Flat corannulene: when a transition state becomes a stable molecule

Flat corannulene has been considered so far only as a transition state of the bowl-to-bowl inversion process. This study was driven by the prediction that substituents with strong steric repulsion could destabilize the bowl-shaped conformation of this molecule to such an extent that the highly unstable planar geometry would become an isolable molecule. To examine the substituents'' effect on the corannulene bowl depth, optimized structures for the highly-congested decakis(t-butylsulfido)corannulene were calculated. The computations, performed with both the M06-2X/def2-TZVP and the B3LYP/def2-TZVP methods (the latter with and without Grimme''s D3 dispersion correction), predict that this molecule can achieve two minimum structures: a flat carbon framework and a bowl-shaped structure, which are very close in energy. This rather unusual compound was easily synthesized from decachlorocorannulene under mild reaction conditions, and X-ray crystallographic studies gave similar results to the theoretical predictions. This compound crystallized in two different polymorphs, one exhibiting a completely flat corannulene core and the other having a bowl-shaped conformation.

The first flat metal-free corannulene derivative was predicted by computations and achieved by synthesis.     

On-Surface Synthesis and Real-Space Visualization of Aromatic P3N3

On-surface synthesis is at the verge of emerging as the method of choice for the generation and visualization of unstable or unconventional molecules, which could not be obtained via traditional synthetic methods. A case in point is the on-surface synthesis of the structurally elusive cyclotriphosphazene (P₃N₃), an inorganic aromatic analogue of benzene. Here, we report the preparation of this fleetingly existing species on Cu(111) and Au(111) surfaces at 5.2 K through molecular manipulation with unprecedented precision, i.e., voltage pulse-induced sextuple dechlorination of an ultra-small (about 6 Å) hexachlorophosphazene P₃N₃Cl₆ precursor by the tip of a scanning probe microscope. Real-space atomic-level imaging of cyclotriphosphazene reveals its planar D_3h-symmetric ring structure. Furthermore, this demasking strategy has been expanded to generate cyclotriphosphazene from a hexaazide precursor P₃N₂₁ via a different stimulation method (photolysis) for complementary measurements by matrix isolation infrared and ultraviolet spectroscopy.     

Dual‐Functional Semithiobambusurils

Semithiobambusurils, which represent a new family of macrocyclic host molecules, have been prepared by a convenient, scalable synthesis. These new cavitands are double functional: they strongly bind a broad variety of anions in their interiors and metal ions at their sulfur‐edged portals. The solid‐state structure of semithiobambus[4]uril with HgCl₂ demonstrates the ability of these compounds to form linear chains of coordination polymers with thiophillic metal ions. The crystal structure of semithiobambus[6]uril with tetraphenylphosphonium bromide exhibits the unique anion‐binding properties of the host cavity and the characteristics of the binding site.     

Representations of Hardy Algebras: Absolute Continuity,Intertwiners, and Superharmonic Operators

Suppose T₊(E){\mathcal{T}_{+}(E)} is the tensor algebra of a W*-correspondence E and H ^∞(E) is the associated Hardy algebra. We investigate the problem of extending completely contractive representations of T₊(E){\mathcal{T}_{+}(E)} on a Hilbert space to ultra-weakly continuous completely contractive representations of H ^∞(E) on the same Hilbert space. Our work extends the classical Sz.-Nagy–Foiaş functional calculus and more recent work by Davidson, Li and Pitts on the representation theory of Popescu’s noncommutative disc algebra.     

The Poisson Kernel for Hardy Algebras

This note contributes to a circle of ideas that we have been developing recently in which we view certain abstract operator algebras H^∞(E), which we call Hardy algebras, and which are noncommutative generalizations of classical H^∞, as spaces of functions defined on their spaces of representations. We define a generalization of the Poisson kernel, which “reproduces” the values, on , of the “functions” coming from H^∞(E). We present results that are natural generalizations of the Poisson integral formula. They also are easily seen to be generalizations of formulas that Popescu developed. We relate our Poisson kernel to the idea of a characteristic operator function and show how the Poisson kernel identifies the “model space” for the canonical model that can be attached to a point in the disc . We also connect our Poisson kernel to various “point evaluations” and to the idea of curvature. The first named author was supported in part by grants from the National Science Foundation and from the U.S.-Israel Binational Science Foundation. The second named author was supported in part by the U.S.-Israel Binational Science Foundation and by the B. and G. Greenberg Research Fund (Ottawa).     

Hardy algebras, <Emphasis Type="Italic">W</Emphasis>*-correspondences and interpolation theory

Given a von Neumann algebra M and a W*-correspondence E over M, we construct an algebra H(E) that we call the Hardy algebra of E. When M= =E, H(E) is the classical Hardy space H of bounded analytic functions on the unit disc. When M= and E= H(E) is the free semigroup algebra studied by Popescu, Davidson and Pitts and many others. We show that given any faithful normal representation of M on a Hilbert space H there is a natural correspondence E over the commutant (M), called the -dual of E, and that H(E) can be realized in terms of (B(H)-valued) functions on the open unit ball ((E)*) in the space of adjoints of elements in E. We prove analogues of the Nevanlinna-Pick theorem in this setting and discover other aspects of the value distribution theory for elements in H(E). We also analyze the boundary behavior of elements in H(E) and obtain generalizations of the Sz.-Nagy–Foia functional calculus and the functional calculus of Popescu for c.n.c. row contractions. The correspondence E has a dual that is naturally isomorphic to E and the commutants of certain, so-called induced representations of H(E) can be viewed as induced representations of H(E). For these induced representations a double commutant theorem is proved.Supported in part by grants from the National Science Foundation and from the U.S.-Israel Binational Science Foundation.Supported in part by the U.S.-Israel Binational Science Foundation and by the Fund for the Promotion of Research at the Technion.Revised version: 11 March 2004     

Intramolecular van der Waals Interactions Challenge Anion Binding in perthio-Bambusurils

Bambusurils (BUs) are known to be rigid cavitands that feature an extended, jigger-like conformation, and the BU[6]s strongly bind anions within their hydrophobic cavity. These features are not necessarily shared by the family of perthio-BUs. This study reveals that perthio-BUs assume a compact conformation and perthio-BU[6]s are poor anion binders, crystallizing as anion-free species from solutions containing halide salts. Computational studies show that the equatorial sulfur atoms compete against guest anions for binding with the glycoluril methine groups via strong van der Waals (vdW) attractive interactions. These competitive contacts not only account for the diminished anion-binding of perthio-BUs, but also explain their compact conformation. The semithio- and perthio-BU[4]s form linear coordination polymers with Hg^II in the solid-state regardless of their intrinsic molecular conformation. The strong involvement of sulfur atoms in intramolecular interactions differentiates the equatorial from the axial (peripheral) heteroatoms, thus offering chemoselective and regioselective transformations.     

On triangular subalgebras of groupoidC*-algebras

Let ℬ be an AFC*-algebra with Stratila-Voiculescu masaD and letU be a maximal triangular subalgebra of ℬ with diagonalD. Peters, Poon and Wagner showed thatU need not be aC*-subdiagonal subalgebra of ℬ in the sense of Kawamura and Tomiyama. We investigate and explain this phenomena here from the perspective of groupoidC*-algebras by representing257-7 as the “incidence algebra” associated with a topological partial order. A number of examples are given showing what can keep a maximal triangular algebra from beingC*-subdiagonal. Supported by a grant from the National Science Foundation.     

Isometries of Hilbert -modules

Let and be right, full, Hilbert -modules over the algebras and respectively and let be a linear surjective isometry. Then can be extended to an isometry of the linking algebras. then is a sum of two maps: a (bi-)module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-)module actions. If (or ) is a factor von Neumann algebra, then every isometry is either a (bi-)module map or reverses the (bi-)module actions.