Massive Assessment of the Binding Energies of Atmospheric Molecular Clusters

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.

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.

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.

Limited Role of Malonic Acid in Sulfuric Acid-Dimethylamine New Particle Formation

Aerosols play an important role in climate and air quality; however, the mechanisms behind aerosol particle formation in the atmosphere are poorly understood. Studies have identified sulfuric acid, water, oxidized organics, and ammonia/amines as key precursors for forming aerosol particles in the atmosphere. Theoretical and experimental investigations have indicated that other species, such as organic acids, may be involved in atmospheric nucleation and growth of freshly formed aerosol particles. Organic acids, such as dicarboxylic acids, which are abundant in the atmosphere, have been measured in ultrafine aerosol particles. These observations suggest that organic acids may contribute to new particle formation in the atmosphere but their role remains ambiguous. This study examines how malonic acid interacts with sulfuric acid and dimethylamine to form new particles at warm boundary layer conditions using experimental observations from a laminar flow reactor and quantum chemical calculations coupled with cluster dynamics simulations. Observations reveal that malonic acid does not contribute to the initial steps (formation of <1 nm diameter particle) of nucleation with sulfuric acid-dimethylamine. In addition, malonic acid was found to not participate in the subsequent growth of the freshly nucleated 1 nm particles from sulfuric acid-dimethylamine reactions to diameters of 2 nm.

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.