Relaxation of (111) silicon surface atoms from studies of Si4H9 clusters

Self-consistent Hartree-Fock and generalized valence bond calculations have been performed on clusters modeling the (111) silicon surface. We find that the surface state is accurately described as a dangling bond surface orbital with 93% p character. We determined the optimum relaxation of the surface layer to be 0.08 Å toward the second layer. In the positive ion, the surface atom relaxes toward the second layer by an additional 0.30 Å and for the negative ion the surface atom moves toward the vacuum 0.25 Å. The vertical ionization potential was found to be 5.78 eV (experimental values are 5.6 – 5.9 eV) while the calculated adiabatic electron affinity is 3.02 eV.     

The neutral vacancy in silicon and diamond: Generalized valence bond studies

Self-consistent ab initio generalized valence bond and configuration interaction calculations are presented for molecular cluster models of the electronic states of the neutral vacancy in diamond and silicon. In each case the ground state of the vacancy is found to be ¹E (T_d designation) with the ³T₁ and ⁵A₂ states slightly higher (0.18 eV and 0.60 eV for Si and 0.33 eV and 1.2 eV for C). The first excited singlest state is ¹T₂ in each case. The ¹E-¹T₂ excitation energy is foundto be 1.7 ± 0.7 eV for diamond and 1.3 ± 0.5 eV in silicon, the range being due to uncertainty in the model used for estimating the polarization effects due to the remainder of the infinite crystal.     

Relaxation of (111) silicon surface atoms from studies of Si4H9 clusters

Self-consistent Hartree-Fock and generalized valence bond calculations have been performed on clusters modeling the (111) silicon surface. We find that the surface state is accurately described as a dangling bond surface orbital with 93% p character. We determined the optimum relaxation of the surface layer to be 0.08 Å toward the second layer. In the positive ion, the surface atom relaxes toward the second layer by an additional 0.30 Å, and for the negative ion the surface atom moves toward the vacuum 0.25 Å. The vertical ionization potential was found to be 5.78 eV (experimental values are 5.6 – 5.9 eV) while the calculated adiabatic electron affinity is 3.02 eV.     

Characterization of organosulfates from the photooxidation of isoprene and unsaturated fatty acids in ambient aerosol using liquid chromatography/(-) electrospray ionization mass spectrometry

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.     

Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

Organosulfate formation in biogenic secondary organic aerosol

Organosulfates of isoprene, alpha-pinene, and beta-pinene have recently been identified in both laboratory-generated and ambient secondary organic aerosol (SOA). In this study, the mechanism and ubiquity of organosulfate formation in biogenic SOA is investigated by a comprehensive series of laboratory photooxidation (i.e., OH-initiated oxidation) and nighttime oxidation (i.e., NO3-initiated oxidation under dark conditions) experiments using nine monoterpenes (alpha-pinene, beta-pinene, d-limonene, l-limonene, alpha-terpinene, gamma-terpinene, terpinolene, Delta(3)-carene, and beta-phellandrene) and three monoterpenes (alpha-pinene, d-limonene, and l-limonene), respectively. Organosulfates were characterized using liquid chromatographic techniques coupled to electrospray ionization combined with both linear ion trap and high-resolution time-of-flight mass spectrometry. Organosulfates are formed only when monoterpenes are oxidized in the presence of acidified sulfate seed aerosol, a result consistent with prior work. Archived laboratory-generated isoprene SOA and ambient filter samples collected from the southeastern U.S. were reexamined for organosulfates. By comparing the tandem mass spectrometric and accurate mass measurements collected for both the laboratory-generated and ambient aerosol, previously uncharacterized ambient organic aerosol components are found to be organosulfates of isoprene, alpha-pinene, beta-pinene, and limonene-like monoterpenes (e.g., myrcene), demonstrating the ubiquity of organosulfate formation in ambient SOA. Several of the organosulfates of isoprene and of the monoterpenes characterized in this study are ambient tracer compounds for the occurrence of biogenic SOA formation under acidic conditions. Furthermore, the nighttime oxidation experiments conducted under highly acidic conditions reveal a viable mechanism for the formation of previously identified nitrooxy organosulfates found in ambient nighttime aerosol samples. We estimate that the organosulfate contribution to the total organic mass fraction of ambient aerosol collected from K-puszta, Hungary, a field site with a similar organosulfate composition as that found in the present study for the southeastern U.S., can be as high as 30%.     

Characterization of 2-methylglyceric acid oligomers in secondary organic aerosol formed from the photooxidation of isoprene using trimethylsilylation and gas chromatography/ion trap mass spectrometry

In the present work, we have characterized in detail the chemical structures of secondary organic aerosol (SOA) components that were generated in a smog chamber and result from the photooxidation of isoprene under high-NO(x) conditions typical for a polluted atmosphere. Isoprene high-NO(x) SOA contains 2-methylglyceric acid (2-MG) and oligoester derivatives thereof. Trimethylsilylation, in combination with capillary gas chromatography (GC)/ion trap mass spectrometry (MS) and detailed interpretation of the MS data, allowed structural characterization the polar oxygenated compounds present in isoprene SOA up to 2-MG trimers. GC separation was achieved between 2-MG linear and branched dimers or trimers, as well as between the 2-MG linear dimer and isomeric mono-acetate derivatives thereof. The electron ionization (EI) spectra of the trimethylsilyl derivatives contain a wealth of structural information, including information about the molecular weight (MW), oligoester linkages, terminal carboxylic and hydroxymethyl groups, and esterification sites. Only part of this information can be achieved with a soft ionization technique such as electrospray (ESI) in combination with collision-induced dissociation (CID). The methane chemical ionization (CI) data were used to obtain supporting MW information. Interesting EI spectral differences were observed between the trimethylsilyl derivatives of 2-MG linear and branched dimers or trimers and between 2-MG linear dimer mono-acetate isomers.