The SMILES to AIOMFAC subgroups (S2AS) tool is a new, automated algorithm written in Python. It is designed to identify and classify functional groups comprising organic aerosol components in the input format required by the AIOMFAC model. Details of AIOMFAC's representation of molecular structures by a so-called subgroup notation are provided elsewhere ; see also examples at https://aiomfac.lab.mcgill.ca/about.html (last access: 25 May 2026). Briefly, the notation of aromatic and aliphatic organic compounds in AIOMFAC is based on that of UNIFAC; e.g. a molecule like ferulic acid (SMILES code: COc1cc(ccc1O)/C=C/C(=O)O), is comprised of the following AIOMFAC subgroups: 1 × (CH=CH), 3 × (ACH), 2 × (AC), 1 × (ACOH), 1 × (CH3O), 1 × (COOH), where AC denotes aromatic carbon (lower-case c in SMILES). Unlike in SMILES notation, the subgroup input format for AIOMFAC explicitly states the hydrogen atoms, yet the subgroup notation does not contain information about how the subgroups are connected to each other (because AIOMFAC does not require that information). Previously, AIOMFAC subgroup assignments for organic molecules had to be determined either manually (for small sets of structures) or using limited tool-specific pattern matching e.g., the UManSysProp facility;. Our S2AS tool automates this process for arbitrary molecules. It can process tens of thousands of compounds in a consistent way, whereas manual assignment would be prohibitively laborious and prone to errors or inconsistencies.

We note that the existing list of subgroups in AIOMFAC (about 60 subgroups supported for organic compounds plus special subgroups for inorganics) has limitations when it comes to representing rather exotic, highly functionalized compounds, which may not allow for a perfect mapping by the S2AS tool. Consequently, we implemented a mechanism for detecting and handling exceptions, in most cases by introduction of additional SMARTS patterns to cover these cases. Encountering an exception typically means either that not all atoms can be uniquely associated with only one AIOMFAC subgroup, that a functionality needs to be approximated by an imperfect combination of existing subgroups, e.g. in the case of secondary ozonide functionalities, or that after parsing all existing SMARTS patterns, one or several unmatched atoms remain. Treating such exceptions by an algorithm allows for a consistent, user-independent approximation of the suboptimal mapping. Furthermore, encountered exception cases can be flagged to indicate the potential need for an additional SMARTS pattern to recognize a special case and/or to motivate future improvements by introducing new subgroups into AIOMFAC. To this end, based on our tests with tens of thousands of compounds generated by GECKO-A or MCM (see Sect. ), unhandled exception cases are a rare occurrence.

The S2AS program carries out the following key steps: (i) parsing of each SMILES string from an input list to determine whether the SMILES input is valid and whether the component falls into the special category of being a pure alcohol or polyol according to the definition used by AIOMFAC; (ii) rendering of molecules for structure visualization as portable network graphics (.png) or scalable vector graphics (.svg) files (this step is optional); (iii) matching substructures to related AIOMFAC subgroups by iterating over a list of SMARTS as outlined in the flowchart of Fig. . During step (i), a character string filter is also applied to remove chirality information from input SMILES, which is unnecessary for AIOMFAC subgroups, and to replace radical atoms in a SMILES string by the corresponding non-radical atom (e.g., [O.] by O). The latter is done since AIOMFAC does not support radicals. The pure-component properties and thermodynamic mixing behaviour of such a compound is then approximated by that of a similar non-radical molecule.

Our implemented SMARTS pattern matching process follows a hierarchical, priority-based querying approach, with relatively large subgroups, such as peroxy acyl nitrate (SMARTS: [CH0;X3](=O)OO[NX3;0,+1](=O)-,=[O;0,-1]), assigned one of the highest matching priorities, while the SMARTS pattern for a single aliphatic carbon bonded to two non-hydrogen atoms and two hydrogens (SMARTS: [CH2]), is among the last patterns applied. The query list and order of SMARTS patterns is provided in Table . The company Daylight Chemical Information Systems, Inc., provides manuals, examples and tutorials for understanding and customizing the SMARTS and SMILES languages on their website (https://www.daylight.com, last access: 16 June 2025).

Figures  and provide examples of the individual mappings of AIOMFAC subgroups by SMARTS. Alkyl groups, having the lowest matching priority, are matched after all other groups. Pure aliphatic alcohols and polyols are initially detected as such and treated in a separate code branch based on a distinct list of SMARTS, as demonstrated in the example of Fig. . Based on the polyol-specific subgroups and nomenclature introduced into a variant of UNIFAC by , which is also supported in AIOMFAC, the alcohols and polyols make use of a set of special alkyl subgroups for added specificity and better accuracy of AIOMFAC water uptake and liquid–liquid equilibrium predictions for this class of compounds. A key strength of the S2AS tool is its ability to systematically and efficiently account for the special alkyl groups in a wide variety of straight-chain, branched and cyclical aliphatic alcohols/polyols. For these compounds, the algorithm in S2AS follows a three-step procedure. In step (1) we determine and count the CHn (n=0, 1, 2, 3) directly bonded to OH groups as well as the associated OH groups, which are separate subgroups. In step (2), we match all alkyl groups belonging to hydrophobic tails by first marking alkyl chains that terminate in -CHn-CH3 (where n=0, 1, 2) as tails and then iteratively following along those alkyl chains one CHn group at a time. An alkyl group is part of a hydrophobic tail if, and only if, it connects to at least one other alkyl group known to be part of a hydrophobic tail, while not being bonded to an OH group (those were already determined in step 1). In step (3) all thus far unassigned alkyl groups are detected and classified as being of “alkyl within alcohols” CHn (n=0, 1, 2, 3) subgroup type.

In general, the implementation of a hierarchical order and processing of the list of SMARTS is highly advantageous. It allows one to write the SMARTS codes for subgroups of lower priority in a far simpler notation than when each SMARTS code were required to work correctly regardless of the order of execution. For example, if [CH2] were applied as one of the first SMARTS pattern tested, it would likely result in several unwanted matches, such as matching the CH2 atoms associated with a ketone subgroup (e.g., CH2CO in AIOMFAC notation); subsequently, the >C=O of the remaining atoms of the ketone group would not be detected as being part of a full ketone subgroup (clearly a mistake). To avoid this, the SMARTS pattern for only detecting intended CH2 groups would need to be much more complicated, such that it would avoid matching atoms that could be matched as part of a bigger substructure. When a SMARTS match is found for the molecule under consideration, the corresponding matched atoms are marked and excluded from further parsing if unmatched atoms remain in the component; the Indigo toolkit provides “ignore atom” and “highlight atom” functions that conveniently aid in avoiding any unwanted double-matching of atoms. A numerical counter corresponding to the key of the matched SMARTS rule and associated subgroup is incremented for each successful pattern match and added to the subgroup-array representation of the compound for later S2AS output. After all atoms have been matched or when the end of the list of SMARTS is reached, a check is performed to determine whether any unmatched atoms remain in a given molecule, potentially indicating an exception case (very rare). After, the next molecule from the SMILES list is processed. Once all SMILES have been processed, the S2AS program outputs a text file in the format of AIOMFAC-web input files (see examples at https://aiomfac.lab.mcgill.ca/about.html, last access: 25 May 2026).

To validate the S2AS tool and associated SMARTS patterns, we used a comprehensive data set of aerosol-relevant organic compounds, including those produced by MCM v3.3.1 simulations for monoterpenes and alkanes, an excerpt is shown in Fig. . These tests serve as proof of concept of the tool's ability to extract and convert detailed molecular information from a diverse range of compounds commonly encountered in atmospheric chemistry simulations.

The UManSysProp project developed by is an open-source facility that employs cheminformatics tools for molecular and mixture property predictions. This facility allows users to input molecular information in the SMILES format, from which the relevant information for aerosol property calculations are extracted . This tool utilizes the Open Babel and pybel cheminformatics libraries for the parsing of molecules using tool-specific SMARTS pattern matching, similar to the AIOMFAC-specific S2AS procedure described in Sect. . Of most relevance for this study, the pure-component, liquid-state saturation vapour pressure tool, available as part of the UManSysProp facility, provides several methods for estimating temperature-dependent vapour pressures. It uses method-specific SMARTS pattern matching to calculate the pure-component vapour pressures using predictive models, including the Estimation of VApour Pressure of ORganics, Accounting for Temperature, Intramolecular, and Non-additivity effects (EVAPORATION) model , the model by , hereafter called Nanoolal method, and the SIMPOL method . The source code for the original and subsequent releases of UManSysProp is available from an online repository (see code and data availability). We note that UManSysProp also includes a few tools for aerosol mixture predictions, including a version of the AIOMFAC model and related SMARTS patterns for generating AIOMFAC input data. However, the list of SMARTS patterns for AIOMFAC in UManSysProp differs in several ways from the more extensive SMARTS list and related S2AS program introduced in this study. Specifically, do not follow the same SMARTS priority order, use a different, less comprehensive approach for handling matching exceptions, and the way pure alcohol compounds are detected and mapped may differ as well for more complex polyols. Hence, SMARTS codes from their study are not directly transferrable for use in the S2AS tool.

Several studies have compared liquid-state pure-component vapour pressure prediction methods suitable for SOA systems alongside with critical evaluations of existing experimental data for the particularly relevant semi-volatile and low-volatility compounds. It has been shown that, when applicable, the EVAPORATION method and the Nanoolal method are among the best performing options in those volatility ranges of particular importance for the gas–particle partitioning of SOA e.g.,. The Nanoolal method is more versatile in terms of the variety of functional groups and chemical elements covered, while the EVAPORATION method is constrained to compounds containing the elements C, H, O, N. However, these are also the main elements supported in AIOMFAC and we opted to use the EVAPORATION method as our first choice for the lumping framework and the gas–particle partitioning calculations.

The parameterization of the temperature-dependence of pure-component vapour pressures used in our work is identical to the two-parameter relation introduced for the EVAPORATION model : 1log⁡10pj∘pref=Aj+BjTκ. Here, pj∘ denotes the pure-component, liquid-state (saturation) vapour pressure of component j in units of atmospheres (atm) and pref=1atm is the unit reference pressure. T is the temperature (K), and Aj and Bj are two component-specific parameters. A common value of κ=1.5 was adopted based on optimization tests by . It was shown to be appropriate for estimating vapour pressure of hydrocarbons with or without heteroatoms across a wide temperature range. The Aj and Bj values are directly predicted by the EVAPORATION model. Alternatively, they can be determined by running any pure-component vapour pressure prediction method at two sufficiently distinct temperatures (typically ΔT>30K), including the temperature interval of interest, followed by solving the system of two linear equations for Aj and Bj. The use of Eq. () enables the flexibility of pj∘ estimation at any reasonable temperature for the given set of input molecules, serving as a key input to the gas–particle partitioning model. Computing the Aj, Bj parameters for all organic aerosol system components once eliminates the need for calling the EVAPORATION model repeatedly when the temperature changes, thus improving computational efficiency.

This approach streamlines the application of distinct SMILES-based tools for (any) pure-component properties and enhances the flexibility of the gas–particle partitioning model in terms of its readiness for computations being carried out over a range of temperatures. In summary, the UManSysProp pure-component property models (written in Python) are run for a given list of SMILES characterizing a system. The Aj and Bj parameters and corresponding SMILES of all organic system components are then written to a text file for read-access by other tools. In particular, the list of parameters is read by the Fortran code of the AIOMFAC equilibrium model, which makes subsequent use of Eq. () to obtain the pj∘ at a temperature of interest. The pure-component vapour pressure files are also used in the 2D lumping framework described next.

The idea of using an activity coefficient ratio (ACR) as a polarity metric is inspired by liquid–liquid equilibrium (LLE) thermodynamics. In a macroscopic LLE state, the chemical potential of a component present in both coexisting phases must be identical. Consequently, the way a component j partitions between two liquid phases, α and β, can be described using an equilibrium partitioning constant Kj(x) : 4Kj(x)=xjαxjβ=LLEγjβ,(x)γjα,(x). Here, xjα and xjβ are mole fractions in phases α and β; γjα,(x) and γjβ,(x) are the activity coefficients in those phases under LLE conditions. Equation () indicates that knowledge of the γjβ,(x)/γjα,(x) ratio provides an accurate representation of the thermodynamic phase preference of organic components by quantifying the relative enrichment or depletion of a component via the equivalent mole fraction ratio, with a value greater than 1 indicating enrichment in phase α. Since activity coefficients depend on a phase's mixture composition established by all components, the values are sensitive to various forms of molecular interactions (e.g., dipole–dipole, dispersion) and reflect the chemical affinity for a phase. That is, activity coefficients are influenced by molecular structure properties, such as whether an oxygen-bearing functional group is more polar (e.g., hydroxyl, carboxyl) or less polar (e.g., ether, ester) and how it interacts with other organic and inorganic components present. Thus, the ACR encompasses more detailed functional group characteristics than simpler metrics like the O:C ratio.

In this work, the ACR of a component j is based on a prediction of the component's activity coefficient when present as a dilute solute in a weakly polar organic reference solvent, here we use 1,2-hexanediol, relative to that of being a dilute solute in a strongly polar reference solvent, here water. This metric is therefore similar to the well-established octanol–water partitioning coefficient e.g.,, but our choice of organic reference solvent differs. We elected to use a slightly more polar organic than octanol, with 1,2-hexanediol serving as a more typical representation of an organic-rich phase medium in aerosols.

While inspired by the LLE isoactivity condition (Eq. ), the procedure of obtaining our ACR metric differs from that of solving a ternary solute–solvent-1–solvent-2 LLE problem. This is because in the ternary LLE system the present solvents may be partially miscible, while we choose to compute the activity coefficients of each component independently based on evaluating two binary solute–solvent mixtures. Using binary systems as a gauge is computationally simpler and substantially faster. Specifically, our polarity metric ACR is defined by the following dimensionless quantity: 5log⁡10γj,hex(x)γj,w(x). Here, γj,hex(x) is the (predicted) mole-fraction-based activity coefficient of solute j in a binary mixture with the solvent 1,2-hexanediol, in which the mass fraction of j is wj=0.01 (therefore, whex=0.99). Analogously, for γj,w(x), except for the solvent being water. These activity coefficients are typically evaluated at a reference temperature of 298.15 K. Given this definition, one can think of these two separate activity coefficients, as well as their ratio, as pure-component properties. In principle, those values would only need to be computed once for each component (each SMILES code) and could then be saved and retrieved from a look-up table.

The selection of the two reference solvents provides a robust basis for characterizing the behaviour of organic components across a wide range of polarities spanning several orders of magnitude (see Sect. ). In our framework, the AIOMFAC model is employed to compute activity coefficients for Eq. (). Since AIOMFAC is run only for binary, single-phase systems, the calculations are fast; they are comparable or faster than the pure-component vapour pressure predictions with UManSysProp. Of note, for a system consisting of tens of thousands of organic components, computing activity coefficients of all species simultaneously using the related multicomponent mixtures (containing as many components) with AIOMFAC, is prohibitively slow due to the many functional groups present, all the possible group–group and molecule–molecule interactions that need to be summed over and the associated computer memory requirements. In contrast, computing the ACR values based on the binary solute–solvent mixtures for all those components is fast and small in memory footprint.

We implemented four distinct methods to analyze organic aerosol data in the 2D lumping framework and to objectively select a set of surrogate components. These methods are designed to reduce the complexity of the gas–aerosol system while preserving important physicochemical aspects, such as the conservation of total mass concentration and the consideration of the system's diversity in terms of volatility and polarity ranges. The four methods are: (a) the grid cell midpoint method, (b) the grid cell medoid method, (c) the grid cell mass-weighted medoid method, and (d) the k-means-based medoids method. The latter is a grid-independent 2D clustering method.

The 2D space is subdivided into a number of grid cells (or clusters) based on the targeted reduction in system complexity. This division is accomplished by specifying the number of rows and columns, followed by identification of the component coordinates that set the upper and lower coordinate limits within the range that should be gridded (see use of a volatility threshold below). The grid resolution is adjustable, but typical choices range from 2×1 to 20×10 in terms of setting the number of grid subdivisions and associated nx×my grid cells.

A crucial aspect of our methodology is the primary focus of the gridded domain on the compound volatility ranges of interest for substantial partitioning of organics to the particle phase. These volatility ranges includes semi-volatile (SVOC), low-volatility (LVOC) and extremely low-volatility (ELVOC) organic compounds, while intermediate volatility (IVOC) and volatile organic compounds (VOC) are too volatile under typical tropospheric aerosol mass loading conditions . As such, an adjustable high-volatility vapour pressure threshold (phigh) is introduced, typically set to log⁡10(phigh/[1Pa])>-1. Regardless of the polarity range, all compounds with pj∘>phigh are identified and lumped into a single high-volatility surrogate component using the mass-weighted medoid method defined below. Examples for this are shown in Sect. , e.g., Figs.  and . Since the phigh threshold value is an input parameter, this special VOC lumping step can also be avoided entirely by setting a very high threshold value. Similarly, a low-volatility threshold and related lumping of LVOC and ELVOC compounds into a single (or a few), quasi-nonvolatile surrogate could be introduced to focus the majority of surrogates on representing the SVOC range at comparably higher resolution. However, in this work we have not included a low-volatility threshold since we are interested in a diverse surrogate-based representation of all PM-relevant volatility ranges to better resolve potential trends in polarity with decreasing volatility accross the SVOC, LVOC, and ELVOC ranges.

Our lumping process adheres to the principle of mass conservation for the entire system. This is achieved by aggregating the mass concentrations of components within each grid cell or cluster into the selected surrogate component. This approach differs from methods that choose to conserve the number of carbon atoms during lumping. The surrogate component selection process for each of the four methods is visually depicted in Fig. . The shown examples illustrate how one surrogate component is chosen within a single grid cell (or cluster in case of k-means).

The midpoint method operates on the simple principle that the component closest to a grid cell's midpoint coordinates should be a reasonable choice representing all other components within the same cell. This method involves determining the normalized distance of each grid cell component's location to the grid cell midpoint. The squared Euclidean distance, Dmid,i2, of each component i within a grid cell is calculated by 6Dmid,i2=xmid-xixrange⋅χ2+ymid-yiyrange2. Here, xmid and ymid denote the midpoint coordinates of the grid cell, xi and yi are the coordinates of component i, and xrange and yrange denote the magnitudes of the x and y axes ranges of the 2D space over which the lumping grid was placed. They normalize the distances expressed along the two axes. The x-to-y aspect ratio χ is introduced to scale the normalized length scales of the grid space. That is, χ is the (prescribed) multiplying factor of the normalized, dimensionless value range along the x axis that is regarded as equivalent to the normalized, dimensionless range along the y axis. To express the importance of volatility in gas–particle partitioning, we elected to set a 2:1 aspect ratio as the default choice. If the number of grid lines along the x-dimension is already set as twice that of the y-dimension (e.g., 8 by 4), then χ will account for this (χ=1 in that case). In this study, the x-coordinate refers to the logarithm of the pure-component vapour pressure (log⁡10(pi∘/[1Pa])), while the y-coordinate corresponds to one of the proxies for polarity (ACR, O:C ratio, OS‾C). The value ranges of the components along the x and y coordinates may differ substantially, possibly by several orders of magnitude. Therefore, we chose to normalize and scale the magnitudes of the x and y axes ranges relative to each other, as shown by Eq. (). The xrange (=|xmax⁡-xmin⁡|) is determined by the maximum and minimum x-coordinates from the set of all system components that contribute nonzero mass concentration and belong to the regular lumping space, i.e., those not lumped to the single high-volatility surrogate compound. The yrange is determined analogously. Finally, within each grid cell containing at least one component, the component of minimum Dmid2 is selected as surrogate and the mass concentrations of all other grid cell members are lumped (additively) into the surrogate. Except for the method-specific expressions for computing a component's distance metric within a grid cell, the variable definitions and steps outlined for this method also apply to the other methods described in the following sub-sections.

The grid cell midpoint method is straightforward to understand and implement. It has the advantage of providing unbiased coverage of the 2D space by ensuring that surrogate components are nearly evenly distributed across the grid domain. The approach demonstrates scalability, as it can be easily applied to systems with a large number of components, making it suitable for complex mixture analyses. Additionally, the method offers computational efficiency since the calculation of midpoints and distances is relatively fast, even for large datasets. However, this method may not always select the most representative component, especially when a low-resolution grid is applied in which the few cells may exhibit unevenly distributed components (e.g., all components clustered around the lower left corner of a cell). This method is visualized in Fig. a.

The grid cell medoid method operates by selecting the medoid component of each grid cell as the surrogate. The medoid member is the component in closest cumulative proximity to all other components of the same cell. Therefore, the main step involves calculating the cumulative squared Euclidean distance of each component from all other components of the grid cell, as follows: 7ΣDmed,i2=∑j=1mxj-xixrange⋅χ2+yj-yiyrange2. Here, index j covers the 1,…,m components of the grid cell, with other variables as defined for Eq. ().

The medoid method offers potential advantages over the midpoint method. First, it may provide better representation by selecting a surrogate that is located close to most other components, which is especially of importance in the case of a grid space with only a few large cells filled with geometrically uneven component distribution. Second, the medoid method demonstrates robustness to outliers, being less influenced by extreme values or uneven clustering of points within a cell compared to the midpoint. In comparison to the midpoint method, the medoid method is computationally more costly, especially for cells that contain a large number of components. However, in practice this is rarely a concern. Figure b illustrates the grid cell medoid method.

The mass-weighted medoid method prioritizes surrogate selection based on a combination of a component's importance, as measured by its mass concentration, and the cumulative distance from other components of a grid cell, as in the unweighted medoid method. Using such a mass-weighted approach is particularly useful in the case of systems consisting of many components, yet with the majority of the mass contributed by a small minority of molecules. The mass-weighting ensures that the important components are more likely to be selected as surrogates, so that their particular molecular properties are then also more appropriately considered in subsequent equilibrium partitioning computations. The core of this method lies in the calculation of the squared distance between a component and the coordinates of the centre of mass of the cell, Dwmed,i2, as follows: 8Dwmed,i2=xmc-xixrange⋅χ2+ymc-yiyrange2, with 9xmc=∑j=1mwj⋅xj,ymc=∑j=1mwj⋅yj,andwi=Ci∑j=1mCj. Here, xmc and ymc are the coordinates of the centre of mass of the grid cell under consideration. These coordinates are determined by computing the mass-weighted average coordinates of the j=1,…,m grid cell components, as shown by Eq. (), only requiring information about the cell's components of nonzero mass concentration. wj and Cj represent a component's grid-cell mass fraction and mass concentration, respectively. Components of large mass concentration relative to others in a grid cell have the effect of “pulling” the centre of mass toward their location, thereby benefiting from a smaller Dwmed,i2. Among the grid cell components of nonzero mass concentration, the component of minimum Dwmed,i2 value is identified as the surrogate. Components of zero mass concentration are excluded from the calculation and from being selected as surrogate.

This method strongly favours the selected surrogate components to be from the subset of most abundant species in the gas–aerosol system. The mass-weighted medoid method offers several advantages. The method provides improved representation of dominant components. The resulting lumped system is likely to reflect bulk aerosol properties more accurately, especially when only a low-resolution grid is applied. To aid in understanding the interplay between mass concentration and spatial distribution in the surrogate selection process, Fig. c exemplifies how the component of highest mass concentration, which is also closest to the centre of mass within the grid cell, is selected as the surrogate component.

The mass-weighted, k-means-based medoid clustering method, for brevity hereafter referred to as the k-means method, is employed to generate a predefined number of centroids (k clusters) in the 2D space. The clustering process is implemented using a variant of the weighted k-means clustering algorithm; specifically, subroutine kmeans_w_01, from the Fortran 90 implementation provided by . The Fortran code is based on the theory, algorithm and existing code from the works by and . This algorithm iteratively reassigns points (here chemical components) to clusters, minimizing the total energy of the system. Refer to and for a detailed description of the k-means method and its variants.

In our approach for surrogate selection with the k-means method, we combine the mass-weighted clustering with a final, distance-based surrogate component selection process. Figure d visualizes an example cluster's surrogate selection. Specifically, k-means returns the coordinates of a predefined number of cluster centres, which usually do not coincide with any actual component's coordinates. Among each cluster's population, we then select the component of nonzero mass concentration that is located closest to the cluster centre coordinates as the cluster's surrogate. Similar to the mass-weighted medoid approach, the distance of each cluster component to the centre is determined by the squared Euclidean distance based on normalized coordinates. In outcome, this is therefore akin to (but algorithmically not identical with) the method of k-medoids clustering.

By selecting surrogate species that are typically centrally located within their clusters and of significant mass concentration, this approach ensures that the set of surrogate components represents the overall physicochemical characteristics of the system well. This approach is particularly valuable in atmospheric chemistry, where reducing the complexity of chemical mechanisms while retaining properties of the most abundant components is crucial, since mass or number concentration of components is a critical factor in understanding subsequent partitioning or chemical reaction behaviour.

In our implementation, the clustering process begins by setting the desired number of k clusters. The initial cluster centre coordinates are then set based on the grid cell midpoints (since in our code the grid-based methods are run prior to running k-means). For comparison with the grid-based methods, we typically chose the cluster numbers as being equal to the number of populated grid cells. However, the k-means clustering method can also be run independently from the gridded approaches. If a higher number of clusters is set as target than the number of populated grid cells, additional initial cluster centre coordinates are generated using pseudo-random coordinates within the scaled 2D space. This initialization step ensures a broad distribution of initial cluster centres across the normalized 2D space. Components associated with the special high-volatility surrogate are filtered out, since they are marked as being part of a special cluster; these are not considered during the k-means clustering.

An innovation of the weighted k-means variant is the incorporation of, in our case, mass-concentration-based weighting during the algorithm's assignment of components to clusters. When k-means computes each cluster's “energy” and iteratively assigns components to a certain cluster, the weights are factored in. As discussed in Sect. , actual example cases indicate that the mass concentrations of components may range over several orders of magnitude. Therefore, the weighting aids in prioritizing components with relatively high mass concentrations as potential cluster surrogates, ensuring that the clustering process is not solely based on spatial proximity. The algorithm considers the entire dataset simultaneously and can effectively handle cases in which data points are not uniformly distributed in a 2D space. While we favour weighted k-means clustering, if desired, one can assign each component the same weight, thereby returning to the non-weighted k-means method.

Overall, the k-means method offers several advantages. The method can identify natural groupings in the data, independent of the arbitrary limits of an imposed grid, potentially leading to more meaningful, unbiased surrogate selection. However, this method is computationally the most costly of the four outlined in this study. Users can adjust the targeted number of k-means clusters to strike a balance between model simplicity and resolution of the original data. We note that the computational cost of this method is relatively insensitive to the number of clusters targeted.

The S2AS tool demonstrated high accuracy in identifying AIOMFAC functional groups for the α-pinene and toluene oxidation products. The 174 α-pinene-derived products were mapped to AIOMFAC subgroups without needing any exception treatments, while an average of 0.5 exceptions (special SMARTS mappings) per molecule were encountered in case of the ∼68000 toluene-derived products. The latter exhibited a higher level of nitrogen-containing functional groups, some of which were responsible for most of the exception cases triggered. Given the systematic handling of exception cases, the S2AS tool was successful in mapping all carbon, oxygen and nitrogen atoms to relevant subgroups. This is particularly noteworthy given the structural complexity of many of the oxidation products, which often contain multiple functional groups, branched functionalized chains and ring structures. The S2AS tool is also more reliable than manual classification in cases involving complex molecular structures, for which human experts may occasionally overlook less prominent functional groups or perform inconsistent exception treatments when an imperfect mapping to the available set of AIOMFAC subgroups is present.

The S2AS tool showed high computational efficiency in processing large datasets. It successfully processed the list of 174 α-pinene oxidation product SMILES in less than 0.8 s, and the ∼68000 SMILES from the toluene system in ∼5 min – a processing rate of ∼13800 SMILES per minute on a single laptop processor core (1 thread, Intel Core i7-10710U CPU). This automatic classification rate represents a tremendous advance over manually assigning AIOMFAC subgroups for each component, which would be an infeasible task for systems containing thousands of components. The S2AS tool's processing speed scales linearly with dataset size. Further speedup via parallelization on multi-core computers is possible, but such enhancements have not been attempted in the current version of the source code.

The UManSysProp pure-component vapour pressure estimation tool demonstrated robust performance across the wide range of molecular structures present in the α-pinene and toluene oxidation systems. It successfully parsed the list of SMILES and predicted the vapour pressures for all molecules. For the examples shown in this study, we used the output from the EVAPORATION method, yet the seven other pure-component vapour pressure prediction methods available from UManSysProp were also completed successfully.

The version of UManSysProp we employed in this work includes a new module we developed to determine a two-parameter temperature dependence parameterization of pure-component vapour pressures using the form of Eq. () for each of the vapour pressure methods included (not just EVAPORATION). In a first step, a component's vapour pressure is predicted by each method at seven temperatures equally spaced between 260 and 320 K. In a second step, the two parameters of Eq. () are fitted to these data for each method. In the case of EVAPORATION, no fitting is required since one can solve for parameters Aj and Bj using the output from the end points of the temperature range (two equations, two unknowns). If speed is of the essence, the parameter fitting step can also be bypassed for all other methods by solving for the parameters in the same way, usually yielding similar parameter values to those obtained from a more elaborate fit. The single-thread processing of the ∼68000 toluene-derived product SMILES took 482 s on a Intel Core i7-10710U CPU (one thread) for the vapour pressure data creation plus 83 s for determining the parameters Aj and Bj pertaining to each method when bypassing the parameter fitting step. This amounts to a SMILES processing rate of ∼120s-1 or ∼7200 SMILES per minute (including the parameter fitting step reduces the rate to ∼1650 SMILES per minute). As in the case of the S2AS tool, further speed-up is possible by introducing parallel processing (with good scaling potential) in the case of extensive lists of SMILES.

Together with the introduced S2AS, these two pure-component property prediction tools enable automated and efficient processing of SMILES data for atmospheric and environmental chemistry applications.

We compare three choices for the polarity axis of our 2D lumping framework: ACR, O:C ratio, and OS‾C. Figure  shows examples of the 2D representations of the α-pinene-derived components when either the O:C ratio or the mean carbon oxidation state are selected as polarity axis. These polarity metrics show a surprisingly large degree of variation in representing the polarity-related molecular properties, as demonstrated in Fig.  for the components from the toluene SOA system. While O:C ratio and OS‾C serve as well-established polarity proxies, the ACR captures additional functional-group-level information, resulting in a wide spread of ACR values for a given O:C ratio or OS‾C, e.g. compare the spread at OS‾C=1 in Fig. . This demonstrates that compounds with similar OS‾C can have distinctly different relative affinities for water, as expressed by their predicted ACR.

The accuracy of the grid-based and clustering approaches, as measured by MPE and MAPE, varies notably depending on the surrogate selection method and grid resolution chosen; refer to Tables –. This variability underscores the importance of selecting appropriate methods for specific modelling objectives. At high resolutions, e.g. 10×5, the polarity axis choice has a modest impact, while it can be substantial at lower resolutions, especially in terms of predicted κ values when using the O:C polarity axis paired with one of the non-weighted gridded surrogate selection methods, in which case MAPE>50% can occur.

In the case of the α-pinene system (Tables  and ), the grid-based methods generally exhibit higher MAPE compared to the clustering-based k-means approach, especially at lower resolutions. This trend is consistent across the evaluated metrics and resolutions, highlighting the potential limitations of the simpler grid-based techniques in accurately reducing and representing complex chemical systems. Higher resolutions typically yield lower MAPE, especially in case of the two mass-weighted surrogate selection methods, indicating improved accuracy and preference in applications.

Overall, the activity coefficient ratio as polarity metric choice slightly outperformed the O:C ratio and the OS‾C in case of the systems studied, demonstrating its ability in representing polarity in the context of subsequent gas–particle partitioning impacts on aerosol mass and hygroscopicity. In the case of the α-pinene system, the mass-weighted k-means approach using ACR achieved impressively low MAPE values, ranging from 2.0 % (4×2 resolution) to 0.1 % (10×5 resolution). The toluene system also showed good performance of the mass-weighted k-means approach with ACR, with MAPE values ranging from 6.0 % (4×2 resolution) to 4.3 % (10×5 resolution).

In a comparison of the different surrogate selection methods, the mass-weighted k-means method consistently scored as the most consistent and accurate across both systems. This is evident in case of the α-pinene SOA system when using the O:C ratio for polarity. The mass-weighted k-means method demonstrated superior performance with low MAPE values (0.2 % to 6.7 %) for predicted SOA mass concentrations across various system resolutions. In contrast, the midpoint method showed significant variability, with the MAPE ranging from 6.6 % to 51.2 %. The medoid and weighted medoid methods also displayed lower consistency with the MAPE reaching up to 39.8 %. In terms of the predicted hygroscopicity parameter of the α-pinene SOA, MAPE values spanned from 0.0 % (high resolution, ACR, k-means method) to 89.1 % (low resolution, O:C ratio, medoid method).

In the case of the toluene SOA system using the O:C ratio, k-means performed again well and consistently accros different resolutions in terms of predicted SOA mass concentrations, with MAPE values ranging from 1.3 % to 4.9 %. The other surrogate selection methods showed higher variability, with MAPE values of up to 13 % in case of the midpoint method at 4×2 grid resolution. Although, we note that a MAPE of 13 % could still be considered a good performance compared to uncertainties in field measurements of mass concentrations and aerosol composition. The predicted κ values for the toluene system showed a broader range of MAPE values, in the case of the O:C ratio axis ranging from 1.0 % (weighted medoid, highest resolution) to 143 % (midpoint method, lowest resolution) and substantial MPE variability (-143 % to +131 %), indicating significant over- and under-predictions by different methods at the lowest grid resolution studied (4×2).

When using the OS‾C metric, the mass-weighted k-means method again outperformed alternative approaches at most resolutions. In case of the α-pinene SOA system, k-means resulted in MAPE values ranging from 0.9 % to 1.7 % for predicted SOA mass concentrations across various grid resolutions, approximately as accurate as with the ACR polarity axis. The other surrogate selection methods exhibited higher variability, with the midpoint method showing MAPE values as high as 71.4 % for the 4×2 grid resolution. For the predicted κ values, MAPE ranges from 2.5 % (k-means) to 36 % (midpoint method).

In the case of the toluene SOA system, using OS‾C, the k-means method continued to perform well and consistently, with a MAPE between 0.8 % and 4.7 % for predicted SOA mass concentrations. The other methods showed relatively good performance as well, with a maximum MAPE of 11 % (weighted medoid method, 4×2 grid resolution). In terms of the predicted SOA κ, MAPE values ranged from 8.5 % to 90 %, and MPE values spanned from -49 % (k-means, 6×3 resolution) to 90 % (medoid, 8×4 resolution), again showing higher variability in case of this metric, even when using the mass-weighted k-means method (MAPE from 10 % to 70 %). In comparison, when using ACR as polarity axis, the k-means method achieves a worst MAPE for κ of 31 % for the 4×2 resolution – approximately equivalent to the MAPE of 30 % for an 8×4 resolution when using OS‾C for polarity. This is also consistent with ACR leading to better k-means performance compared to OS‾C in case of the α-pinene SOA system.