Linear Independence of q-Analogues of Certain Classical Constants

Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σ_n≥1 a_n/(qⁿ ? 1) ? K for non-zero periodic sequences (a_n) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82     

Synthesis and coordinating ability of an anionic cobaltabisdicarbollide ligand geometrically analogous to BINAP

The anionic chelating ligand [1,1'-(PPh2)2-3,3'-Co(1,2-C2B9H10)2]- has been synthesized from [3,3'-Co(1,2-C2B9H11)2]- in very good yield in a one-pot process with an easy work-up procedure. The coordinating ability of this ligand has been studied with Group 11 metal ions (Ag, Au) and with transition-metal ions (Pd, Rh). The two dicarbollide halves of the [1,1'-(PPh2)2-3,3'-Co(1,2-C2B9H10)2]- ligand can swing about one axis in a manner analogous to the constituent parts of BINAP and ferrocenyl phosphine derivatives. All these ligands function as hinges, with the most important property in relation to the coordination requirements of the metal being the PP distance. [1,1'-(PPh2)2-3,3'-Co(1,2-C2B9H10)2]-, BINAP, ferrocenyl phosphine derivatives, and other hinge ligands present a range of different PP separations, and consequently different coordination spheres and dispositions around metal cations. To account for these differences, the equation Dphi2 = D02 + 4 R2cos2(90-phi/2) has been developed. It relates the PP distance (Dphi) in a complex with the minimum PP distance (D0) that is characteristic of the hinge-type ligand.     

Formation of bridging alkene and conjugated dialkenes exclusively generated from alkynes on the [3,3'-Co(1,2-C2B9H11)2]- platform. The unique hydroboration role of [3,3'-Co(1,2-C2B9H11)2]-

The unprecedented metal-mediated transformation of an alkyne into a B,B' bridging alkene is reported. Also, the unprecedented synthesis of a conjugated dialkene derivative of [3,3'-Co(1,2-C2B9H11)2]- generated only from an alkyne, contrary to the usual case where an alkyne and an alkene are needed, is described. This has been possible through the singular capacity of a B-H to produce hydroboration.     

X-ray crystal structures of [XF(6)][Sb(2)F(11)] (X = Cl, Br, I); (35,37)Cl, (79,81)Br, and (127)I NMR studies and electronic structure calculations of the XF(6)(+) cations

The single-crystal X-ray structures of [XF(6)][Sb(2)F(11)] (X = Cl, Br, I) have been determined and represent the first detailed crystallographic study of salts containing the XF(6)(+) cations. The three salts are isomorphous and crystallize in the monoclinic space group P2(1)/n with Z = 4: [ClF(6)][Sb(2)F(11)], a = 11.824(2) A, b = 8.434(2) A, c = 12.088(2) A, beta = 97.783(6) degrees , V = 1194.3(4) A(3), R(1) = 0.0488 at -130 degrees C; [BrF(6)][Sb(2)F(11)], a = 11.931(2) A, b = 8.492(2) A, c = 12.103(2) A, beta = 97.558(4) degrees , V = 1215.5(4) A(3), R(1) = 0.0707 at -130 degrees C; [IF(6)][Sb(2)F(11)], a = 11.844(1) A, b = 8.617(1) A, c = 11.979(2) A, beta = 98.915(2) degrees , V = 1207.8(3) A(3), R(1) = 0.0219 at -173 degrees C. The crystal structure of [IF(6)][Sb(2)F(11)] was also determined at -100 degrees C and was found to crystallize in the monoclinic space group P2(1)/m with Z = 4, a = 11.885(1) A, b = 8.626(1) A, c = 12.000(1) A, beta = 98.44(1), V = 1216.9(2) A(3), R(1) = 0.0635. The XF(6)(+) cations have octahedral geometries with average Cl-F, Br-F, and I-F bond lengths of 1.550(4), 1.666(11) and 1.779(6) [-173 degrees C]/1.774(8) [-100 degrees C] A, respectively. The chemical shifts of the central quadrupolar nuclei, (35,37)Cl, (79,81)Br, and (127)I, were determined for [ClF(6)][AsF(6)] (814 ppm), [BrF(6)][AsF(6)] (2080 ppm), and [IF(6)][Sb(3)F(16)] (3381 ppm) in anhydrous HF solution at 27 degrees C, and spin-inversion-recovery experiments were used to determine the T(1)-relaxation times of (35)Cl (1.32(3) s), (37)Cl (2.58(6) s), (79)Br (24.6(4) ms), (81)Br (35.4(5) ms), and (127)I (6.53(1) ms). Trends among the central halogen chemical shifts and T(1)-relaxation times of XF(6)(+), XO(4)(-), and X(-) are discussed. The isotropic (1)J-coupling constants and reduced coupling constants for the XF(6)(+) cations and isoelectronic hexafluoro species of rows 3-6 are empirically assessed in terms of the relative contributions of the Fermi-contact, spin-dipolar, and spin-orbit mechanisms. Electronic structure calculations using Hartree-Fock, MP2, and local density functional methods were used to determine the energy-minimized gas-phase geometries, atomic charges, and Mayer bond orders of the XF(6)(+) cations. The calculated vibrational frequencies are in accord with the previously published assignments and experimental vibrational frequencies of the XF(6)(+) cations. Bonding trends within the XF(6)(+) cation series have been discussed in terms of natural bond orbital (NBO) analyses, the ligand close-packed (LCP) model, and the electron localization function (ELF).     

Synthesis and stereochemical studies of 1- and 2-phenyl-substituted 1,3-oxazino[4,3-a]isoquinoline derivatives

Starting from the 1′- or 2′-phenyl-substituted 1-(2′-hydroxyethyl)-6,7-dimethoxy-1,2,3,4-tetrahydroisoquinoline diastereomers 3 and 6, 4-unsubstituted and 4-(p-nitrophenyl)- and 4-oxo-substituted 1-phenyl- and 2-phenyl-9,10-dimethoxy-2H,4H-1,6,7,11b-tetrahydro-1,3-oxazino[4,3-a]isoquinolines (7-12) were prepared. The relative configurations and the predominant conformations of the products were determined by NMR spectroscopy, by quantum chemical calculations and, for (2R^∗,4S^∗,11bR^∗)-9,10-dimethoxy-4-(p-nitrophenyl)-2-phenyl-2H,4H-1,6,7,11b-tetrahydro-1,3-oxazino[4,3-a]isoquinoline (11), by X-ray diffraction.     

Computational studies of the cationic aluminium(chloro) hydroxides by quantum chemical ab initio methods

Cationic aluminium(chloro) hydroxide complexes with two to four aluminium atoms were studied using quantum chemical methods. Complexes were studied in both gas and liquid phase. The liquid environment was modeled by using a conductor-like screening model (COSMO). COSMO calculations were carried out as a single point calculation at the optimized gas phase structures. Water (epsilon = 78.54) was used as the solvent. The minimum energy structures obtained from the gas phase studies were mostly compact cyclic structures. Aluminium preferred to be five-coordinated in oxygen rich clusters. Core oxygen preferred three-fold coordination but in the largest clusters the four-coordinated oxygen was observed. Water reacted dissociatively with hydrogen poor clusters. The COSMO calculations showed that the optimal structures of cationic aluminium(chloro) hydroxides tend to be more open in the liquid than in the gas phase.     

Diferratricarbaboranes of the subcloso-[(eta5-C5H5)2Fe2C3B8H11] type, the first representatives of the 13-vertex dimetallatricarbaborane series

Treatment of the [2-Cp-9-tBuNH-closo-2,1,7,9-FeC(3)B(8)H(10)] (1) ferratricarbollide (Cp = eta(5)-C(5)H(5) (-)) with Na(+) C(10)H(8) (-) in 1,2-dimethoxyethane (DME) at room temperature produced an air-sensitive transient anion with a tentatively identified nido-[tBuNH-CpFeC(3)B(8)H(10)](2-) constitution. In-situ reaction of this low-stability ion with [CpFe(CO)(2)I] or [CpFe(CO)(2)](2) generated three violet diferratricarbaboranes identified as paramagnetic subcloso complexes [4,5-Cp(2-)-4,5,1,6,7-Fe(2)C(3)B(8)H(11)] (2; yield 2 %), [4,5-Cp(2-)-4,5,1,7,12-Fe(2)C(3)B(8)H(11)] (3; yield 2 %), and [7-tBuNH-4,5-Cp(2-)-4,5,1,7,12-Fe(2)C(3)B(8)H(10)] (4; yield 14 %). These first representatives of the 13-vertex dimetallatricarbaborane family were characterized by EPR and IR spectroscopy, and mass spectrometry, and their structures were determined by X-ray diffraction analysis.     

Proton double quantum coherence and cross-relaxation in (NH4)2SnBr6

A proton double quantum coherence signal can be observed exclusively from the T species NH4 groups (with the total spin I = 1) in ammonium compounds at low temperatures by the three-pulse sequence 90x degrees - tpr - 90x degrees - tev - 90x degrees - ta, where tpr and ta are of the magnitude of the inverse line width and tev very short. The usefulness of this pulse sequence, preceded by the additional pulse sequence 90x degrees - t1 -90(-x) degrees - t2 for creating an unbalance between the A and T species magnetizations, was demonstrated by applying it to cross-relaxation studies in (NH4)2SnBr6.     

Liquid chromatography–mass spectrometry for C60 fullerene analysis: optimisation and comparison of three ionisation techniques

The increasing use and production of nanomaterials have led to growing concern over the release of new pollutants to the environment. Fullerenes have been a subject of intense research, both because of their unique chemistry and because of technological applications. The development of analytical methods to quantify the fullerenes in complex sample matrices is a crucial step in the study of their occurrence and exposure, and thus in risk assessment. This paper reports the development and optimisation of a method combining liquid chromatography with ion-trap mass spectrometry (LC-ITMS) for analysis of the fullerene C(60). Under the optimised chromatogram conditions, a C(18) analytical column had good selectivity for fullerenes C(60) and C(70), with retention times of 3.0 and 4.1 min, respectively. Mass spectrometric detection was tested and optimised using three common ionisation techniques-atmospheric-pressure chemical ionisation (APCI), atmospheric-pressure photoionisation (APPI), and electrospray ionisation (ESI). The molecular ion was most abundant for C (60) (-) (m/z=720) in APCI and APPI, whereas adduct ions were formed with the molecular ion in ESI. Finally, the performance of the three ionisation techniques examined was compared by use of five validation criteria. The instrument detection limit (8 ng mL(-1)), quantification limit (27 ng mL(-1)), detection sensitivity (90.2 ng mL(-1)), linear range (8-1,000 ng mL(-1)), and repeatability (15 %) of APPI make it the most promising ionisation technique for fullerene C(60) analysis.