Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres

In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singular orbits except for the case where both are equal to two, where existence of non-negatively curved metrics is known.Comment: 10 page

Crystal structure of NiFe(CO)5[tris(pyridyl-meth-yl)aza-phosphatrane]: a synthetic mimic of the NiFe hydrogenase active site incorporating a pendant pyridine base.

The reaction of Ni(TPAP)(COD) {where TPAP = [(NC5H4)CH2]3P(NC2H4)3N} with Fe(CO)5 resulted in the isolation of the title heterobimetallic NiFe(TPAP)(CO)5 complex di-μ-carbonyl-tricarbon-yl[2,8,9-tris-(pyridin-2-yl-meth-yl)-2,5,8,9-tetra-aza-1-phosphabi-cyclo-[3.3.3]undeca-ne]ironnickel, [FeNi(C24H30N7P)(CO)5]. Characterization of the complex by 1H and 31P NMR as well as IR spectroscopy are presented. The structure of NiFe(TPAP)(CO)5 reveals three terminally bound CO mol-ecules on Fe0, two bridging CO mol-ecules between Ni0 and Fe0, and TPAP coordinated to Ni0. The Ni-Fe bond length is 2.4828 (4) Å, similar to that of the reduced form of the active site of NiFe hydrogenase (∼2.5 Å). Additionally, a proximal pendant base from one of the non-coordinating pyridine groups of TPAP is also present. Although involvement of a pendant base has been cited in the mechanism of NiFe hydrogenase, this moiety has yet to be incorporated in a structurally characterized synthetic mimic with key structural motifs (terminally bound CO or CN ligands on Fe). Thus, the title complex NiFe(TPAP)(CO)5 is an unique synthetic model for NiFe hydrogenase. In the crystal, the complex mol-ecules are linked by C-H⋯O hydrogen bonds, forming undulating layers parallel to (100). Within the layers, there are offset π-π [inter-centroid distance = 3.2739 (5) Å] and C-H⋯π inter-actions present. The layers are linked by further C-H⋯π inter-actions, forming a supra-molecular framework

Installation of internal electric fields by non-redox active cations in transition metal complexes.

Local electric fields contribute to the high selectivity and catalytic activity in enzyme active sites and confined reaction centers in zeolites by modifying the relative energy of transition states, intermediates and/or products. Proximal charged functionalities can generate equivalent internal electric fields in molecular systems but the magnitude of their effect and impact on electronic structure has been minimally explored. To generate quantitative insight into installing internal fields in synthetic systems, we report an experimental and computational study using transition metal (M1) Schiff base complexes functionalized with a crown ether unit containing a mono- or dicationic alkali or alkaline earth metal ion (M2). The synthesis and characterization of the complexes M1 = Ni(ii) and M2 = Na+ or Ba2+ are reported. The electronic absorption spectra and density functional theory (DFT) calculations establish that the cations generate a robust electric field at the metal, which stabilizes the Ni-based molecular orbitals without significantly changing their relative energies. The stabilization is also reflected in the experimental Ni(ii/i) reduction potentials, which are shifted 0.12 V and 0.34 V positive for M2 = Na+ and Ba2+, respectively, compared to a complex lacking a proximal cation. To compare with the cationic Ni complexes, we also synthesized a series of Ni(salen) complexes modified in the 5' position with electron-donating and -withdrawing functionalities (-CF3, -Cl, -H, -tBu, and -OCH3). Data from this series of compounds provides further evidence that the reduction potential shifts observed in the cationic complexes are not due to inductive ligand effects. DFT studies were also performed on the previously reported monocationic and dicatonic Fe(ii)(CH3CN) and Fe(iii)Cl analogues of this system to analyze the impact of an anionic chloride on the electrostatic potential and electronic structure of the Fe site

New string vacua from twistor spaces

We find a new family of AdS_4 vacua in IIA string theory. The internal space is topologically either the complex projective space CP^3 or the "flag manifold" SU(3)/(U(1)xU(1)), but the metric is in general neither Einstein nor Kaehler. All known moduli are stabilized by fluxes, without using quantum effects or orientifold planes. The analysis is completely ten--dimensional and does not rely on assumptions about Kaluza--Klein reduction.Comment: 19 pages. v3: published version, further minor correction

The dependence of the molecular first hyperpolarizabilities of merocyanines on ground-state polarization and length

We report here the dipole moment (µ) and first hyperpolarizability (β) determined by electric field-induced second harmonic generation, for several merocyanine dyes containing an 1,3,3-trimethylindoline heterocycle as a ‘donor’ in which the ‘acceptor’ end of the molecule and the polyene bridge length was systematically varied; dyes with hexamethine bridges gave positive β, while that with a dimethine bridge gave a negative β value

On the terms violating the custodial symmetry in multi-Higgs-doublet models

We prove that a generic multi-Higgs-doublet model (NHDM) generally must contain terms in the potential that violate the custodial symmetry. This is done by showing that the O(4) violating terms of the NHDM potential cannot be excluded by imposing a symmetry on the NHDM Lagrangian. Hence we expect higher-order corrections to necessarily introduce such terms. We also note, in the case of custodially symmetric Higgs-quark couplings, that vacuum alignment will lead to up-down mass degeneration; this is not true if the vacua are not aligned.Comment: 16 pages, 1 figure. Title and abstract are modified, conclusions remain the same. Section on Yukawa couplings is extended. Published versio