We focus this analysis on a specific simulation scenario of in which comparison of model results to reference measurements had the smallest discrepancy according to relative molar abundance of FGs, until model–measurement agreement diverged on what was attributed to the role of heterogeneous chemistry and aging not implemented in the model. To briefly describe the simulation, the MCMv3.2 gas-phase chemistry module generated by the Kinetic Pre-Processor was coupled with a gas/particle organic absorptive partitioning scheme via operator splitting . The SIMPOL.1 group contribution model was used to estimate the equilibrium vapor pressure for individual molecules, and the dynamics of mass transfer to a monodisperse particle population were simulated using LSODE (Livermore Solver for Ordinary Differential Equations; ). Wall losses of particles and semivolatile volatile organic compounds (SVOCs) were neglected. The scenario we further analyze for this study was defined by initial α-pinene and NOx concentrations of 300 and 240 ppb, respectively. The relative humidity was fixed at 61 %, which influenced the rate of HO2 radical self reaction to form hydrogen peroxide, but water uptake and influence on G/P partitioning was not considered. The light intensity was fixed to be consistent with experimental conditions. This scenario was labeled the “APIN-lNOx” simulation. In this work, we will refer to this as the APIN simulation, as we discuss none of the other scenarios and thus eliminate the need for an additional modifier to the label. To focus on a particular mixture, we select a reference period as the apex in SOA concentration occurring at 9.3 h (labeled as tmax⁡SOA) of the 22 h simulation as used by to examine molecular contributions to overall SOA mass and FG abundance. With detailed knowledge of molecular structure and composition in this simulation, we apply the analysis described in Sect. –.

The conditions for the simulations described above were selected to mimic chamber experiments in which FG composition was measured by . collected particles between 86 and 343 nm onto (infrared-transparent) zinc selenide crystals by impaction, and samples were analyzed immediately afterward to minimize storage artifacts. Samples were scanned rapidly to minimize evaporative losses in the FT-IR sample compartment. report that repeated analysis of the same samples by FT-IR yielded consistent results, suggesting robustness in reported values. Samples collected during 3.1–4.2 and 17.6–21.6 h (which we label as “4 h” and “21 h”, respectively) were selected by for comparison against model simulation for the corresponding periods, and we will follow this convention here.

Only relative metrics are used as reported measurements in mole fractions of FGs, and the simulations do not include wall losses of particles and SVOCs that affect overall estimates of yield. Neglecting compound-specific SVOC deposition to walls may further incur biases in relative compositions as raised by , but for this conceptual study we neglect its effect as its parameters are not precisely known.

The molar abundance of molecules nmolec=[ni] in a mixture (consisting of a set of molecules denoted by M) can be related to FG abundance ngroup=[nj] (for each FG in J) obtained by FT-IR – or other means – by invoking a group composition matrix X=[xij], which describes the FG makeup of each molecule. Using scalar notation, we write nj=∑i∈Mnixij∀j∈J. nj is the observed quantity from measurement and represents the sum of FG composition of molecules weighted by their molar abundance.

A statement of atom balance is enabled by the group-atom matrix Λ=[λaj] by relating nj to the atomic abundance natom=[na] in the mixture: na=∑j∈Jλajnj. However, the fact that the same polyfunctional carbon atom can be associated with several FGs poses challenges for reasoning out λC,j for carbon. Therefore, we introduce a carbon type matrix Y=[yik] that enumerates the composition of each molecule in terms of specific number of carbon types, and a carbon-group matrix Θ=[θkj] that relates each carbon type to its unique structure of functionalization.

A statement of FG balance can be constructed from the carbon type matrix, carbon-group matrix, and group composition matrix: ∑k∈Cyikθkj=xij∀i∈M,j∈J. Conversely, a statement of carbon type balance can be made by introducing a matrix, Φ=[ϕjk], from which carbon type abundance can be obtained with FG abundance to construct a statement of carbon type balance: yik=∑j∈Jxijϕjk∀i∈M,j∈J. A minimal illustration for two simple molecules, ethane and ethanol, is shown in Fig. . Symbols are tabulated in Table  . Explanation of additional arrays Λ (atom-group matrix), ζ (carbon oxidation state vector), and z (oxidation state contribution vector) completing the atom and oxidation state balance follow below. In contrast to concise expressions used in Fig. , we continue with use of scalar notation below to more conveniently invoke element-wise, row-wise, and column-wise summations, but we will return to array notation for describing solutions to system of equations (Sect. ).

In our APIN mechanism, there are 327 molecules, 22 FGs, and 41 carbon types (Fig. ), though several are associated with radical structures or unusual structures that are not found in the most abundant compounds. These do not contribute to the organic aerosol mass, but they are included for a complete description of the APIN mechanism. Furthermore, while the equalities introduced in Fig.  are formulated to hold at the level of individual molecules, we demonstrate their application in describing the underlying relationships in molecular mixtures.

The carbon type matrix provides a conceptual relationship for relating FGs to number of carbon atoms in a mixture (Eq.  for carbon is also restated on the right-hand side), nC=∑i∈M∑k∈Cniyik=∑i∈M∑j∈JniλC,jxij, and we can see from Eqs. () and () that λC,j is equivalent to the column-wise summation of ϕjk: λC,j=∑k∈Cϕjk∀j∈J. Previous values for λC are shown in Table . The atomic abundance for each carbon type k is calculated as nka=∑j∈Jλajθkj, as follows from Eqs. () and ().

The mean carbon oxidation state can be estimated from (1) yik through the oxidation state ζ=[ζk] specific to carbon type, and (2) xij and individual FG contributions z=[zj] to carbon oxidation state: OS‾C=1nC∑i∈M∑k∈Cniyikζk=1nC∑i∈M∑j∈Jnixijzj From Eq. (), we can see that ζk and zj are related through the following equality: ζk=∑j∈Jθkjzj∀k∈C

All elements in Eq. can be known precisely for any set of molecules M from the chemometric patterns and atom-level validation described by , which are summarized in Sect. S1. Furthermore, the FGs included in the APIN system are all those which are defined by association only to single carbon atoms (e.g., alcohol, carboxylic, methylene groups). Methods for extending this analysis to FGs containing multiple carbon atoms (e.g., anhydride, ester, and organic peroxide groups) are described in Sect. S2. Solution methods for ϕjk and λC,j are presented in Sect. .

This section describes methods for determining whether the carbon type is detected by FT-IR and how relationships introduced in Sect.  can be modified for a more direct comparison with measurements. The main idea is to consider only the subset of carbon atoms which is bonded to any of the FGs measured in a given experiment and to analyze properties only for those carbon atoms as to what is the achievable degree of characterization of the SOA.

Given a set of FG which are measured J*⊆J and the corresponding subset of carbon atoms C*⊆C which only contain these FGs, we can estimate the number of carbon atoms measured from a modification of Eq. (): nC*=∑i∈M∑k∈C*niyik=∑i∈M∑k∈Cniyik⋅sgn∑j∈J*θkj. sgn is the signum function, which will return 0 when its argument is 0 (no FGs associated with carbon type k are in the measured set) and 1 when its argument is positive (one or more FGs belong to the measured set). The total carbon recovery is calculated as nC*/nC.

We consider three sets of FGs for J*. Set1 = {aCH, aCOH, COOH, ketone and aldehyde carbonyl, CONO2} and comprises FGs reported by and many others e.g.,. Set2 = Set1 + {eCH, hydroperoxide, peroxyacyl nitrate}, and comprises Set1 and three additional FGs that are not commonly reported for OM characterization but have medium to strong absorption bands in the mid-infrared wavelengths (Appendix ) (not inclusive) and relevant for this system. The set labeled as “Full” comprises all groups present in OM, including quaternary and tertiary sp2 carbon (carbon atoms that are only bonded to other carbon atoms) that account for 7 % of the mass in the APIN simulation at tmax⁡SOA, and also the remaining groups (Fig. ) that accounts for < 1 % of the remaining mass.

We can estimate OM as the sum of elements multiplied by their respective molecular weights using Eq. (). Atomic ratios are calculated as na/nC for all heteroatoms a={H,N,O} (S is not included in this chemical mechanism, but this principle can be extended for mechanisms that include it): na*=∑j∈J*λajnj. Atomic ratios are calculated as na*/nC*.

To estimate the mean carbon oxidation state, we can replace nC with nC* and sum over J* instead of J in Eq.() by corollary with Eq. (): OS‾C≈1nC*∑j∈J*zjnj.

In this section, we describe methods for estimating nC from measured abundance of FGs. The main objective is to arrive at a set of coefficients λ^C that, when multiplied by FG abundance nj for measured FGs J*, provides an estimate n^C* that does not count multiples of the same carbon atoms which are attached to the suite of FGs analyzed: n^C*=∑j∈J*λ^C,jnj. The use of the hat over a symbol denotes a statistically estimated quantity.

It is convenient to continue discussion of solutions to a system of equations in array notation (similar to what is used in Fig. ). Let Y=[niyik], X=[nixij], Θ=[θkj], Φ=[ϕjk], λC=[∑k∈Cϕjk], and nC=[∑k∈Cyik]. The FGs and carbon type abundances can be written as YΘ=X. The most obvious solution is to take the generalized or Moore–Penrose inverse, Φ^=Θ+. In the example illustrated in Fig. , the solution to Φ=Θ-1 and λC (a row of ΛT) using such an approach is provided. The elements of Φ satisfy the carbon type balance (Eq. ) but are not required to be non-negative, but their summation across rows (Eq. ) yields values for λC that corresponds to the number of carbon atoms per FG associated with them. While exact solutions can be found for this illustration because Θ is square (i.e., the number of carbon types equals the number of types of FGs), the pseudo-inverse solution will not be meaningful in a more general case as the number of ways in which FGs are arranged on carbon atoms exceeds the number of measured FG used for discrimination. λC may also not correspond to a physically interpretable quantity in such instances, as a single set of coefficients is insufficient to estimate the exact abundances of carbon atoms under these circumstances.

Therefore, while carbon types are a useful concept to describe the underlying representation of functionalized organic compounds, it is generally not possible to retrieve the exact abundance of each carbon type from FG measurements. To arrive at an approximate solution for estimation of the total carbon atoms without discrimination of carbon types, we consider the three approaches described below.

First, we consider each carbon type in isolation (“COUNT” method) and average the reciprocal of measured FGs per carbon enumerated for each carbon type: λ^C,j=1|Cj|∑k∈Cj1∑j′∈J*θkj′. |⋅| denotes the cardinality of (i.e., number of elements in) a set and Cj is the set of carbon types in which FG j appears, and is the origin of the dependence of λC on j. The main premise of this approach is to apportion fractional units of carbon to each measured FG such that their sum equals unity. The rationale can be supported by the illustration (Fig. ) in which 1/3 for λC reflects the number of measured FGs attached to each carbon atom.

In the second approach (“COMPOUND” method), we find Φ that corresponds to the least squares solution to the following equation: Y^=XΦ^. λ^C is found by row-wise summation of Φ^ (Eq. ) (which is also equivalent to solving for λ^C directly in the reduced expression, n^C=Xλ^C). Given the wide range of possibilities in composition, we set molar abundances to unity such that each compound within each group (SVOC) is uniformly weighted. We average over carbon types present in molecules relevant to certain mixture classes with uniform weighting such that the derived coefficients are not overly specific to any particular mixture.

In the third approach (“MIXTURE” method), we reformulate Y=[nmiyij] and X=[nmixij] such that its rows contain the FG abundance of the mixture of each time step tm of the APIN simulation, and λC is found by fitting X to nC*, the time series of carbon atom concentration in the condensed phase at each time step. For MIXTURE, we use a constrained least squares approach where the values of the regression coefficients are bounded between 0 and 1 as the coefficients for FGs with low abundance (e.g., eCH and CONO2) are not well constrained (the solution is insensitive to their values).

Numerical details aside, the main differences among the three are the data sets used for estimation. COUNT uses information from Θ only (defined for the FGs in the APIN mechanism), COMPOUND uses carbon type abundances in compounds (limited to SVOCs in the APIN mechanism), and MIXTURE uses mixture information of the condensed phase (from different periods in the APIN simulation). The resulting differences in estimates of λ^C are largely due to weighting of FGs associated with each carbon type: each type receiving equal weight (COUNT), by frequency of occurrence in SVOCs (COMPOUND), and by abundance in SOA formed in the APIN simulation (MIXTURE). While the COUNT method is physically significant at the level of individual carbon atoms, the representativeness of estimated values for use in mixtures can vary according to composition. Direct fitting methods, on the other hand, may lead to insignificant coefficients from under-represented or redundant FGs, or be overly specific such that they cannot be generalized to other systems. Therefore, the results from all three methods are evaluated to explore the range of plausible values.

Each of the solutions produces a series of irrational numbers (due to the multiplicitous configurations of FGs on carbon atoms) that may be overly precise for the data set used for estimation. As later shown, we will also adjust the COUNT solutions to rational values of {1/4, 1/3, 1/2, 1} (with exception for λC,aCH which we fix to a value of 0.45 as explained in Sect. ), and we will refer to this as the “NOMINAL” solution. For the COMPOUND and MIXTURE methods, FGs and carbon types with a unique (one-to-one) correspondence (e.g., carbon atoms associated with carboxylic acid and ketonic and aldehydic carbonyl groups) are excluded from the fitting, as their coefficients are known unambiguously. Evaluations of estimates are expressed as a ratio of the estimate over the reference value: n^C*/nC*. We remark that we focus on harvesting information from the APIN simulation results only, but these methods can (and should) be applied to study abundances in molecular speciation data from chamber experiments under different oxidation and environmental conditions e.g., in future work.

The time series of carbon type abundance is shown by its contribution fraction for each time period in Fig. , and the carbon type composition of the most abundant molecules at tmax⁡SOA is depicted in Fig. . Descriptions for the carbon types found in tmax⁡SOA are shown in Fig. . We observe that changes in carbon type composition is rapid within the first four hours, but generally changes much more slowly after this period. Many of the dominant carbon types are generally similar between the gas and aerosol phases and include: methyl (CH3), methylene (CH2), ketone, primary alcohol, and secondary alcohols, acid (COOH), hydroperoxides, and peroxyacyl nitrate groups. However, the order of abundance is different between phases – for instance, the peroxyacyl nitrate is more abundant in the gas phase (carbon type 10; Fig. ). As visualized in Fig.  and described by , the molecular abundance is dominated by a small number of polyfunctional compounds (out of the [200] compounds in the mechanism), so their carbon types are weighted heavily in the overall carbon type composition.

The ordered contribution to mass recoveries of OC and OM for the most dominant carbon types at tmax⁡SOA are displayed in Fig. . Greater than 99.9 % of the OC and OM mass is accounted for by 15 carbon types during this period, while more than 20 compounds are required to reconstruct aerosol OC mass with > 99.9 % recovery (Fig. ). Mass recovery with Set1 is on the order of 80 %. The fraction of OC estimated by FT-IR relative to OC measured by thermal optical methods are often within a similar range e.g.,. With additional bonds in Set2, 93 % carbon recovery is achieved. The unmeasured carbon types are quaternary and tertiary sp2 carbon that are bonded to C-bonds only, and together comprise 7 % of the OC (Full case).

Going from Set1 to Set2, the increase in fraction of recovered OM is greater than recovered OC because of the hydroperoxide and peroxyacyl nitrate mass is much greater than the mass of carbon bearing these FGs. The resulting effect on estimated properties is shown in Fig. . H / C recovery is high for Set1 already, but we are missing the oxygen from hydroperoxide and peroxyacyl nitrate. eCH is small. N / C is very small (low-NOx conditions). OM / OC can be off by 0.2. Even with nearly full mass recovery, ratios are often inflated by a small amount on account of the unmeasured carbon (i.e., nC*≤nC).

The carbon oxidation state distribution and recoverable portions for tmax⁡SOA are shown in Fig. a. This figure visually reinforces the abundance of methyl carbons (CH3, OSC=-3) and methylene carbons (CH2, OSC=-2) discussed above, though there are other carbon types contributing to the OSC=-2 category (Fig. ). The unmeasurable carbon types with FT-IR are those with OSC = 0, which are the quaternary and tertiary sp2 carbon (carbon types which are measurable in the OSC= 0 category have a balance of negative and positive values from aCH and electronegative heteroatoms). The value of the additional FGs in Set2 are for characterization of oxidizing FGs (hydroperoxide and peroxyacyl nitrate) that on carbon atoms with overall oxidation states of 1 and 3. Estimates of the mean OS‾C is shown in Fig. , panel b. We can see that the bias in estimation for neglecting hydroperoxide and peroxyacyl nitrate is not as great as for the O / C ratio, since the OSC is determined by the atom and bond connected to the carbon atom directly, and the rest of the multiple oxygen atoms in the FG are not considered. The 2O / C–H / C estimate commonly used with elemental analysis will lead to a slight overestimation of the OS‾C in the event that oxygen single-bonded to carbon (hydroxyl and hydroperoxide groups) exist in large abundance proportionally to double-bonded carbonyl groups .

Table  summarizes the new values for λ^C obtained by the different estimation methods described in Sect. . Comparison of n^C* estimated using these values against nC* in individual compounds is shown in Fig. , and the comparison of n^C* and nC* in overall aerosol mixtures at different time periods in the APIN simulation is shown in Fig. .

Values for λ^C are roughly similar among estimation methods, with the exception of the MIXTURE estimate. Overall, we find that the coefficient for aCH is close to but less than the often assumed value of 0.5 (Table ), which can play an important role on account of the abundance of aCH bonds and carbon types associated with aCH. For the MIXTURE estimate, λ^C,aCH=0.5 but is balanced by exceptionally small coefficients for aCOH and hydroperoxide. This combination of coefficients essentially downweights the contributions from carbon types associated with aCH and hydroperoxide, which we know to be present in abundance (within top 6 for the APIN simulation at tmax⁡SOA, but remains significant throughout the simulation as seen in Fig. ). Therefore, we conclude that the estimates obtained for this fit are statistically convenient but less physically relevant than the other estimates. For the NOMINAL case, we fix the aCH to λC,aCH=0.45 and the rest to the nearest rational numbers.

For individual compounds, we note that using either Set1 and Set2 reproduce nC* with similar biases on average: 11 % for COUNT and within 4 % for the others. COUNT underestimates nC* in large compounds with lower oxidation states containing many aCH groups, because of the low estimate of λ^C,aCH. COMPOUND reproduces nC* well because this is the data set COMPOUND was fit to, but MIXTURE also does well. The NOMINAL solution also does well, but largely owing to the λC,aCH adjustment.

For reproducing mixture composition, trends in biases are similar to individual compounds, with underestimation by as much as 18 % for COUNT and within 7 % for the other estimation methods. MIXTURE performs the best because this is the data set it was fitted to, but we see that the COMPOUND and NOMINAL are also acceptable. There is generally a trend toward increasing n^C*/nC* over the duration of the simulation, which indicates an evolving relationship between FGs and carbon abundance with mixture composition. Time-dependent (i.e., mixture-specific) estimates of λC may be warranted when the change in composition becomes more significant.

We therefore conclude that errors for estimation of nC* can be quite low and are well below 10 % according to our evaluation. Even a 10 % error in estimation of nC* will lead to a 9 % error in the estimation of any individual atomic ratio, and 5 % estimation in the OM / OC ratio (Appendix ). Therefore, in applying the NOMINAL coefficients to measured values of FGs under conditions upon which the APIN simulations were based (Sect. ), we discuss deterministic explanations for model–measurement discrepancies with less consideration toward statistical estimation error of nC*.

In this section, we discuss O / C, OM / OC, and OS‾C estimated from measurements ending at hours 4 and 21 and APIN simulation results integrated over the same periods (Fig. ). We label the interpretation of measurements with previous estimates of λC (Table ) as “MEAS-PREV”, measurements with revised estimates of λC (Table ) as “MEAS-NOM”, simulation results using FGs from Set1 as “SIM-SET1”, and full simulation results as “SIM-FULL”; further adjustments are made for the last three estimates as justified next. In Sect. , we presented an estimate of mass recovery (nC*/nC*) and how this led to biased estimates of atomic ratios and OM / OC ratio. In Sect. , we also showed that we can derive estimates of λC such that errors in estimation of nC* was small (i.e., n^C*/nC* near unity). Therefore, for the following comparisons, we neglect the latter error and correct biases due to carbon mass recovery by using our best estimate of nC*, rather than nC*, as the normalization factor. The proportion of detected carbon to make this correction is obtained from SIM-SET1, in which the same FGs as measurements are used. While the adjustment is only approximate on account of differences in the real experimental system and model simulation, it reduces systematic biases in carbon-centric metrics as described in Sect.  such that deviations from true ratios can be largely attributed to the unmeasured heteroatoms. For MEAS-NOM, the atomic ratio is then estimated as na*/nC*=na*/nC*×(nC*/nC*)SIM-SET1 and the OM / OC and OS‾C by similar adjustment. MEAS-PREV remains unadjusted to be used as a reference estimated without prior knowledge about the underlying molecular structures of the SOA products.

First, we remark on differences for estimated metrics from two sets of coefficients applied to the same FG measurements. MEAS-PREV overestimates the nC* compared to MEAS-NOM by 21–28 % on account of higher λC coefficients used in the former. However, the uncorrected bias due to lower mass recovery of carbon is approximately the same magnitude, and ultimately leads to ratioed values (O / C, H / C, OM / OC, OS‾C) similar to MEAS-NOM. While it is not clear that λC derived in this work accurately represents the true mixture, we posit that the degree of functionalization characterized by the new estimate is likely to be more representative for the product mixture after successive oxidation of the APIN, rather than APIN itself (as assumed by MEAS-PREV). report O / C and H / C estimates from FT-IR using coefficients of MEAS-PREV and found that they were within range of aerosol mass spectrometer (AMS) values; this is possibly due to the offsetting of errors as demonstrated here. In further discussion, we will discuss the interpretation of observations based on MEAS-NOM.

MEAS-NOM and SIM-SET1 are the two estimates intended to provide the most direct comparison between experiment and numerical simulation. While the discrepancy in carbonyl and carboxyl groups at 4 h is only 2 and 3 % in mole fraction, respectively , this leads to an overall discrepancy of 0.16 for O / C and 0.2 for OM / OC. Since aCOH, carbonyl, and COOH groups are a larger contributor to the mass relative to the aCH group, discrepancies in molar abundance of oxygenated FGs are magnified when represented in OM / OC ratios and can have a non-negligible influence on interpretation of mass yields. After 21 h, the difference is 0.38 in O / C and 0.48 in OM / OC. attributed the apparent divergence to mechanisms not included in the model. Oligomerization was not considered a likely candidate as this process not expected to contribute to increased oxygenation reported by FT-IR. Condensed-phase photolysis can lead to conversion of hydroperoxides to carbonyls (some of which are lost to the vapor phase as more volatile molecules) , but even a hypothetical full molar conversion is insufficient to explain the model–measurement differences in carbonyl groups . Other missing mechanisms may include autoxidation , which can produce extremely low volatility (ELVOC; ) or highly oxygenated molecules (HOM; ) in the gas phase, or radical reactions in the condensed phase that lead to highly oxidized products containing these measured FGs. In these comparisons, we cannot rule out that some biases in measurement may originate from molar absorption coefficients estimated for each FG in FT-IR. The absorption intensity is determined by a change in the magnitude of the dipole moment and can vary according to molecule or mixture environment; the representativeness of applied absorption coefficients in these SOA mixtures is a possible area for future inquiry. However, cite variations on the order of 20 % for oxygenated FGs in several carboxylic acid and ketone species, which provide some constraints on this uncertainty for the range of compound classes evaluated in their study.

As reported by , SIM-FULL has similar O / C of observations in similar chamber studies where aerosol mass spectrometer (AMS) measurements were available . OM in MEAS-NOM is less functionalized than in SIM-FULL at hour 4, but the opposite is true at hour 21 even while hydroperoxide and peroxyacyl nitrate is not included. The rate of transformation of these FGs remains uncertain – for instance, reported lifetimes of hydroperoxides range from less than an hour to many days ; resolving their reaction pathways may play a critical role in understanding model–measurement discrepancies . Using the estimates of MEAS-NOM, the additional oxidation and aging process between 4 and 21 hours leads to an increase in O / C of about 0.24, including a 0.09 difference in O / C from carbonyl (a product of hydroperoxide photolysis). If we extrapolate the O / C of MEAS-NOM to that which includes hydroperoxide and peroxyacyl nitrate groups by assuming the same hydroperoxide and peroxyacyl nitrate contributions from SIM-FULL, we would obtain an overall O / C ratio of 0.7 at hour 4 and 0.9 at hour 21. The latter value is at the higher end of O / C values by reported by AMS e.g.,. A concurrent measurement of overall O / C and O / C partitioned by measured FG may provide better constraints on our understanding of OM transformations.

As with O / C and OM / OC, OS‾C also highlights the greater extent of functionalization in observations than in simulations between hours 4 and 21. OS‾C estimated from MEAS-NOM is in the range of low-volatility oxygenated organic aerosol (LV-OOA) , while they are in the range of semi-volatile oxygenated organic aerosol (SV-OOA) in the simulations as consistent with the species included in the MCMv3.2 mechanism. In simulation, the products found in the aerosol phase are contain more than six carbon atoms, and the smaller, highly oxidized molecules remain in the gas phase (Sect. S3, Fig. S1 in the Supplement). As discussed in Sect.  and shown in comparison between SIM-MEAS1 and SIM-FULL (Fig. c), the missing contributions from hydroperoxide and peroxyacyl to OS‾C are likely to be small as only the valence of the bonded atoms, and not the total atomic count of the FGs, contributes to the carbon oxidation state.