Congruence criteria for finite subsets of complex projective and complex hyperbolic spaces

We investigate congruence classes and direct congruence classes of m-tuples in the complex projective space ℂP ⁿ . For direct congruence one allows only isometries which are induced by linear (instead of semilinear) mappings. We establish a canonical bijection between the set of direct congruence classes of m-tuples of points in ℂP ⁿ and the set of equivalence classes of positive semidefinite Hermitean m×m-matrices of rank at most n+1 with 1's on the diagonal. As a corollary we get that the direct congruence class of an m-tuple is uniquely determined by the direct congruence classes of all of its triangles, provided that no pair of points of the m-tuple has distance π/2. Examples show that the situation changes drastically if one replaces direct congruence classes by congruence classes or if distances π/2 are allowed. Finally we do the same kind of investigation also for the complex hyperbolic space ℂH ⁿ . Most of the results are completely analogous, however, there are also some interesting differences. Received: 15 January 1996     

The shape invariant of triangles and trigonometry in two-point homogeneous spaces

We define a fourth basic invariant, which, besides the lengths of the three sides of a triangle, determines a triangle in the complex and quaternion projective spaces P ⁿ and P ⁿ (n2) uniquely up to isometry. We give inequalities describing the exact range of the four basic invariants. We express the angular invariants of a triangle with our basic invariants, giving a new completely elementary proof of the laws of trigonometry. As a corollary we derive a large number of congruence theorems. Finally we get, in exactly the same way, the corresponding results for triangles in the complex and quaternion hyperbolic spaces H ⁿ and H ⁿ (n2).     

Binding N2, N2H2, N2H4, and NH3 to transition-metal sulfur sites: modeling potential intermediates of biological N2 fixation

In the quest for low-molecular-weight metal sulfur complexes that bind nitrogenase-relevant small molecules and can serve as model complexes for nitrogenase, compounds with the [Ru(PiPr(3))('N(2)Me(2)S(2)')] fragment were found ('N(2)Me(2)S(2)'(2-)=1,2-ethanediamine-N,N'-dimethyl-N,N'-bis(2-benzenethiolate)(2-)). This fragment enabled the synthesis of a first series of chiral metal sulfur complexes, [Ru(L)(PiPr(3))('N(2)Me(2)S(2)')] with L=N(2), N(2)H(2), N(2)H(4), and NH(3), that meet the biological constraint of forming under mild conditions. The reaction of [Ru(NCCH(3))(PiPr(3))('N(2)Me(2)S(2)')] (1) with NH(3) gave the ammonia complex [Ru(NH(3))(PiPr(3))('N(2)Me(2)S(2)')] (4), which readily exchanged NH(3) for N(2) to yield the mononuclear dinitrogen complex [Ru(N(2))(PiPr(3))('N(2)Me(2)S(2)')] (2) in almost quantitative yield. Complex 2, obtained by this new efficient synthesis, was the starting material for the synthesis of dinuclear (R,R)- and (S,S)-[micro-N(2)[Ru(PiPr(3))('N(2)Me(2)S(2)')](2)] ((R,R)-/(S,S)-3). (Both 2 and 3 have been reported previously.) The as-yet inexplicable behavior of complex 3 to form also the R,S isomer in solution has been revealed by DFT calculations and (2)D NMR spectroscopy studies. The reaction of 1 or 2 with anhydrous hydrazine yielded the hydrazine complex [Ru(N(2)H(4))(PiPr(3))('N(2)Me(2)S(2)')] (6), which is a highly reactive intermediate. Disproportionation of 6 resulted in the formation of mononuclear diazene complexes, the ammonia complex 4, and finally the dinuclear diazene complex [micro-N(2)H(2)[Ru(PiPr(3))('N(2)Me(2)S(2)')](2)] (5). Dinuclear complex 5 could also be obtained directly in an independent synthesis from 1 and N(2)H(2), which was generated in situ by acidolysis of K(2)N(2)(CO(2))(2). Treatment of 6 with CH(2)Cl(2), however, formed a chloromethylated diazene species [[Ru(PiPr(3))('N(2)Me(2)S(2)')]-micro-N(2)H(2)[Ru(Cl)('N(2)Me(2)S(2)CH(2)Cl')]] (9) ('N(2)Me(2)S(2)CH(2)Cl'(2-) =1,2-ethanediamine-N,N'-dimethyl-N-(2-benzenethiolate)(1-)-N'-(2-benzenechloromethylthioether)(1-)]. The molecular structures of 4, 5, and 9 were determined by X-ray crystal structure analysis, and the labile N(2)H(4) complex 6 was characterized by NMR spectroscopy.     

Highly oriented self-assembled monolayers as templates for epitaxial calcite growth

The lateral alignment of [012] habit-modified calcite crystals with respect to a carboxylic acid terminated self-assembled monolayer (SAM) of thiols has been determined. The crystals were grown from a Kitano solution (pH 5.6-6.0), and the samples were investigated with scanning electron microscopy, X-ray diffraction, and polarization microscopy. For the first time, a lattice match in one direction, which is the nearest neighbor direction of the SAM and the calcite <100> direction, has been experimentally shown. The experimental results are in good agreement with the theoretical models proposed in previous work, and it is expected that this method can be applied to similar systems where inorganic crystals nucleate with a preferred orientation to a SAM.     

RESONANCE-ENHANCED CARS SPECTROSCOPY OF BILIPROTEINS. INFLUENCE OF AGGREGATION and LINKER PROTEINS ON CHROMOPHORE STRUCTURE IN ALLOPHYCOCYANIN (Mastigocladus laminosus)

Abstract— Resonance-enhanced coherent anti-Stokes Raman spectra (CARS) are reported for monomers and for trimers with and without linker proteins of allophycocyanin isolated from Mastigocladus laminosus. The CARS spectrum of the monomer is independent of the presence of linker proteins and is very similar to that of phycocyanin monomers indicating that the equivalent chromophores exhibit like structures in both biliproteins. Large differences are, however, observed between the spectra of phycocyanin trimers and those of allophycocyanin trimers with or without linker proteins (L_c^8,9). The observed differences between monomer and trimer spectra are consistent with a change of the α-chromophore-protein arrangement upon aggregation without linker. If linker proteins are present in the trimer, then additional geometry changes of the β-chromophores are induced; these could relate to a transition from the 15Z- anti to 15Z- syn conformation.     

A stereochemical anomaly: the cyclised (R)-AMPA analogue (R)-3-hydroxy-4,5,6,7-tetrahydroisoxazolo[5,4-c]pyridine-5-carboxylic acid [(R)-5-HPCA] resembles (S)-AMPA at glutamate receptors

(RS)-3-Hydroxy-4,5,6,7-tetrahydroisoxazolo[5,4-c]pyridine-5-carboxylic acid (5-HPCA)(), which is a conformationally constrained cyclised analogue of AMPA has previously been described as causing glutamate receptor mediated excitations of spontaneously firing cat spinal interneurons in a similar fashion to AMPA. We have now prepared the enantiomers of through chiral chromatographic resolution of (RS)-3-(carboxymethoxy)-4,5,6,7-tetrahydroisoxazolo[5,4-c]pyridine-5-carboxylic acid () followed by a stereoconservative hydrolysis resulting in the enantiomers of with high enantiomeric excess (% ee [greater-than-or-equal] 99). The absolute configurations indicated by an X-ray analysis of (-)- monohydrate were confirmed by comparing observed and ab initio calculated electronic circular dichroism spectra and by stereoconservative synthesis of (S)- from (S)-AMPA, the pharmacologically active form of AMPA. The pharmacological effects at native and cloned (GluR1-4) AMPA receptors were shown to reside exclusively with (R)-(+)-, in striking contrast to the usual stereoselectivity trend among AMPA receptor agonists. The reasons for this anomalous behaviour became clear upon docking both enantiomers of to the agonist binding site of GluR2.     

Quantitative determination of toluene,ethylbenzene, and xylene degradation products in contaminated groundwater by solid-phase extraction and in-vial derivatization

Benzylsuccinic acid (BSA) and methylbenzylsuccinic acids (mBSAs) are unambiguous indicators of anaerobic toluene and ethylbenzene/xylene degradation, and so the determination of these compounds in landfill leachates and contaminated groundwater is highly relevant. Samples were diluted to <0.8?mS?cm^?1 in order to reduce their ionic strength, and subsequently extracted through strong anion exchange disks, followed by simultaneous in-vial elution and methylation. A detection limit of 0.1?µg?L^?1 was obtained for 100?mL samples. Using this method, 19.3?µg?L^?1 of BSA was measured in a landfill leachate, and low µg?L^?1 levels of all of the mBSAs were measured in gasoline-contaminated groundwater. The results were compared with the findings of BSAs at 16 other contaminated sites, and BSAs as indicators of biodegradation were evaluated. The estimation of biodegradation rates based on parent hydrocarbons and BSA concentrations or ratios is questionable. However, the degradation products serve as good qualitative in situ indicators for anaerobic biodegradation in contaminated groundwater.     

Raman Optical Activity of N-Acetyl-L-Cysteine in Water and in Methanol: The “Clusters-in-a-Liquid” Model and ab Initio Molecular Dynamics Simulations

Raman and Raman Optical Activity (ROA) spectra of N-acetyl-L-cysteine (NALC), a flexible chiral molecule, were measured in water and in methanol to evaluate the solvent effects. Two different solvation approaches, that is, the DFT based “clusters-in-a-liquid” solvent model and the ab initio molecular dynamics (AIMD) simulations, were applied to simulate the Raman and ROA spectra. Systematic conformational searches were carried out using a recently developed conformational searching tool, CREST, with the inclusion of polarizable continuum model of water and of methanol. The CREST candidates of NALC and the NALC-solvent complexes were re-optimized and their Raman and ROA simulations were done at the B3LYP−D3BJ/def2-TZVP and the B3LYP-aug-cc-pVDZ//cc-pVTZ levels. Also, AIMD simulations, which includes some anharmonic effects and all intermolecular interactions in solution, were performed. By empirically weighting the computed Raman and ROA spectra of each conformer, good agreements with the experimental data were achieved with both approaches, while AIMD offered some improvements in the carbonyl and in the low wavenumber regions over the static DFT approach. The pros and cons of these two different approaches for accounting the solvent effects on Raman and ROA of this flexible chiral system will also be discussed.