Origin of the Photoinduced Geometrical Change of Copper(I) Complexes from the Quantum Chemical Topology View

Copper(I) complexes (CICs) are of great interest due to their applications as redox mediators and molecular switches. CICs present drastic geometrical change in their excited states, which interferes with their luminescence properties. The photophysical process has been extensively studied by several time-resolved methods to gain an understanding of the dynamics and mechanism of the torsion, which has been explained in terms of a Jahn–Teller effect. Here, we propose an alternative explanation for the photoinduced structural change of CICs, based on electron density redistribution. After photoexcitation of a CIC (S₀→S₁), a metal-to-ligand charge transfer stabilizes the ligand and destabilizes the metal. A subsequent electron transfer, through an intersystem crossing process, followed by an internal conversion (S₁→T₂→T₁), intensifies the energetic differences between the metal and ligand within the complex. The energy profile of each state is the result of the balance between metal and ligand energy changes. The loss of electrons originates an increase in the attractive potential energy within the copper basin, which is not compensated by the associated reduction of the repulsive atomic potential. To counterbalance the atomic destabilization, the valence shell of the copper center is polarized (defined by ∇²ρ(r) and ∇²V_ne(r)) during the deactivation path. This polarization increases the magnitude of the intra-atomic nuclear–electron interactions within the copper atom and provokes the flattening of the structure to obtain the geometry with the maximum interaction between the charge depletions of the metal and the charge concentrations of the ligand.     

First-Order Necessary Conditions in Optimal Control

Journal of Optimization Theory and Applications - In an earlier analysis of strong variation algorithms for optimal control problems with endpoint inequality constraints, Mayne and Polak provided...     

Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials

Journal of Optimization Theory and Applications - A framework for monitoring a target modeled as Dubins car using multiple UAVs is proposed. The UAVs are subject to minimum and maximum speed,...     

C−C Bond Formation of Benzyl Alcohols and Alkynes Using a Catalytic Amount of KOtBu: Unusual Regioselectivity through a Radical Mechanism

We report a C?C bond‐forming reaction between benzyl alcohols and alkynes in the presence of a catalytic amount of KO^tBu to form α‐alkylated ketones in which the C=O group is located on the side derived from the alcohol. The reaction proceeds under thermal conditions (125 °C) and produces no waste, making the reaction highly atom efficient, environmentally benign, and sustainable. Based on our mechanistic investigations, we propose that the reaction proceeds through radical pathways.     

Frustrated Lewis Pair Chemistry Enables N2 Borylation by Formal 1,3-Addition of a B−H Bond in the Coordination Sphere of Tungsten

The first example of a formal 1,3-B−H bond addition across the M−N≡N unit of an end-on dinitrogen complex has been achieved. The use of Piers’ borane HB(C₆F₅)₂ was essential to observe this reactivity and it plays a triple role in this transformation: 1) electrophilic N₂-borylation agent, 2) Lewis acid in a frustrated Lewis pair-type B−H bond activation, and 3) hydride shuttle to the metal center. This chemistry is supported by NMR spectroscopy and solid-state characterization of products and intermediates. The combination of chelate effect and strong σ donation in the diphosphine ligand 1,2-bis(diethylphosphino)ethane was mandatory to avoid phosphine dissociation that otherwise led to complexes where borylation of N₂ occurred without hydride transfer.     

Resonances in bounded media: Nonlinear and boundary effects

We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.     

Synthesis of Functionalized Tetrahydropyridines by SnCl4-Mediated [4+2] Cycloaddition between Donor–Acceptor Cyclobutanes and Nitriles

Cycloadditions of strained carbocycles promoted by Lewis acids are powerful methods to construct heterocyclic frameworks. In fact, the formal [3+2] cycloadditions of donor–acceptor (DA) cyclopropanes with nitriles has seen particular success in synthesis. In this work, we report on the first [4+2] cycloaddition of nitriles with DA cyclobutanes by Lewis acid activation. Tetrahydropyridine derivatives were obtained in up to 91 % yield from various aryl-activated cyclobutane diesters and aliphatic or aromatic nitriles.     

Paramagnetic Lanthanide NMR Probes Signalling Changes in Zinc Concentration by Emission and Chemical Shift: A Proof of Concept Study

A zinc-selective probe based on a set of rare earth complexes of a modified DO3A macrocyclic ligand incorporating a tris-pyridylamine (TPA) moiety has been structurally characterised in solution and in the solid-state. One pyridine group possesses a tert-butyl substituent to serve as an NMR reporter group. The mono-capped square-antiprismatic Dy complex has a long bond (2.83 Å) to an apical N atom (pK_a 5.70 Eu) and binds to one water molecule on zinc binding. Zinc binding is reversible and involves all of the exocyclic ligand N donors; it is signalled by large (ratiometric) changes in Eu emission intensity, and by dramatic changes in the size (>50 ppm) and sign of the chemical shift of the paramagnetically shifted tBu resonances in Tb, Dy and Tm complexes. Slow trans-metallation was observed, leading to formation of an unusual di-zinc species in which one zinc ion is seven-coordinate and the other is six-coordinate.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.