Constraints on two-dimensional conformal field theories from knot invariants

The connection between Witten's topological three-dimensional gauge theory and RCFTs provides a natural setting to study the interplay between surface diffeomorphisms and intertwining of Wilson loops. These considerations lead directly to constraints on RFCTs including those previously derived by Vafa.     

Synthesis and spectroscopy of nickel(II) complexes with 5-methyl-3-formylpyrazole N(4)-methyl-N(4)-cyclohexyl thiosemicarbazone (HMPz4MCy): X-ray crystal structure of [Ni(HMPz4MCy)2]Cl2·2.5H2O

The coordination behaviour of a new pyrazolyl thiosemicarbazone, HMPz4MCy, synthesized and characterized (elemental analyses, mass spectrum, i.r. and ¹H-n.m.r) for the first time, is reported via solid state isolation of Ni^II complexes, [Ni(HMPz4MCy)₂]X₂·nH₂O (X = Cl, Br, NO₃, ClO₄ and BF₄; n = 2–3). The complex species were spectroscopically and structurally characterized. I.r. data for the free ligand and its Ni^II complexes indicate that the ligand, HMPz4MCy, exhibits a neutral NNS tridentate function via the pyrazolyl nitrogen (tertiary), azomethine nitrogen and thione sulphur. Electronic spectral data are suggestive of a distorted octahedral environment for the six-coordinate Ni^II species. X-ray crystallography of a representative species, [Ni(HMPz4MCy)₂]Cl₂·2.5H₂O (P2₁/c, monoclinic) has shown unambiguously that the crystallographic asymmetric unit consists of a [Ni(HMPz4MCy)₂]²⁺ cation and two Cl^– anions with the solvent of crystallization consisting of two H₂O molecules with full occupancy and a third H₂O molecule with half occupancy. The two NNS ligands orthogonally coordinate to the central nickel(II) ion with two azomethine nitrogen atoms in trans and the pyrazolyl nitrogen and the thione sulphur atoms in cis-positions. The crystal structure is stabilized by an extensive network of hydrogen bonds and is also additionally stabilized by C—HS contacts restricting free rotation about the N—C single bonds.     

Gas‐Phase Electron‐Diffraction Investigation and Quantum‐Chemical Calculations of the Structure of 1,5‐Dimethylsemibullvalene‐2,4,6,8‐tetracarboxylic Dianhydride

The bridged homotropilidines have been of interest for decades because their molecules offer the potential for homoaromaticity. Although many of these have been shown not to be homoaromatic, the energy differences of the delocalized (homoaromatic) forms and the localized (nonhomoaromatic) ones, and the barriers to the interconversion of the localized forms via a Cope rearrangement, have been found to vary greatly. The title compound is a strong candidate for homoaromaticity, and, since the structures of the possible localized and delocalized forms could differ significantly, we have carried out an electron‐diffraction investigation of it augmented by quantum‐mechanical calculations with different basis sets at several levels of theory. Three models were explored: one representing a localized form of C_s symmetry, one a delocalized form of C_2v symmetry, and one a 2 : 1 mixture of the localized/delocalized forms. Although none of the models could be ruled out, the experimental evidence slightly favors the C_s form. These results are consistent with those from the DFT B3PW91 calculations with basis sets ranging from 6‐31G(d) to cc‐pVTZ, which, surprisingly, predict essentially equal thermally corrected free energies for each. The results are discussed.     

General synthesis of di-mu-oxo dimanganese complexes as functional models for the oxygen evolving complex of photosystem II

A series of complexes with the formula [Mn(III/IV)2(mu-O)2(L)2(X)2]3+ have been prepared in situ from Mn(II)LCl2 precursors by a general preparative method (L = terpy, Cl-terpy, Br-terpy, Ph-terpy, tolyl-terpy, mesityl-terpy, t Bu3-terpy, EtO-terpy, py-phen, dpya, Me2N-terpy, or HO-terpy, and X = a labile ligand such as water, chloride, or sulfate). The parent complex, where L = terpy and X = water, is a functional model for the oxygen-evolving complex of photosystem II (Limburg, et al. J. Am. Chem. Soc. 2001, 123, 423-430). Crystals of Mn(II)(dpya)Cl2, Mn(II)(Ph-terpy)Cl2, Mn(II)(mesityl-terpy)Cl2, and an organic-soluble di-mu-oxo di-aqua dimanganese complex, [Mn(III/)(IV)2(mu-O)2(mesityl-terpy)2(OH2)2](NO3)3, were obtained and characterized by X-ray crystallography. Solutions of the in situ-formed di-mu-oxo dimanganese complexes were characterized by electrospray mass spectrometry, EPR spectroscopy, and UV-visible spectroscopy, and the rates of catalytic oxygen-evolving activity were assayed. The use of Mn(II)LCl2 precursors leads to higher product purity of the Mn dimers while achieving the 1:1 ligand to Mn stoichiometry appropriate for catalytic activity assay. These methods can be used to screen the catalytic activity of other di-mu-oxo dimanganese complexes generated by using a ligand library.     

Molecular complexes of copper(I): Easy access to CuF(PPh3)3 · 2ROH (R = Me or Et)

Treatment of a CuSO₄ · 5H₂O solution with NH₂OH · HCl and NaOH produces orange–yellow Cu₂O, which on being reacted with Ph₃P and aqueous HF (48%) in MeOH or EtOH yields CuF(PPh₃)₃ · 2ROH (R = Me or Et) in high yield. The volatile compounds have been characterised by spectroscopic techniques in addition to chemical analyses and solution electrical conductance measurements. Typically, CuF(PPh₃)₃ · 2MeOH appears to be stable up to 118 °C and loses 2 MeOH and 3 PPh₃ between 118 and 274 °C yielding volatile CuF at 274 °C.     

Synthesis,spectroscopy and cyclic voltammetry of cobalt(III) complexes with 5-methyl-3-formylpyrazole N(4)-cyclohexylthiosemicarbazone (HMPz4Cy): X-ray crystal structure of [Co(MPz4Cy)2]Cl · 2.75H2O

The coordination behaviour of the novel ligand, HMPz4Cy, is reported, together with solid state isolation of its diamagnetic cobalt(III) complexes, [Co(MPz4Cy)₂]X · nH₂O (X = Cl, Br, NO₃, ClO₄ and BF₄). I.r. and ¹H-n.m.r. data for the free ligand and its Co^III complexes confirm that the ligand, HMPz4Cy, acts as a uninegative anion with NNS tridentate function via the pyrazolyl nitrogen (tertiary), azomethine nitrogen and thiol sulphur. Electronic spectra (both solid and solution) are commensurate with a distorted octahedral environment for the reported Co^III species. Cyclic voltammograms of Co^III complexes indicate a quasireversible Co⁺³/Co⁺² couple. X-ray crystallography of a representative species, [Co(MPz4Cy)₂]Cl · 2.75H₂O (C2, monoclinic), has shown unambiguously that the two ligands are orthogonally coordinated to the central Co^III ion with both the thiolato sulphurs and both pyrazolyl nitrogen atoms in cis positions.