Search

In this paper, we give a detailed introduction to the theory of (curved) L ∞ -algebras and L ∞ -morphisms, avoiding the concept of operads and providing explicit formulas. In particular, we recall the notion of (curved) Maurer–Cartan elements, their equivalence classes and the twisting procedure. The main focus is then the study of the homotopy theory of L ∞ -algebras and L ∞ -modules. In particular, one can interpret L ∞ -morphisms and morphisms of L ∞ -modules as Maurer–Cartan elements in certain L ∞ -algebras, and we show that twisting the morphisms with equivalent Maurer–Cartan elements yields homotopic morphisms. We hope that these notes provide an accessible entry point to the theory of L ∞ -algebras. [ABSTRACT FROM AUTHOR]

The global formality of Dolgushev depends on the choice of a torsion-free covariant derivative. We prove that the globalized formalities with respect to two different covariant derivatives are homotopic. More explicitly, we derive the statement by proving a more general homotopy equivalence between L∞-morphisms that are twisted with gauge equivalent Maurer-Cartan elements. [ABSTRACT FROM AUTHOR]

In this paper we investigate the compatibility of the BRST reduction procedure with the Hermiticity of star products. First, we introduce the generalized notion of abstract BRST algebras with corresponding involutions. In this setting we define adjoint BRST differentials and as a consequence one gets new BRST quotients. Passing to the quantum BRST setting we show that for compact Lie groups the new quantum BRST quotient and the quantum BRST cohomology are isomorphic in zero degree implying that reduction is compatible with Hermiticity. [ABSTRACT FROM AUTHOR]

Four different three-dimensional metal-fullerene frameworks were synthesized through polymerization of two C60-derived dodecaacids with varying alkyl spacers in the presence of Ca2+, Cu2+ or Cd2+ ions. Structural analysis of the frameworks was performed by single-crystal X-ray diffraction and porosity of the materials was investigated by sorption measurements. [ABSTRACT FROM AUTHOR]

The well-established exohedral functionalization chemistry of fullerenes, with C 60 as the most prevalent example, provides easy access to a variety of functionalized carbon nanostructures with great structural diversity and unusual spatial orientation of the attached moieties. Therefore, such molecular nanostructures can be identified as promising building blocks for the design and synthesis of three-dimensionally cross-linked molecular architectures giving rise to novel topologies which would not be accessible from other organic building blocks. Within this perspective, we would like to give an overview on recent progress in the design and synthesis of metal–organic hybrid architectures composed of highly functionalized fullerene derivatives as organic connectivity centers and metal ions or clusters as cross-linking nodes. The ultimate goal of these investigations is the precise control of three-dimensional arrangements of fullerene units in the solid state and the implementation of such carbon derivatives as organic connectivity centers into porous functional materials such as metal–organic frameworks (MOFs). [ABSTRACT FROM AUTHOR]

Hexakis-substituted [60]fullerene adducts with icosahedral symmetry provide an unprecedented scaffold for the spatial arrangement of twelve functional groups with high geometric precision. This unique molecular symmetry identifies such polyfunctional organic building blocks as potential highly connective linkers for coordination polymer and metal-organic framework synthesis. Hereby, the linker exhibits a higher connectivity than the metal ions and with the main connectivity based on the ligand, this can create a new type of inversely cross-linked framework. Two hexakis adducts bearing either twelve glycolic acid or 3-hydroxypropionic acid side chains attached to its malonate units were incorporated as organic connectivity centers in the first fullerene-containing three-dimensional frameworks by coordination with Zn2+. [ABSTRACT FROM AUTHOR]

Multivalent organic molecules possessing spherically well-arranged functionalities are promising building blocks for extended molecular networks. [60]Fullerene hexakisadducts are intriguing candidates allowing the organization of up to 12 functional groups within one molecule with high geometric precision. We have synthesized a hexakisadduct bearing 12 glycolic acid side-chains in good yield and with high regioisomeric purity and elucidated its solid-state structure from single crystals grown by the slow diffusion of dichloromethane into a methanol solution. Individual fullerene moieties are arranged in cubic close-packing mode and form an extended network by means of multiple supramolecular interactions. Each molecule forms 24 hydrogen bonds and is connected to six neighbouring fullerene derivatives. The crystal structure showcases the first example of a 3D arrangement of fullerene derivatives by directed hydrogen bonding in the solid state. These findings indicate the high potential of six-fold substituted fullerene derivatives as building blocks for crystalline frameworks. [ABSTRACT FROM AUTHOR]

Bridging the gap between fullerenes and MOFs: Against the background of the Golden Gate Bridge, various metal‐organic coordination motifs illustrate the great potential of highly functionalized [60]fullerene derivatives as organic connectivity centers in metal‐organic frameworks. In their Communication on page 15864 ff., Beuerle et al. report on the synthesis and crystallographic analysis of four new metal‐fullerene frameworks cross‐linked by Cu2+, Ca2+, or Cd2+ clusters that feature chiral pores or extended hydrogen‐bonding networks throughout the crystals. [ABSTRACT FROM AUTHOR]

Review: 71 refs. [ABSTRACT FROM AUTHOR]

We describe a method for recording the Rabi nutation of nuclear spin polarized He by optically pumped cesium magnetometers. The measurement is performed by detecting the time-dependent magnetic field produced by the He magnetization. The observed signals are compared to theoretical models and the results are used to precisely trace the evolution of the magnetization. This procedure represents a convenient way to control and measure the Rabi flip angle and the degree of spin polarization in experiments using He magnetometers. The method requires only very coarse knowledge of the applied magnetic field's magnitude. Graphical abstract: [ABSTRACT FROM AUTHOR]