Synthesis and Reactivity of Cationic Boron Complexes Distorted by Pyridine-based Pincer Ligands: Isolation of a Photochemical Hofmann–Martius-type Intermediate

A family of cationic boron complexes was synthesized, using a dianilidopyridine pincer ligand, which imposes in-plane distortion of the geometry at boron towards T-shaped. Reactivity of these cations toward hydride and base was investigated, and the utility of these cations as precursors to a variety of π-conjugated BN heterocycles was demonstrated. 300 nm irradiation of a deprotonated pincer boron complex triggered a C−N cleavage/C−C formation yielding a dearomatized boryl imine, which has a structure akin to the long-proposed intermediate in the photochemical Hofmann–Martius rearrangement. The photo-rearrangement triggers relief of the distortion imposed by the pincer ligand.     

Synthesis and characterization of Au102(p-MBA)44 nanoparticles

The synthesis of Au(102)(p-MBA)(44) nanoparticles on a preparative scale in high yield is described. Various analytical methods are shown to give results consistent with the composition and known structure of the particles, showing the preparation is essentially homogeneous, and attesting to the validity of the methods as well. Derivatization of the particles with proteins and DNA is demonstrated, and conditions are described for imaging individual particles by cryo-EM at low electron dose, close to focus, conditions optimal for recording high-resolution details.     

Electronic and vibrational signatures of the Au102(p-MBA)44 cluster

Optical absorption of a gold nanocluster of 102 Au atoms protected by 44 para-mercaptobenzoic acid (p-MBA) ligands is measured in the range of 0.05-6.2 eV (mid-IR to UV) by a combination of several techniques for purified samples in solid and solution phases. The results are compared to calculations for a model cluster Au(102)(SMe)(44) based on the time-dependent density functional theory in the linear-response regime and using the known structure of Au(102)(p-MBA)(44). The measured and calculated molar absorption coefficients in the NIR-vis region are comparable, within a factor of 2, in the absolute scale. Several characteristic features are observed in the absorption in the range of 1.5-3.5 eV. The onset of the electronic transitions in the mid-IR region is experimentally observed at 0.45 ± 0.05 eV which compares well with the lowest calculated transition at 0.55 eV. Vibrations in the ligand layer give rise to fingerprint IR features below the onset of low-energy metal-to-metal electronic transitions. Partial exchange of the p-MBA ligand to glutathione does not affect the onset of the electronic transitions, which indicates that the metal core of the cluster is not affected by the ligand exchange. The full spectroscopic characterization of the Au(102)(p-MBA)(44) reported here for the first time gives benchmarks for further studies of manipulation and functionalization of this nanocluster to various applications.     

Hydrodynamic pair attractions between driven colloidal particles

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well-defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.     

A polynomial-time method to compute all Nash equilibria solutions of a general two-person inspection game

We consider a two-person nonzero-sum simultaneous inspection game that takes place at multiple sites. The inspector has a limited inspection resource. She needs to decide which sites to inspect, and with how much effort, while adhering also to local restrictions on the permitted inspections levels at the sites. The inspectee has several employees who work on his behalf. He needs to decide how to distribute them across the sites, and how they should act there. Computation of Nash equilibria is challenging for this sort of games. Still, we develop a linear-time algorithm that determines all Nash equilibria solutions of the game, and provide explicit (easily computable) expressions for all possible Nash equilibria. We then derive some managerial insights by applying the algorithm to several examples, and examining the Nash equilibria, including an outcome that an increase in the inspection resource may induce the inspectee to cooperate more at sites without increasing the inspection levels at them.     

Charge regulation with fixed and mobile charged macromolecules

Uncompensated charges do not usually occur in Nature and any local charge should be a result of charge separation. Dissociable chemical groups at interfaces in contact with ions in solution, whose chemical equilibrium depends both on short-range non-electrostatic and long-range electrostatic interactions, are the physical basis of this charge separation, known as charge regulation phenomena. The charged groups can be either fixed and immobile, as in the case of solvent-exposed solid substrate and soft bounding surfaces (e.g., atomically smooth mica surfaces and soft phospholipid membranes), or free and mobile, as in the case of charged macro-ions (e.g., protein or other biomolecules). Here, we review the mean-field formalism used to describe both cases, with a focus on recent advances in the modeling of mobile charge-regulated macro-ions in an ionic solution. The general form of the screening length is derived, and is shown to combine the concept of intrinsic capacitance (introduced by Lund and Jönsson) with bulk capacitance, resulting from the mobility of small ions and macro-ions. The advantages and disadvantages of different formulations, such as the cell model vs. the collective approach, are discussed, along with several suggestions for future experiments and modeling.     

Tensor Products and Support Varieties for Some Noncocommutative Hopf Algebras

We explore questions of projectivity and tensor products of modules for finite dimensional Hopf algebras. We construct many classes of examples in which tensor powers of nonprojective modules are projective and tensor products of modules in one order are projective but in the other order are not. Our examples are smash coproducts with duals of group algebras, some having algebra and coalgebra structures twisted by cocycles. We apply support variety theory for these Hopf algebras as a tool in our investigations.     

Effect of CO on the Oxidative Addition of Arene C?H Bonds by Cationic Rhodium Complexes

Sequential addition of CO molecules to cationic aryl–hydrido Rh^III complexes of phosphine‐based (PCP) pincer ligands was found to lead first to C? H reductive elimination and then to C? H oxidative addition, thereby demonstrating a dual role of CO. DFT calculations indicate that the oxidative addition reaction is directly promoted by CO, in contrast to the commonly accepted view that CO hinders such reactions. This intriguing effect was traced to repulsive π interactions along the aryl‐Rh‐CO axis, which are augmented by the initially added CO ligand (due to antibonding interactions between occupied Rh d_π orbitals and occupied π orbitals of both CO and the arene moiety), but counteracted by the second CO ligand (due to significant π back‐donation). These repulsive interactions were themselves linked to significant weakening of the π‐acceptor character of CO in the positively charged rhodium complexes, which is concurrent with an enhanced σ‐donating capability. Replacement of the phosphine ligands by an analogous phosphinite‐based (POCOP) pincer ligand led to significant changes in reactivity, whereby addition of CO did not result in C? H reductive elimination, but yielded relatively stable mono‐ and dicarbonyl aryl–hydrido POCOP–Rh^III complexes. DFT calculations showed that the stability of these complexes arises from the higher electrophilicity of the POCOP ligand, relative to PCP, which leads to partial reduction of the excessive π‐electron density along the aryl‐Rh‐CO axis. Finally, comparison between the effects of CO and acetonitrile on C? H oxidative addition revealed that they exhibit similar reactivity, despite their markedly different electronic properties. However, DFT calculations indicate that the two ligands operate by different mechanisms.