For the peaks that have had chemical formulae assigned, oxidation state of carbon, or OSc, can be used to describe their bulk oxidation chemistry. OSc is defined as (Kroll et al., 2011) 2OSc=(2×O:C)-H:C. This does not account for the presence of nitrate ester groups, which has been accounted for previously by subtracting 5 times the N : C ratio (Massoli et al., 2018), under the assumption that all nitrogen-containing functionality is in the form of nitrate ester (RONO2) groups. In Beijing, multiple sources of nitrate-containing organic compounds are seen, in the forms of amines, nitriles, and heterocycles. The variation in oxidation state with carbon number (Cn) without correction for nitrate esters is plotted in Fig. 1. The average oxidation state of carbon in this dataset tends to decrease with an increase in Cn, highest where Cn=5, attributable to both high O : C and peak area, for the peak assigned to C5H10N2O8 at m/Q 288. Cn=5 also shows the greatest distribution of oxidation states, likely due to the high ambient concentration of isoprene and therefore its many oxidation products being of high enough signal for many well-resolved peaks to be seen in this dataset. It is worth noting that some of the ions plotted here may not form through peroxy radical autoxidation, such as C5H10N2O8, which may be a second-generation oxidation product of isoprene under high NOx (Lee et al., 2016). Cn=10 and 15 also see a small increase in average oxidation number compared to their neighbours. The lower oxidation state of the larger products is likely a function of two things. First and foremost, any autoxidation mechanism must undergo more steps in order for a larger molecule to reach an O : C ratio equivalent to that of a smaller one, and the equivalent O : C ratio is ultimately less likely to be reached before the radical is terminated (Massoli et al., 2018). Secondly, the lower vapour pressures of these larger products will lead to their partitioning into the condensed phase more readily than the smaller; thus they are more rapidly lost (Mutzel et al., 2015).

The degrees of OSc observed here are similar to those seen in other environments such as during the SOAS campaign in 2013 in the southern United States, characterized by low NO/NO2 and high temperatures, where campaign averages of 0.3 ppb, 0.4–0.5 ppb, and 25 ∘C respectively were measured, although an additional parameter to account for nitrogen-containing VOCs is included in the calculation (Massoli et al., 2018). The OSc observed in Beijing is also higher than that seen in the boreal forest environment of Hyytiälä, despite extremely low NOx concentrations, likely due to low temperature conditions dominating in those conditions (Schobesberger et al., 2013). These degrees of oxidation relatively similar to those seen in other, cleaner environments are likely due to an interplay between the higher temperatures facilitating rapid hydrogen abstractions (Crounse et al., 2013; Quéléver et al., 2019) and the higher concentrations of NOx, HO2⚫, and other RO2⚫ molecules terminating the autoxidation sequence more efficiently (Praske et al., 2018; Rissanen, 2018; Garmash et al., 2019).

A mass defect plot is shown in Fig. 2, which shows nominal mass plotted against mass defect for all peaks in this dataset. Mass defect is defined as the ion mass minus integer mass. This is shown for two separate daytime periods, one where nucleation was not occurring and HOM concentrations are lower (10:30–12:00 CST 23 June 2017) and one where nucleation was occurring under high HOM concentrations (10:30–12:00 CST 25 June 2017). The band of lower mass defect is characterized by a number of large peaks with high signal, for example, at m/Q 436 the ion (C2H7N)2(H2SO4)2HSO4-. The upper component of the mass defect is dominated by organic compounds, and the upper end of the more positive mass defect is occupied by molecules with more 1H (mass defect 7.825 mDa) and 14N (mass defect 3.074 mDa). The end of the less positive mass defect has lower 1H and more 16O (mass defect -5.085 mDa); alternatively put, the mass defect reflects the variation in OSc. The organic components with more positive mass defects will be more volatile than their lower mass defect counterparts as they will contain fewer oxygen functionalities (Tröstl et al., 2016; Stolzenburg et al., 2018). These higher-volatility products may still contribute to larger size particle growth. The more negative mass defect components will be those of greater O : C and therefore lower volatility, LVOCs, and the yet larger and more oxidized components, ELVOCs (Tröstl et al., 2016). During the nucleation period, the signal intensity for the species in the upper band of more negative mass defect have the most marked increase in concentration, with significantly less difference >500 m/Q. This region 200–400 m/Q will contain most of the > C5 monomer HOMs seen in this dataset.

Temporal trends of HOMs in the urban atmosphere can reveal their sources and behaviour in the atmosphere. Most of the HOM species peak in the daytime. These species all follow a similar diurnal trend, as shown in Fig. 3. The concentrations of both O3 and OH⚫ are high during the summer period in Beijing (although the nitrate chemical ionization technique is not sensitive to all OH⚫ oxidation products; Berndt et al., 2015). Figure S1 shows the time series of concentrations of NO, which is considered a dominant peroxy radical terminator of particular importance in the polluted urban environment (Khan et al., 2015). Radicals such as HO2⚫ and RO2⚫ also typically peak during daytime. The HOM components peaking in the daytime are presumed to be the oxidation products of a mixture of anthropogenic and biogenic components, such as alkylbenzenes, monoterpenes, and isoprene. The oxidation of monoterpenes, specifically the monoterpene α-pinene, has been the subject of extensive study recently, with the O3-initiated autoxidation sequence being the best characterized (Ehn et al., 2014; Jokinen et al., 2014; Kurtén et al., 2015; Kirkby et al., 2016); ozonolysis of α-pinene opens the ring structure and produces a RO2⚫ radical (Kirkby et al., 2016). In the case of aromatics, OH⚫ addition to the ring and the subsequently formed bicyclic peroxy radical are the basis for the autoxidation of compounds such as xylenes and trimethylbenzenes (Molteni et al., 2018; Wu et al., 2017).

The identified compounds have been roughly separated into several categories, each of these plotted in Fig. 3. Figure 3a shows the separation of components into non-nitrogen-containing HOMs and nitrogen-containing HOMs, or organonitrates (ONs). The ON signal is much higher than that of the HOM, attributable in part to a few ions of high signal, such as the isoprene organonitrate C5H10N2O8. A few similar structural formulae are seen (C5H10N2O6, C5H11NO6, C5H11NO7, etc.), some of which have been identified as important gas-phase oxidation products of isoprene under high-NOx conditions (Xiong et al., 2015), and their contribution to secondary organic aerosol (SOA) has been explored previously (Lee et al., 2016). A high nitrophenol signal is also seen, C6H5NO3. The signal for HOM compounds is less dominated by a few large ions. The prevalence of ON compounds points towards the important role of NOx as a peroxy radical terminator, with the probability of the RO2⚫+NOx reaction producing nitrate ester compounds increasing with the size of the RO2⚫ molecule (Atkinson et al., 1982). The NOx concentrations in urban Beijing are approximately a factor of 10 higher than seen at the Hyytiälä station in Finland as reported by Yan et al. (2016), and hence it is expected to be a more significant peroxy radical terminator.

Despite the very large fluxes of anthropogenic organic pollutants in Beijing, biogenic emissions are still an important source of reactive VOCs in the city, with abundant isoprene oxidation products observed (see above), as well as monoterpene monomers (C10H16O9, C10H15O9N) and some dimer products (C20H30O11, C20H31O11N). The time series of the signals of all C5, C10, and C20 molecules is plotted in Fig. 3b, with C5 species assumed to be isoprene-dominated and C10 and C20 assumed to be monoterpene-dominated. Signals for isoprene oxidation products are higher, with abundant isoprene nitrate and dinitrate products. C10 products show similar behaviour, with, for example, several C10H15OxN x=5–9 compounds seen. The C20 signal intensities are low and follow the general formula C20HxOyNz, where x=26–32, y=7–11, and z=0–2; in Fig. 3 the signal for C20 compounds has been multiplied by a factor of 50 for visibility. The low signals reflect the lack of RO2⚫ cross reactions necessary for the production of these accretion products.

Other identified peaks are plotted in Fig. 3c. The C2–C4 components are summed together, these being small organic acids such as malonic acid and oxalic acid, as well as products such as C4H7O6N. Malonic acid is the most prominent here, seen as both an NO3- adduct (C3H4O4NO3-) and a proton transfer product (C3H3O4-) at a ratio of around 2 : 3. Measurements of particle-phase dicarboxylic acids in cities typically show greater concentrations of oxalic acid than malonic acid (Ho et al., 2010), and these acids are primarily produced in the aqueous phase (Bikkina et al., 2014). Primary sources of dicarboxylic acid include fossil fuel combustion (Kawamura and Kaplan, 1987) and biomass burning (Narukawa et al., 1999), which are both plentiful in urban Beijing. The C6–C9 components are assumed to be dominated by oxidation products of alkylbenzenes such as C8H12O5, although fragments of other compounds, i.e. monoterpenes, can also occupy this region (Isaacman-Vanwertz et al., 2018). It is assumed the majority of the signal for these peaks come from alkylbenzenes. This assumption is supported by the relative signal intensity ratios of the oxygen numbers of monomer C8H12On compounds being similar to those seen for xylene oxidation products in previous work (Molteni et al., 2018). The largest fraction, C11 through C18, includes the larger compounds, oxidation products of larger aromatics, or products of the cross reaction of smaller RO2⚫ radicals. Here they are grouped without more sophisticated disaggregation as they all follow much the same time series, with species such as C11H11O8N following the same temporal trends as C15H16O9 and C16H24O12.

Nearly all ions with the exception of the larger compounds attributed to the cross reaction of C10 monomers follow similar temporal patterns, with the majority of peaks occurring in the daytime. This reflects the importance of the concentration of atmospheric oxidants. Some selected oxidation products are plotted against their precursor VOCs in Fig. 4. The concentration of isoprene is plotted against the signal of a nitrate HOM product, C5H9NO6 (Xiong et al., 2015; Lee et al., 2016), while monoterpenes are plotted against C10H16O9 (Ehn et al., 2014; Berndt et al., 2016; Yan et al., 2016; Kirkby et al., 2016; Massoli et al., 2018) and C2 benzenes against C8H12O6 (Molteni et al., 2018; Wang et al., 2017). The first half of the time series shows little correlation between the VOC species and the resultant oxidation products, while isoprene, monoterpenes, and C2 benzenes follow their usual diurnal cycles, with isoprene having the most distinct cycle with a strong midday peak. The last 2 d, however, show similar and coinciding peaks in both the VOCs and HOMs – HOMs show afternoon peaks on both days and an initial shelf on the final half day. The C5H9NO6 peak follows some of the peaks of the isoprene, but not all (e.g. morning shelf of isoprene on 24 June). Concentrations of isoprene do not seem to determine directly the signal of HOM, as the day with the lowest isoprene of all is the day with the highest C5H9NO6. The C10H16O9 trace also has coincidental peaks with the monoterpene trace, including two 4 h separated simultaneous peaks on 25 June. The peaks in the concentrations of C2 benzenes are nearly synchronous with the peaks in C8H12O6, for which the data exhibit a strong mid-afternoon peak likely due to the lack of an efficient ozonolysis reaction pathway; the main oxidant of C2 benzenes is the OH⚫ radical. Trends of both C3 benzenes and their HOMs are much the same as C2 benzenes as discussed above, pointing to similar sources and oxidation chemistries. The concentration of precursor VOC is likely a driving force in the identity and quantity of various HOM products, but not the sole determinant, as while there are simultaneous peaks of VOCs and HOMs, both the condensation sink and oxidant concentrations also influence HOM product signals.

The first half of campaign measurements are marked by an episode of low HOM signals. A diurnal cycle still exists but it is weak. The radiation intensity was significantly lower on these prior days than it was on 24 June. No data are available for the final period of measurement. Ozone is higher on the prior measurement days with lower HOM signals (see Fig. S1). Little agreement is seen between VOC concentration and HOM signals on these days. The condensational sinks are roughly similar to those on days of higher HOM concentrations, but temperature and solar radiation are much lower. HOM formation is largely dependent upon VOC concentration, oxidant concentration (which will be lower if solar radiation is lower, especially in the case of OH⚫, the main oxidant of aromatic species especially), and temperature (as H shifts are highly temperature-dependent) (Quéléver et al., 2019), as well as losses by RO2⚫ termination before a molecule can become HOM and losses to condensational sink. The low HOM concentration is likely due to these lower temperatures and weaker solar radiation not facilitating HOM formation.

The C20 compounds plotted in Fig. 3b show no strong diurnal sequence, contrasting with other HOMs. We can presume that all C20 compounds identified are the result of the reaction of two monoterpenoid C10 RO2⚫ radicals, a reasonable assumption as all identified C20 species follow the general formula outlined for these reactions (C20H28–32O6–16). The formation of C20 dimers is dependent upon two processes, initial oxidation of monoterpenes and RO2–RO2 termination. Initial oxidation is contingent upon oxidant concentration, which is highest in the daytime, and RO2⚫–RO2⚫ termination is contingent upon the probability of the molecular collision between the RO2⚫ molecules occurring before other radical termination (i.e. RO2⚫–NOx or RO2⚫–HO2⚫). There is likely a strong diurnal sequence in the dominant RO2⚫ termination mechanisms across the daytime period, and the combination of the two factors discussed above results in there being no strong diurnal trend in these molecules. A lower oxidant concentration at night results in fewer RO2⚫ molecules, but less NO and HO2⚫ results in a greater chance for those RO2⚫ molecules to dimerise (Rissanen, 2018; Garmash et al., 2019). As the levels of NOx in Beijing fall, the peroxy radical termination reactions will be less probable compared to continued autoxidation (Praske et al., 2018), and it is expected that more oxidized HOM products will be seen with lower volatilities and therefore a greater potential contribution to earlier stage particle formation and growth.