Chasing BODIPY: Enhancement of Luminescence in Homoleptic Bis(dipyrrinato) ZnII Complexes Utilizing Symmetric and Unsymmetrical Dipyrrins

Dipyrromethene metal complexes are fascinating molecules that have applications as light-harvesting systems, luminophores, and laser dyes. Recently, it has been shown that structurally rigid bis(dipyrrinato) zinc(II) complexes exhibit high fluorescence with comparable quantum yields to those of boron dipyrromethenes or BODIPYs. Herein, eight new bis(dipyrrinato) Zn^II complexes, obtained from symmetric and unsymmetrical functionalization of the dipyrromethene structure through a Knoevenagel reaction, are reported. It was possible not only to vary the maximum visible absorption from 490 to 630 nm, but also to enhance the emission quantum yield up to 66 %, which is extraordinarily high for homoleptic bis(dipyrrinato) zinc complexes. These results pave the way for designing highly luminescent bis(dipyrrinato) zinc complexes.     

A Tris(3-pyridyl)stannane as a Building Block for Heterobimetallic Coordination Polymers and Supramolecular Cages

The systematic assembly of supramolecular arrangements is a persistent challenge in modern coordination chemistry, especially where further aspects of complexity are concerned, as in the case of large molecular mixed-metal arrangements. One targeted approach to such heterometallic complexes is to engineer metal-based donor ligands of the correct geometry to build 3D arrangements upon coordination to other metals. This simple idea has, however, only rarely been applied to main group metal-based ligand systems. Here, we show that the new, bench-stable tris(3-pyridyl)stannane ligand PhSn(3-Py)₃ (3-Py=3-pyridyl) provides simple access to a range of heterometallic Sn^IV/transition metal complexes, and that the presence of weakly coordinating counter anions can be used to build discrete molecular arrangements involving anion encapsulation. This work therefore provides a building strategy in this area, which parallels that of supramolecular transition metal chemistry.     

The coordination number calculation from total structure factor measurements

In the structural characterization of amorphous materials, the knowledge of the correlation distances and coordination numbers has a key importance. When several correlation distances overlap in the same diffractogram, obtaining the coordination numbers is a quite difficult task. In this work the method to obtain coordination numbers from total structure factor measurements is described in detail. The procedure is focussed in neutron diffraction experiments, but it is also applicable for X-ray diffraction. In order to illustrate the method, it was chosen as example a chalcogenide glass (Ag₂₅Ge_18.75Se_56.25), a member of a series of ionic conductors that have been studied by neutron diffraction. In particular, the coordination numbers corresponding to the first diffraction peak, involving Ge–Se and Se–Se correlations, are discussed.     

Small Chvátal Rank

We propose a variant of the Chvátal-Gomory procedure that will produce a sufficient set of facet normals for the integer hulls of all polyhedra {x : A x ≤ b} as b varies. The number of steps needed is called the small Chvátal rank (SCR) of A. We characterize matrices for which SCR is zero via the notion of supernormality which generalizes unimodularity. SCR is studied in the context of the stable set problem in a graph, and we show that many of the well-known facet normals of the stable set polytope appear in at most two rounds of our procedure. Our results reveal a uniform hypercyclic structure behind the normals of many complicated facet inequalities in the literature for the stable set polytope. Lower bounds for SCR are derived both in general and for polytopes in the unit cube.     

A practical error formula for multivariate rational interpolation and approximation

We consider exact and approximate multivariate interpolation of a function f(x ₁?,?.?.?.?,?x _d ) by a rational function p _n,m /q _n,m (x ₁?,?.?.?.?,?x _d ) and develop an error formula for the difference f???p _n,m /q _n,m . The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on.