Highly oxygenated compounds assigned to be oxidation products of α‐pinene have recently been observed in substantial concentrations in ambient aerosols. Here, we confirm the unknown α‐pinene tracer compound with molecular weight (MW) 204 as the C8‐tricarboxylic acid 3‐methyl‐1,2,3‐butanetricarboxylic acid. Its gas and liquid chromatographic behaviors and its mass spectral characteristics in electron ionization and negative ion electrospray ionization perfectly agree with those of a synthesized reference compound. The formation of this compound is explained by further reaction of cis‐pinonic acid involving participation of the OH radical. This study illustrates that complex, multi‐generation chemistry holds for the photooxidation of α‐pinene in the presence of NOx.

In the present study, we have characterized in detail the MS(2) and MS(3) fragmentation behaviors, using electrospray ionization (ESI) in the negative ion mode, of previously identified sulfated isoprene secondary organic aerosol compounds, including 2-methyltetrols, 2-methylglyceric acid, 2-methyltetrol mononitrate derivatives, glyoxal and methylglyoxal. A major fragmentation pathway for the deprotonated molecules of the sulfate esters of 2-methyltetrols and 2-methylglyceric acid and of the sulfate derivatives of glyoxal and methylglyoxal is the formation of the bisulfate [HSO(4)](-) anion, while the deprotonated sulfate esters of 2-methyltetrol mononitrate derivatives preferentially fragment through loss of nitric acid. Rational interpretation of MS(2), MS(3) and accurate mass data led to the structural characterization of unknown polar compounds in K-puszta fine aerosol as organosulfate derivatives of photooxidation products of unsaturated fatty acids, i.e. 2-hydroxy-1,4-butanedialdehyde, 4,5- and 2,3-dihydroxypentanoic acids, and 2-hydroxyglutaric acid, and of alpha-pinene, i.e. 3-hydroxyglutaric acid. The deprotonated molecules of the sulfated hydroxyacids, 2-methylglyceric acid, 4,5- and 2,3-dihydroxypentanoic acid, and 2- and 3-hydroxyglutaric acids, showed in addition to the [HSO(4)](-) ion (m/z 97) neutral losses of water, CO(2) and/or SO(3), features that are characteristic of humic-like substances. The polar organosulfates characterized in the present work are of climatic relevance because they may contribute to the hydrophilic properties of fine ambient aerosol. In addition, these compounds probably serve as ambient tracer compounds for the occurrence of secondary organic aerosol formation under acidic conditions.

SummaryThere are 9 pages in this Supporting Information, including 1 table, 4 figures, 5 schemes, and 10 references. S1. Aerosol samplesThe α-pinene SOA samples used for the time course analysis (Fig. S1) were obtained from an ozonolysis experiment carried out at the IfT in the 9 m 3 Teflon smog chamber (S1). Briefly, α-pinene ozonolysis was performed in the presence of acidic seed particles (0.03 M (NH 4 ) 2 SO 4 /H 2 SO 4 ). No OH scavenger was used in this experiment. The relative humidity and temperature of the chamber were around 50% and 23 ºC. The initial concentrations of α-pinene, ozone, and seed particles were 100 ppb, 60 ppb, and 20,000 cm -3 , respectively. A more detailed description of the experimental procedure is given in (S1). Samples were collected using a condensation-growth and impaction system (C-GIS). Details about the C-GIS sampling system are reported in a previous study (S2). S2. Preparation of standardsTerpenylic acid was prepared from homoterpenyl methyl ketone as reported by Baeyer (S3) (Scheme S1). 5 g of cis-pinonic acid (Aldrich, cis-3-acetyl-2,2-dimethylcyclobutaneacetic acid) was dissolved in 60 g of H 2 SO 4 (50%) at 100 °C and left for 30 min, resulting in a brown mixture with yellow-green fluorescence. Subsequently, 150 mL of water was added to the mixture, the mixture was further saturated with (NH 4 ) 2 SO 4 and the organic phase was extracted with CHCl 3 . The resulting extract was dried over Na 2 SO 4 , the solvent was evaporated to yield homoterpenyl methyl ketone, and the product was re-crystallized from water. In a subsequent step, homoterpenyl methyl ketone was oxidized as reported by Wallach (S4) (Scheme S1). 3 g of homoterpenyl methyl ketone was dissolved in a 0.93 M KOH solution (60 ml), and 300 mL of 0.158 M KMnO 4 solution was added to the solution within 20 min. After filtration of the brown precipitate, the solution was acidified with 10% H 2 SO 4 and repeatedly extracted with diethyl ether. The extract was dried over Na 2 SO 4 and the solvent was evaporated to yield terpenylic acid.The preparation of diaterpenylic acid acetate is given in the supporting information of Iinuma et al. (S5).

In this work, a new partitioning method is presented which allows one to calculate properties of radicals, in particular, atomic spin populations. The method can be seen as an extension of the Hirshfeld-I method [ Bultinck , P. et al. J. Chem. Phys. 2007 , 126 , 144111 ], in which the atomic weight functions, defining the atoms-in-molecules, are constructed by means of an iterative scheme in which the charges of the atoms-in-molecules are altered but the spin remains fixed. The Hirshfeld-I method is therefore not suitable for the calculation of atomic spin populations of open-shell systems. The new fractional occupation Hirshfeld-I (FOHI) uses an iterative scheme in which both the atomic charge and spin are optimized, resulting in a self-consistent method for the calculation of atomic spin populations. The results obtained with the FOHI method are compared with experimental results obtained using polarized neutron diffraction, thus serving as a validation of the FOHI method as well as the Hirshfeld definition of atoms-in-molecules in general.

Abstract. We show in the present study that the unsaturated aldehydes 2-E-pentenal, 2-E-hexenal, and 3-Z-hexenal are biogenic volatile organic compound (BVOC) precursors for polar organosulfates with molecular weights (MWs) 230 and 214, which are also present in ambient fine aerosol from a forested site, i.e., K-puszta, Hungary. These results complement those obtained in a previous study showing that the green leaf aldehyde 3-Z-hexenal serves as a precursor for MW 226 organosulfates. Thus, in addition to isoprene, the green leaf volatiles (GLVs) 2-E-hexenal and 3-Z-hexenal, emitted due to plant stress (mechanical wounding or insect attack), and 2-E-pentenal, a photolysis product of 3-Z-hexenal, should be taken into account for secondary organic aerosol and organosulfate formation. Polar organosulfates are of climatic relevance because of their hydrophilic properties and cloud effects. Extensive use was made of organic mass spectrometry (MS) and detailed interpretation of MS data (i.e., ion trap MS and accurate mass measurements) to elucidate the chemical structures of the MW 230, 214 and 170 organosulfates formed from 2-E-pentenal and indirectly from 2-E-hexenal and 3-Z-hexenal. In addition, quantum chemical calculations were performed to explain the different mass spectral behavior of 2,3-dihydroxypentanoic acid sulfate derivatives, where only the isomer with the sulfate group at C-3 results in the loss of SO3. The MW 214 organosulfates formed from 2-E-pentenal are explained by epoxidation of the double bond in the gas phase and sulfation of the epoxy group with sulfuric acid in the particle phase through the same pathway as that proposed for 3-sulfooxy-2-hydroxy-2-methylpropanoic acid from the isoprene-related α,β-unsaturated aldehyde methacrolein in previous work (Lin et al., 2013). The MW 230 organosulfates formed from 2-E-pentenal are tentatively explained by a novel pathway, which bears features of the latter pathway but introduces an additional hydroxyl group at the C-4 position. Evidence is also presented that the MW 214 positional isomer, 2-sulfooxy-3-hydroxypentanoic acid, is unstable and decarboxylates, giving rise to 1-sulfooxy-2-hydroxybutane, a MW 170 organosulfate. Furthermore, evidence is obtained that lactic acid sulfate is generated from 2-E-pentenal. This chemistry could be important on a regional and local scale where GLV emissions such as from grasses and cereal crops are substantial.

A uniform derivation is presented of the self-consistent field equations in a finite basis set. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed in the presence of linear dependencies in the basis set. It is argued why iterative diagonalization of the Kohn-Sham-Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are also briefly discussed. Explicit expressions are given for the contributions to the Kohn-Sham-Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are also briefly discussed.

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