Total cross sections and logarithmic slopes of the elastic scattering cross sections for different hadronic processes are calculated in the framework of the model of the stochastic vacuum. The relevant parameters of this model, a correlation length and the gluon condensate, are determined from scattering data, and found to be in very good agreement with values coming from completely different sources of information. A parameter-free relation is given between total cross sections and slope parameters, which is shown to be remarkably valid up to the highest energies for which data exist.PACS number(s): 12.38.Lg. 13.85.Dz, 13.85.Lg @(a. w) = P exp -ig d a ( X -w),[ l1J P denotes path ordering, which is necessary in order togive to the exponential a well-defined meaning. In a nonperturbative way, this ordering is defined, for any operator 0 throughwith 0 < a1 < a 2 . . . < 1, Auk = C T~+~ -uk .The field strength tensor in Eq. (7) transforms with

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The photooxidizing capabilities of selected Cr(III) complexes for promoting radical cation cycloadditions are described. These complexes have sufficiently long-lived excited states to oxidize electron-rich alkenes, thereby initiating [4+2] processes. These metal species augment the spectrum of catalysts explored in photoredox systems, as they feature unique properties that can result in differential reactivity from the more commonly employed ruthenium or iridium catalysts.

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Additional References:Footnote 16: Sparteine has been used as a ligand for palladium-catalyzed allylic substitution reactions and olefin polymerization reactions. (a) Trost, B. M.; Dietsch, T. J. J. Amer. Chem. Soc. 1973, 95, 8200. (b) 2000, 33, 715.Material and Methods. Unless stated otherwise, reactions were performed in flame-dried glassware under a nitrogen or an argon atmosphere, using freshly distilled solvents. All other commercially obtained reagents were used as received. Reaction temperatures were controlled by an IKAmag temperature modulator. Thin-layer chromatography (TLC) was performed using E. Merck silica gel 60 F254 precoated plates (0.25 mm). ICN Silica gel (particle size 0.032-0.063 mm) was used for flash chromatography.Analytical chiral HPLC was performed on a Chiralcel OJ, AS, or OD-H column (each is 4.6 mm x 25 cm) obtained from Daicel Chemical Industries, Ltd. Analytical achiral GC was performed using an Agilent DB-WAX (30.0 m x 0.25 m) column. Analytical chiral GC was carried out using a Chiraldex B-DM column (30.0 m x 0.25 mm) purchased from Bodman Industries. Commercially available racemic alcohols in Table 3 (entries 1, 2, 3, 5, 7, 8, and 9) were purchased from the Sigma-Aldrich Chemical Company, Milwaukee, WI. Non-commercially available racemic alcohols used in Table 3 (corresponding to entries 4, 6, and 10) were prepared as previously described. 1 Commercially available samples of enantiopure alcohols for analytical comparison purposes (entries 1, 4, 7, 8, and 9) were purchased from the SigmaAldrich Chemical Company, Milwaukee, WI. Non-commercially available enantiopure alcohols prepared 1 (a) Ruble, J. C.; Latham, H. A.; Fu, G. C.

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Using a unified analytic representation for the elastic scattering amplitudes of pp scattering valid for all energies above 20 GeV, the behavior of observables in the LHC collisions in the range √ s = 2.76-14 TeV is discussed. After the precise description of dσ/dt at 7 TeV, we discuss the energy dependence of the amplitudes and expect that the proposed analytical forms give equally good predictions for the future experiments.

A combined experimental and theoretical investigation aims to elucidate the necessary roles of oxygen in photoredox catalysis of radical cation based Diels-Alder cycloadditions mediated by the first-row transition metal complex [Cr(Ph2phen)3](3+), where Ph2phen = bathophenanthroline. We employ a diverse array of techniques, including catalysis screening, electrochemistry, time-resolved spectroscopy, and computational analyses of reaction thermodynamics. Our key finding is that oxygen acts as a renewable energy and electron shuttle following photoexcitation of the Cr(III) catalyst. First, oxygen quenches the excited Cr(3+)* complex; this energy transfer process protects the catalyst from decomposition while preserving a synthetically useful 13 μs excited state and produces singlet oxygen. Second, singlet oxygen returns the reduced catalyst to the Cr(III) ground state, forming superoxide. Third, the superoxide species reduces the Diels-Alder cycloadduct radical cation to the final product and reforms oxygen. We compare the results of these studies with those from cycloadditions mediated by related Ru(II)-containing complexes and find that the distinct reaction pathways are likely part of a unified mechanistic framework where the photophysical and photochemical properties of the catalyst species lead to oxygen-mediated photocatalysis for the Cr-containing complex but radical chain initiation for the Ru congener. These results provide insight into how oxygen can participate as a sustainable reagent in photocatalysis.