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.

Roles of Amides on the Formation of Atmospheric HONO and the Nucleation of Nitric Acid Hydrates

Nitrous acid (HONO) is hazardous to the human respiratory system, and the hydrolysis of NO₂ is the source of HONO. Hence, the investigation on the removal and transformation of HONO is urgently established. The effects of amide on the mechanism and kinetics of the formation of HONO with acetamide, formamide, methylformamide, urea, and its clusters of the catalyst were studied theoretically. The results show that amide and its small clusters reduce the energy barrier, the substituent improves the catalytic efficiency, and the catalytic effect order is dimer > monohydrate > monomer. Meanwhile, the clusters composed of nitric acid (HNO₃), amides, and 1-6 water molecules were investigated in the amide-assisted nitrogen dioxide (NO₂) hydrolysis reaction after HONO decomposes by combining the system sampling technique and density functional theory. The study on thermodynamics, intermolecular forces, optics properties of the clusters, as well as the influence of humidity, temperature, atmospheric pressure, and altitude shows that amide molecules promote the clustering and enhance the optical properties. The substituent facilitates the clustering of amide and nitric acid hydrate and lowers the humidity sensitivity of the clusters. The findings will help to control the atmospheric aerosol particle and then reduce the harm of poisonous organic chemicals on human health.

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.

Hydrogen-Bonding Interactions of Malic Acid with Common Atmospheric Bases

Malic acid (MA) (C₄H₆O₅) is one of the most important organic constituents of fruits that is widely used in food and beverage industries. It is also detected in the atmospheric aerosol samples collected in different parts of the world. Considering the fact that secondary organic aerosols have adverse impacts on the global atmosphere and climate and a molecular-level understanding of the compositions and formation mechanism of secondary organic aerosols is necessary, we have performed systematic density functional electronic structure calculations to investigate the hydrogen-bonding interactions between MA and several naturally occurring nitrogen-containing atmospheric bases such as ammonia and amines that are derived from ammonia by the substitution of hydrogens by a methyl group. The base molecules were allowed to interact with the carboxylic COOH and the hydroxyl-OH group of the MA separately. While at both sites, MA produces energetically stable binary complexes with bases with large negative values of binding energy, the thermodynamical stability, at an ambient temperature and pressure of 298.15 K and 1 atm, respectively, is favored only for the clusters formed at the COOH site. A much larger red shift of the carboxylic-OH stretch than that of the hydroxyl-OH reinforces the preference of this site for cluster formation. Both the binding electronic energy and binding free energy of MA-ammonia complexes are lower than those of MA-amine complexes, although the amines are derivatives of NH₃. The large increase in the Rayleigh activities upon cluster formation indicates that the MA-atmospheric base cluster may interact strongly with solar radiation. The detailed analysis of the structural, energetic, electrical, and spectroscopic properties of the binary complexes formed by MA with atmospheric bases shows that MA could participate in the atmospheric nucleation processes and subsequently contribute effectively to new particle formation in the atmosphere.

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.

Interaction of Glutamic Acid/Protonated Glutamic Acid with Amide and Water Molecules: A Theoretical Study

Amino acids are important nitrogen-containing compounds and organic carbon components that exist widely in the atmosphere. The formation of atmospheric aerosols is affected by their interactions with amides. The dimers formed by glutamic acid (Glu) or protonated glutamic acid (Glu⁺) with three kinds of amide molecules (formamide FA, acetamide AA, urea U) and the hydrated clusters formed by Glu or Glu⁺, U molecules along with one to six water molecules were systematically studied at the M06-2X/6-311++G(3df,3pd) level. U is predicted to form a more stable structure with Glu/Glu⁺ than FA and AA by thermodynamics. If the concentration ratio of FA to U is less than 10⁴, U will play a critical role in NPF. The degree of hydration in Glu⁺-mU-nW is higher than that of Glu-mU-nW (m = 0, 1; n = 0-6) clusters. Notably, Glu contributes more to the Rayleigh scattering properties than glutaric acid and sulfuric acid, and thus may lead to the destruction of atmospheric visibility. This study is helpful to better understand the properties of organic aerosols containing amino acids or amides.

Sulfuric acid-dimethylamine particle formation enhanced by functional organic acids: an integrated experimental and theoretical study

Atmospheric new particle formation (NPF), which has been observed globally in clean and polluted environments, is an important source of boundary-layer aerosol particles and cloud condensation nuclei, but the fundamental mechanisms leading to multi-component aerosol formation have not been well understood. Here, we use experiments and quantum chemical calculations to better understand the involvement of carboxylic acids in initial NPF from gas phase mixtures of carboxylic acid, sulfuric acid (SA), dimethylamine, and water. A turbulent flow tube coupled to an ultrafine condensation particle counter with particle size magnifier has been set up to measure NPF. Experimental results show that pyruvic acid (PA), succinic acid (SUA), and malic acid (MA) can enhance sulfuric acid-dimethylamine nucleation in the order PA < SUA < MA with a greater enhancement observed at lower SA concentrations. Computational results indicate that the carboxylic and hydroxyl groups are related to the enhancement. This experiment-theory study shows the formation of multi-component aerosol particles and the role of the organic functional group, which may aid in understanding the role of organics in aerosol nucleation and growth in polluted areas, and help to choose organic molecules of specific structures for simulation.

Theoretical analysis of sulfuric acid–dimethylamine–oxalic acid–water clusters and implications for atmospheric cluster formation

In recent years, organic compounds potentially involved in atmospheric particle formation have received increased attention. However, the contributions of organic acids as precursors in nucleation remain ambiguous. In this study, the low-lying structures and thermodynamics of the sulfuric acid–dimethylamine–oxalic acid–water system are obtained at the M06-2X/6-311+G(2d,p) level, and the single point energy of the clusters has been calculated at the DF-LMP2-F12/VDZ-F12 level. The formations of the multicomponent clusters are predicted based on thermodynamics, involving proton transfer and hydrogen bonding interactions. Oxalic acid can synergistically promote the formation of the sulfuric acid–dimethylamine–oxalic acid–water system while inhibiting this with the addition of more sulfuric acid molecules. The results of hydrate distribution show that un-hydrate clusters play a dominant role during formation. Moreover, dimethylamine and oxalic acid have similar effects on Rayleigh scattering properties, and the clusters involving complex mixtures of compounds can have high optical activities.

The structure of SA₂.DMA.OA.W₄ cluster.

Synergistic effect of glutaric acid and ammonia/amine/amide on their hydrates in the clustering: A theoretical study

The formation of molecular clusters makes influence on the atmosphere. The clusters of glutaric acid (GA) and common ammonia (A), amine (methylamine MA, dimethylamine DMA) and representative amide (urea U) along with water molecule were systematically studied theoretically. GA-A-nW (n = 1, 2), GA-MA-nW (n = 1, 2), GA-DMA-1W and GA-U-nW (n = 1-6) are predicted to be feasible thermodynamically with the hydrogen bonds as interaction force. GA and urea promote the clustering synergistically, and ammonia, methylamine, dimethylamine promote the clustering of small GA hydrates (n = 1-2), while inhibit that of large GA hydrates (n = 3-6). The results of humidity show that un-hydrate or mono-hydrate is the main form of GA-mbase-nW (m = 0, 1; n = 1-6) under relative humidity of 20%, 50% and 80%. The global minima remain dominant over the temperature range of 220-320 K. GA contributes more to the Rayleigh scattering properties than sulfuric acid. More importantly, the local minima can undergo isomerization to form the global minima crossing a free energy barrier ranging from 6.66 to 11.78 kcal mol^-1. This study indicates that GA and base molecules play a synergistic role to promote the formation of clusters. We hope it can provide more insights on interesting clustering in theory.

A theoretical study of hydrogen-bonded molecular clusters of sulfuric acid and organic acids with amides

Amides, a series of significant atmospheric nitrogen-containing volatile organic compounds (VOCs), can participate in new particle formation (NPF) throught interacting with sulfuric acid (SA) and organic acids. In this study, we investigated the molecular interactions of formamide (FA), acetamide (AA), N-methylformamide (MF), propanamide (PA), N-methylacetamide (MA), and N,N-dimethylformamide (DMF) with SA, acetic acid (HAC), propanoic acid (PAC), oxalic acid (OA), and malonic acid (MOA). Global minimum of clusters were obtained through the association of the artificial bee colony (ABC) algorithm and density functional theory (DFT) calculations. The conformational analysis, thermochemical analysis, frequency analysis, and topological analysis were conducted to determine the interactions of hydrogen-bonded molecular clusters. The heterodimers formed a hepta or octa membered ring through four different types of hydrogen bonds, and the strength of the bonds are ranked in the following order: SOH•••O > COH•••O > NH•••O > CH•••O. We also evaluated the stability of the clusters and found that the stabilization effect of amides with SA is weaker than that of amines with SA but stronger than that of ammonia (NH₃) with SA in the dimer formation of nucleation process. Additionally, the nucleation capacity of SA with amides is greater than that of organic acids with amides.

Integrated experimental and theoretical approach to probe the synergistic effect of ammonia in methanesulfonic acid reactions with small alkylamines

While new particle formation events have been observed worldwide, our fundamental understanding of the precursors remains uncertain. It has been previously shown that small alkylamines and ammonia (NH3) are key actors in sub-3 nm particle formation through reactions with acids such as sulfuric acid (H2SO4) and methanesulfonic acid (CH3S(O)(O)OH, MSA), and that water also plays a role. Because NH3 and amines co-exist in air, we carried out combined experimental and theoretical studies examining the influence of the addition of NH3 on particle formation from the reactions of MSA with methylamine (MA) and trimethylamine (TMA). Experiments were performed in a 1 m flow reactor at 1 atm and 296 K. Measurements using an ultrafine condensation particle counter (CPC) and a scanning mobility particle sizer (SMPS) show that new particle formation was systematically enhanced upon simultaneous addition of NH3 to the MSA + amine binary system, with the magnitude depending on the amine investigated. For the MSA + TMA reaction system, the addition of NH3 at ppb concentrations produced a much greater effect (i.e. order of magnitude more particles) than the addition of ∼12 000 ppm water (corresponding to ∼45-50% relative humidity). The effect of NH3 on the MSA + MA system, which is already very efficient in forming particles on its own, was present but modest. Calculations of energies, partial charges and structures of small cluster models of the multi-component particles likewise suggest synergistic effects due to NH3 in the presence of MSA and amine. The local minimum structures and the interactions involved suggest mechanisms for this effect.

Can nitrous acid contribute to atmospheric new particle formation from nitric acid and water?

The properties of (HNO₃)(HONO)(H₂O)_n (n = 1–6) clusters are reported including thermodynamics, structures, temperature-dependence, intermolecular forces, optical properties, and evaporation rates.

Mechanical properties of anhydrous oxalic acid and oxalic acid dihydrate

The mechanical properties of oxalic acid dihydrate and anhydrous oxalic acid (α and β polymorphic forms) were obtained by using rigorous theoretical solid-state methods based on density functional theory using plane waves and pseudopotentials.

A molecular-scale study on the hydration of sulfuric acid-amide complexes and the atmospheric implication

Amides are ubiquitous in atmosphere. However, the role of amides in new particle formation (NPF) is poorly understood. Herein, the interaction of urea and formamide with sulfuric acid (SA) and up to four water (W) molecules has been studied at the M06-2X/6-311++G(3df,3pd) level of theory. The structures and properties of (Formamide)(SA)(W)_n (n = 0-4) and (Urea)(SA)(W)_n (n = 0-4) clusters were investigated. Results show that the interaction of SA with the CO group of amides plays a more important role in amide clusters compared with the NH₂ group. Proton transfer to water molecule become dominant in highly hydrated amide clusters at lower temperatures. There is no proton transfer to CO group in formamide clusters. The Rayleigh light scattering intensities of amide clusters are comparable to that of amine and oxalic acid clusters reported previously. Moreover, unhydrated (Amide)(SA) clusters have similar or even higher ability than hydrated SA clusters to participate in ion-induced nucleation. In comparison with formamide, urea has more interacting sites and its clusters have higher Rayleigh light scattering intensities, larger dipole moment, stronger interaction with SA and lower water affinity. The intermolecular interaction in (Formamide)(SA) is slightly weaker than that of SA dimer, which may be compensated by the high concentration of formamide, thus enabling formamide to participate in initial steps of NPF. This study may bring new insight into the role of amides in initial steps of NPF from molecular scale and could help better understand the properties of amide-containing organic aerosol.

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

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

Closed-Shell Organic Compounds Might Form Dimers at the Surface of Molecular Clusters

The role of covalently bound dimer formation is studied using high-level quantum chemical methods. Reaction free energy profiles for dimer formation between common oxygen-containing functional groups are calculated, and based on the Gibbs free energy differences between transition states and reactants, we show that none of the studied two-component gas-phase reactions are kinetically feasible at 298.15 K and 1 atm. Therefore, the catalyzing effect of water, base, or acid molecules is calculated, and sulfuric acid is identified to lower the activation free energies significantly. We find that the reactions yielding hemiacetal, peroxyhemiacetal, α-hydroxyester, and geminal diol products occur with activation free energies of less than 10 kcal/mol with sulfuric acid as a catalyst, indicating that these reactions could potentially take place on the surface of sulfuric acid clusters. Additionally, the formed dimer products bind stronger onto the pre-existing cluster than the corresponding reagent monomers do. This implies that covalent dimerization reactions stabilize the existing cluster thermodynamically and make it less likely to evaporate. However, the studied small organic compounds, which contain only one functional group, are not able to form dimer products that are stable against evaporation at atmospheric conditions. Calculations of dimer formation onto a cluster surface and the clustering ability of dimer products should be extended to large terpene oxidation products in order to estimate the real atmospheric significance.

Hydration of 3-hydroxy-4,4-dimethylglutaric acid with dimethylamine complex and its atmospheric implications

Changes in temperature affects the distribution of isomers, which facilitates the understanding of new particle formation in the atmosphere.

Hydration of the methanesulfonate–ammonia/amine complex and its atmospheric implications

Methanesulfonate (MSA⁻), found in substantial concentrations in the atmosphere, is expected to enhance aerosol nucleation and the growth of nanoparticles, but the details of methanesulfonate clusters are poorly understood. In this study, MSA⁻ was chosen along with ammonia (NH₃) or three common amines and water (H₂O) to discuss the roles of ternary homogeneous nucleation and ion-induced nucleation in aerosol formation. We studied the structural characteristics and thermodynamics of the clusters using density functional theory at the PW91PW91/6-311++G(3df,3pd) level. The analysis of noncovalent interactions predicts that the amines can form more stable clusters with MSA⁻ than NH₃, in agreement with the results from structures and thermodynamics; however, the enhancement in stability for amines is not large enough to overcome the difference in the concentrations of NH₃ and amines under typical atmospheric conditions. In addition, the favorable free energies of formation for the (MSA⁻)(NH₃/amines)(H₂O)_n (n = 0–3) clusters at 298.15 K show that MSA⁻ could contribute to the aerosol nucleation process with binding NH₃/amines and H₂O up to n = 3. There are strong temperature and humidity dependences for the formation of complexes; higher humidity and temperature promote the formation of larger hydrates. Finally, for the (MSA⁻)(NH₃/amines)(H₂O)_n clusters, the evaporation rates were determined to further investigate the atmospheric implications.

Methanesulfonate (MSA⁻), found in substantial concentrations in the atmosphere, is expected to enhance aerosol nucleation and the growth of nanoparticles, but the details of methanesulfonate clusters are poorly understood.

The Role of Oxalic Acid in New Particle Formation from Methanesulfonic Acid, Methylamine, and Water

Atmospheric particles are notorious for their effects on human health and visibility and are known to influence climate. Though sulfuric acid and ammonia/amines are recognized as main contributors to new particle formation (NPF), models and observations have indicated that other species may be involved. It has been shown that nucleation from methanesulfonic acid (MSA) and amines, which is enhanced with added water, can also contribute to NPF. While organics are ubiquitous in air and likely to be involved in NPF by stabilizing small clusters for further growth, their effects on the MSA-amine system are not known. This work investigates the effect of oxalic acid (OxA) on NPF from the reaction of MSA and methylamine (MA) at 1 atm and 294 K in the presence and absence of water vapor using an aerosol flow reactor. OxA and MA do not efficiently form particles even in the presence of water, but NPF is enhanced when adding MSA to OxA-MA with and without water. The addition of OxA to MSA-MA mixtures yields a modest NPF enhancement, whereas the addition of OxA to MSA-MA-H₂O has no effect. Possible reasons for these effects are discussed.

Particle formation and growth from oxalic acid, methanesulfonic acid, trimethylamine and water: a combined experimental and theoretical study

A combined experimental-theoretical study on the effect of oxalic acid on particle formation and growth from the reaction of MSA with trimethylamine in the absence and presence of water.