Luminescent Di‐ and Trinuclear Boron Complexes Based on Aromatic Iminopyrrolyl Spacer Ligands: Synthesis,Characterization, and Application in OLEDs

New bis‐ and tris(iminopyrrole)‐functionalized linear (1,2‐(HNC₄H₃‐C(H)?N)₂‐C₆H₄ ( 2 ), 1,3‐(HNC₄H₃‐C(H)?N)₂‐C₆H₄ ( 3 ), 1,4‐(HNC₄H₃‐C(H)?N)₂‐C₆H₄ ( 4 ), 4,4′‐(HNC₄H₃‐C(H)?N)₂‐(C₆H₄‐C₆H₄) ( 5 ), 1,5‐(HNC₄H₃C‐(H)?N)₂‐C₁₀H₆ ( 6 ), 2,6‐(HNC₄H₃C‐(H)?N)₂‐C₁₀H₆ ( 7 ), 2,6‐(HNC₄H₃C‐(H)?N)₂‐C₁₄H₈ ( 8 )) and star‐shaped (1,3,5‐(HNC₄H₃‐C(H)?N‐1,4‐C₆H₄)₃‐C₆H₃ ( 9 )) π‐conjugated molecules were synthesized by the condensation reactions of 2‐formylpyrrole ( 1 ) with several aromatic di‐ and triamines. The corresponding linear diboron chelate complexes (Ph₂B[1,3‐bis(iminopyrrolyl)‐phenyl]BPh₂ ( 10 ), Ph₂B[1,4‐bis(iminopyrrolyl)‐phenyl]BPh₂ ( 11 ), Ph₂B[4,4′‐bis(iminopyrrolyl)‐biphenyl]BPh₂ ( 12 ), Ph₂B[1,5‐bis(iminopyrrolyl)‐naphthyl]BPh₂ ( 13 ), Ph₂B[2,6‐bis(iminopyrrolyl)‐naphthyl]BPh₂ ( 14 ), Ph₂B[2,6‐bis(iminopyrrolyl)‐anthracenyl]BPh₂ ( 15 )) and the star‐shaped triboron complex ([4′,4′′,4′′′‐tris(iminopyrrolyl)‐1,3,5‐triphenylbenzene](BPh₂)₃ ( 16 )) were obtained in moderate to good yields, by the treatment of 3 – 9 with B(C₆H₅)₃. The ligand precursors are non‐emissive, whereas most of their boron complexes are highly fluorescent; their emission color depends on the π‐conjugation length. The photophysical properties of the luminescent polyboron compounds were measured, showing good solution fluorescence quantum yields ranging from 0.15 to 0.69. DFT and time‐dependent DFT calculations confirmed that molecules 10 and 16 are blue emitters, because only one of the iminopyrrolyl groups becomes planar in the singlet excited state, whereas the second (and third) keeps the same geometry. Compound 13 , in which planarity is not achieved in any of the groups, is poorly emissive. In the other examples ( 11 , 12 , 14 , and 15 ), the LUMO is stabilized, narrowing the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO), and the two iminopyrrolyl groups become planar, extending the size of the π‐system, to afford green to yellow emissions. Organic light‐emitting diodes (OLEDs) were fabricated by using the new polyboron complexes and their luminance was found to be in the order of 2400 cd m^?2, for single layer devices, increasing to 4400 cd m^?2 when a hole‐transporting layer is used.     

BODIPY: A Highly Versatile Platform for the Design of Bimodal Imaging Probes

In molecular imaging, multimodal imaging agents can provide complementary information, for improving the accuracy of disease diagnosis or enhancing patient management. In particular, optical/nuclear imaging may find important preclinical and clinical applications. To simplify the preparation of dual‐labeled imaging agents, we prepared versatile monomolecular multimodal imaging probe (MOMIP) platforms containing both a fluorescent dye (BODIPY) and a metal chelator (polyazamacrocycle). One of the MOMIP was conjugated to a cyclopeptide (i.e., octreotide) and radiolabeled with ¹¹¹In. In vitro and in vivo studies of the resulting bioconjugate were conducted, highlighting the potential of these BODIPY‐based bimodal probes. This work also confirmed that the biovector and/or the bimodal probes must be chosen carefully, due to the impact of the MOMIP on the overall properties of the resulting imaging agent.     

Dioxygen Binding in the Active Site of Histone Demethylase JMJD2A and the Role of the Protein Environment

JMJD2A catalyses the demethylation of di‐ and trimethylated lysine residues in histone tails and is a target for the development of new anticancer medicines. Mechanistic details of demethylation are yet to be elucidated and are important for the understanding of epigenetic processes. We have evaluated the initial step of histone demethylation by JMJD2A and demonstrate the dramatic effect of the protein environment upon oxygen binding using quantum mechanics/molecular mechanics (QM/MM) calculations. The changes in electronic structure have been studied for possible spin states and different conformations of O₂, using a combination of quantum and classical simulations. O₂ binding to this histone demethylase is computed to occur preferentially as an end‐on superoxo radical bound to a high‐spin ferric centre, yielding an overall quintet ground state. The favourability of binding is strongly influenced by the surrounding protein: we have quantified this effect using an energy decomposition scheme into electrostatic and dispersion contributions. His182 and the methylated lysine assist while Glu184 and the oxoglutarate cofactor are deleterious for O₂ binding. Charge separation in the superoxo‐intermediate benefits from the electrostatic stabilization provided by the surrounding residues, stabilizing the binding process significantly. This work demonstrates the importance of the extended protein environment in oxygen binding, and the role of energy decomposition in understanding the physical origin of binding/recognition.     

A Mononuclear Uranium(IV) Single‐Molecule Magnet with an Azobenzene Radical Ligand

A tetravalent uranium compound with a radical azobenzene ligand, namely, [{(SiMe₂NPh)₃‐tacn}U^IV(η²‐N₂Ph₂^.)] ( 2 ), was obtained by one‐electron reduction of azobenzene by the trivalent uranium compound [U^III{(SiMe₂NPh)₃‐tacn}] ( 1 ). Compound 2 was characterized by single‐crystal X‐ray diffraction and ¹H NMR, IR, and UV/Vis/NIR spectroscopy. The magnetic properties of 2 and precursor 1 were studied by static magnetization and ac susceptibility measurements, which for the former revealed single‐molecule magnet behaviour for the first time in a mononuclear U^IV compound, whereas trivalent uranium compound 1 does not exhibit slow relaxation of the magnetization at low temperatures. A first approximation to the magnetic behaviour of these compounds was attempted by combining an effective electrostatic model with a phenomenological approach using the full single‐ion Hamiltonian.     

Convergence of a non-failable mean-field particle system

The existing literature contains many examples of mean-field particle systems converging to the distribution of a Markov process conditioned to not hit a given set. In many situations, these mean-field particle systems are failable, meaning that they are not well defined after a given random time. Our first aim is to introduce an original mean-field particle system, which is always well defined and whose large number particle limit is, in all generality, the distribution of a process conditioned to not hit a given set. Under natural conditions on the underlying process, we also prove that the convergence holds uniformly in time as the number of particles goes to infinity. As an illustration, we show that our assumptions are satisfied in the case of a piece-wise deterministic Markov process.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

An axiomatic duality framework for the theta body and related convex corners

Lovász theta function and the related theta body of graphs have been in the center of the intersection of four research areas: combinatorial optimization, graph theory, information theory, and semidefinite optimization. In this paper, utilizing a modern convex optimization viewpoint, we provide a set of minimal conditions (axioms) under which certain key, desired properties are generalized, including the main equivalent characterizations of the theta function, the theta body of graphs, and the corresponding antiblocking duality relations. Our framework describes several semidefinite and polyhedral relaxations of the stable set polytope of a graph as generalized theta bodies. As a by-product of our approach, we introduce the notion of “Schur Lifting” of cones which is dual to PSD Lifting (more commonly used in SDP relaxations of combinatorial optimization problems) in our axiomatic generalization. We also generalize the notion of complements of graphs to diagonally scaling-invariant polyhedral cones. Finally, we provide a weighted generalization of the copositive formulation of the fractional chromatic number by Dukanovic and Rendl from 2010.     

Multiscale Structures to Describe Porous Media Part I: Theoretical Background and Invasion by Fluids

A porous medium with a broad pore-size distribution is described on the basis of the Multiscale Percolation System concept. The representative structure is the superposition of several constitutive elementary networks, of which mesh sizes are proportional to the diameter of the class of pores considered. To account for the contribution of each class to the connection of the medium, a recurrent building process, involving rescaling and superposition, is defined. This process leads to an equivalent monoscale network, involving elements representative of the various classes. Mercury intrusion at increasing pressure into a finite-size sample of this equivalent network is modelled. The inverse problem is solved, leading to the identification of the representative multiscale structure of a given material from the experimental intrusion curve.     

A thermodynamic approach with internal variables using Lagrange formalism. Part II. Continuous symmetries in the case of the time–temperature equivalence

In the first part of this contribution, the Lie-symmetries of the principle of least action associated to the constitutive equations of the DNLR formalism of relaxation have been presented. We examine in this second part the continuous symmetries corresponding to the simple case of stress relaxation under isothermal conditions. The well-known principle of time/temperature equivalence is discussed in terms of variational symmetry for the Jacobi’s action functional, and connected to the Onsager’s relation near the thermodynamic equilibrium.