug-cc-pVTZ (normalPNO) calculations or DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 (normalPNO) calculations are required. The most accurate level of theory is found to be DLPNO-CCSD(T0)-F12/cc-pVTZ-F12 using a tightPNO criterion which yields a mean deviation of 0.10 kcal/mol, with a maximum deviation of 0.20 kcal/mol, compared to the CCSD(F12*)(T)/CBS reference.

Formation of atmospheric molecular clusters of methanesulfonic acid–Diethylamine complex and its atmospheric significance

Field observations in a marine atmospheric environment imply the occurrence of significant concentrations of dimethylamine (DMA) and diethylamine (DEA) as well as methanesulfonic acid (MSA) in particulate formation. Among these particulates, studies on the interaction of MSA with DMA are well known; however, fundamental studies relating to the environmental impact of DEA on aerosol formation and its nucleation ability relative to the known ones are lacking. In this research, quantum chemical calculations and cluster kinetic modeling were used to analyze the aerosol formation potential of the reaction of DEA with MSA. Structural and thermodynamic evidence demonstrate a strong clustering stability in the processes of new particle formation (NPF). Driven by proton transfer, the clusters exhibit a low free-energy barrier distributed along the diagonal. The results of cluster kinetic analysis indicate that the aerosol formation potential of the MSA-DEA system at the parts per trillion (ppt) level is inferior to that of sulfuric acid (SA)–DMA, and slightly superior to that of SA–methylamine (MA) but far superior to that of MSA–DMA, implying a relatively strong nucleation capability for MSA-DEA system. This result implies that the MSA-DEA system plays a potentially significant role in NPF in the marine environment.