On the calculation of multiplicities for representations of SU(n)

For some family of representations of SU(n) the explicit formulae for the multiplicity of a given representation in arbitrary tensor product are derived. The adjoint representation and the representations acting in the symmetrical and antisymmetrical tensors are contained in the considered family as the simplest cases.     

The generalization of SU(3)-mass formulae for arbitrary reductive lie algebras

The analogues of Gell-Mann-Okubo and Coleman-Glashow mass formulae are derived for arbitrary reductive Lie algebras.     

Metal ion binding by a bicyclic diamide: deep UV Raman spectroscopic characterization

Deep UV resonance Raman spectroscopy was used for characterizing ligand-metal ion complexes. The obtained results demonstrated a strong intrinsic sensitivity and selectivity of a Raman spectroscopic signature of a bicyclic diamide, a novel chelating agent for lanthanides and actinides (Lumetta, G. J.; Rapko, B. M.; Garza, P. A.; Hay, B. P.; Gilbertson, R. D.; Weakley, T. J. R.; Hutchison, J. E. J. Am. Chem. Soc. 2002, 124, 5644). Molecular modeling, which included structure optimization and calculation of Raman frequencies and resonance intensities, allowed for assigning all strong Raman bands of the bicyclic diamide as well as predicting the band shifts observed because of complex formation with metal ions. A comparative analysis of Raman spectra and the results of the molecular modeling could be used for elucidating the structure of complexes in solution.     

Modified synthesis of Ru–Rh heterobimetallic metallacarboranes based on ruthenium exo-nido complexes and not accompanied by exo-nido → closo rearrangement

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Monitoring of ethanol during fermentation using a microbial biosensor with enhanced selectivity

The present study is concerning the construction of ferricyanide-mediated Gluconobacter oxydans cell ethanol biosensor. The size exclusion effect of a cellulose acetate membrane was used for elimination of glucose interferences during ethanol assays in real samples. A typical response time of the biosensor was 13 s with a high sensitivity of 3.5 microA mM(-1). The microbial biosensor exhibits a very low detection limit of 0.85 microM and a wide linear range from 2 to 270 microM. The operational stability was excellent. During 8.5 h of repetitive ethanol assays, no decrease in the sensor sensitivity was observed. The biosensor was successfully used in the off-line monitoring of ethanol fermentation with a good agreement with HPLC measurements (R(2)=0.998).     

Synthesis and structural characterization of two novel heterometallic clusters: [Rh4Pt2(CO)11(dppm)2] and [Ru2Rh2Pt2(CO)12(dppm)2

Two novel heterometallic octahedral clusters [Rh(4)Pt(2)(CO)(11)(dppm)(2)](1) and [Ru(2)Rh(2)Pt(2)(CO)(12)(dppm)(2)](2) were synthesized by the reaction of [Rh(2)Pt(2)(CO)(6)(dppm)(2)] with [Rh(6)(CO)(14)(NCMe)(2)] and Ru(3)(CO)(12), respectively. Solid state structures of 1 and 2 have been established by a single crystal X-ray diffraction study. Two dppm ligands in 1 are bonded to one platinum and three rhodium atoms, which form an equatorial plane of the Rh(4)Pt(2) octahedron. Two rhodium and two platinum atoms bound to the diphosphine ligands in 2 are nonplanar to give an octahedral C2 symmetric Ru(2)Rh(2)Pt(2)(dppm)2 framework. The (31)P NMR investigation of and (1D, (31)P COSY, (31)P-[(103)Rh] HMQC) and simulation of 1D spectral patterns showed that in both clusters the structures of the M(6)(PP)(2) fragments found in the solid state are maintained in solution.     

Synthesis of unstrained Criegee intermediates: inverse α-effect and other protective stereoelectronic forces can stop Baeyer–Villiger rearrangement of γ-hydroperoxy-γ-peroxylactones

How far can we push the limits in removing stereoelectronic protection from an unstable intermediate? We address this question by exploring the interplay between the primary and secondary stereoelectronic effects in the Baeyer–Villiger (BV) rearrangement by experimental and computational studies of γ-OR-substituted γ-peroxylactones, the previously elusive non-strained Criegee intermediates (CI). These new cyclic peroxides were synthesized by the peroxidation of γ-ketoesters followed by in situ cyclization using a BF₃·Et₂O/H₂O₂ system. Although the primary effect (alignment of the migrating C–R_m bond with the breaking O–O bond) is active in the 6-membered ring, weakening of the secondary effect (donation from the OR lone pair to the breaking C–R_m bond) provides sufficient kinetic stabilization to allow the formation and isolation of stable γ-hydroperoxy-γ-peroxylactones with a methyl-substituent in the C6-position. Furthermore, supplementary protection is also provided by reactant stabilization originating from two new stereoelectronic factors, both identified and quantified for the first time in the present work. First, an unexpected boat preference in the γ-hydroperoxy-γ-peroxylactones weakens the primary stereoelectronic effects and introduces a ∼2 kcal mol⁻¹ Curtin–Hammett penalty for reacquiring the more reactive chair conformation. Second, activation of the secondary stereoelectronic effect in the TS comes with a ∼2–3 kcal mol⁻¹ penalty for giving up the exo-anomeric stabilization in the 6-membered Criegee intermediate. Together, the three new stereoelectronic factors (inverse α-effect, misalignment of reacting bonds in the boat conformation, and the exo-anomeric effect) illustrate the richness of stereoelectronic patterns in peroxide chemistry and provide experimentally significant kinetic stabilization to this new class of bisperoxides. Furthermore, mild reduction of γ-hydroperoxy-γ-peroxylactone with Ph₃P produced an isolable γ-hydroxy-γ-peroxylactone, the first example of a structurally unencumbered CI where neither the primary nor the secondary stereoelectronic effect are impeded. Although this compound is relatively unstable, it does not undergo the BV reaction and instead follows a new mode of reactivity for the CI – a ring-opening process.

Protecting stereoelectronic effects prevent Baeyer–Villiger rearrangement and stabilize γ-OX-γ-peroxylactones (X = H, OH), the previously elusive non-strained Criegee intermediates.     

Hydrogermylation of phenylacetylene catalyzed by onium chlorometallates

Triethylbenzylammonium chlorometallates [Et₃NCH₂Ph][MCl_n]^m? (M = Pt, Pd, Rh, Ir, Fe, Co, Cu, m = 1–3, n = 3–6), polymer-anchored ionic metal complexes [?—CH₂PBu₃][MCl_n]^n? and some other chlorometallates and complexes of platinum, rhodium, ruthenium and osmium were studied as catalysts in the hydrogermylation of phenylacetylene with triethylgermane. All the complexes containing platinum, palladium and rhodium were found to be effective catalysts. The cis/trans ratio of the products obtained is determined by the metal atom involved and decreases in the following order: Ir > Rh ? Pd > Pt.     

Synthesis of Tetrafluoromethane by Graphite Fluorination with Elemental Fluorine

Formation of high-temperature inverse wave of the filtration combustion of graphite fixed bed in fluorine was studied. Scientific principles of the industrial process of the tetrafluoromethane synthesis from graphite and fluorine were developed.     

Stimulated Raman scattering measurements of H2 vibration–vibration transfer

We present a new set of V–V rate coefficients for vibrational levels 0–5 in H₂ at 300 K, measured using a stimulated Raman–spontaneous Raman pump/probe apparatus. The measured rate of the non-resonant process, H₂(v = 1) + H₂(v = 1) → H₂(v = 0) + H₂(v = 2), is consistent with the previously reported experimental value of Kreutz et al. However, semi-classical predictions of such non-resonant processes, using the identical inter-molecular potential and methodology to that given by Cacciatore and Billing, results in rates which are too slow, by a factor of approximately 3. For the “resonant” V–V process, H₂(v = 1) + H₂(v = 0) → H₂(v = 0) + H₂(v = 1), the semi-classical rate is found to be too slow by an even larger factor, of approximately 30, compared to the experimental rate, but consistent with the previously reported experimental result of Farrow and Chandler. Further, unlike the semi-classical model prediction in which the (1, 1 → 2, 0) process rate is predicted to exceed that of the (1, 0 → 0, 1) process, the experimental data shows it to be a factor of approximately 2.5 less, suggesting that semi-classical methods that treat the rotational motion classically are unsuitable for the highly anharmonic H₂ molecule. The ratio of pure rotation and rotation–vibration Raman cross sections for scattering from levels 0 and 1 is also determined, with results which agree with calculations of Schwartz and LeRoy, but are somewhat larger than previous experimental results of Cureton.