On unitary subsectors of polycritical gravities

We study higher-derivative gravity theories in arbitrary space–time dimension $d$ with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to be dual to logarithmic conformal field theories in the $(d-1)$ -dimensional boundary of an AdS solution. We determine the structure of the linearized perturbations and their boundary fall-off behaviour. The linearized modes exhibit the expected Jordan block structure and their inner products are shown to be those of a non-unitary theory. We demonstrate the existence of consistent unitary truncations of the polycritical gravity theory at the linearized level for odd rank.     

A globalized Newton method for the computation of normalized Nash equilibria

The generalized Nash equilibrium is a Nash game, where not only the players’ cost functions, but also the constraints of a player depend on the rival players decisions. We present a globally convergent algorithm that is suited for the computation of a normalized Nash equilibrium in the generalized Nash game with jointly convex constraints. The main tool is the regularized Nikaido–Isoda function as a basis for a locally convergent nonsmooth Newton method and, in another way, for the definition of a merit function for globalization. We conclude with some numerical results.     

Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets

We consider a class of generalized Nash equilibrium problems with quadratic cost functions and common linear constraints for all players. Further we focus on the case where every player has a single strategy variable within a bounded set. For this problem class we present an algorithm that is able to compute all solutions and that terminates finitely. Our method is based on a representation of the solution set as a finite union of polyhedral sets using sign conditions for the derivatives of the cost and constraint functions. The effectiveness of the algorithm is shown in various examples from literature.     

Tricoordinate Coinage Metal Complexes with a Redox-Active Tris-(Ferrocenyl)triazine Backbone Feature Triazine–Metal Interactions

2,4,6-Tris(1-diphenylphosphanyl-1’-ferrocenylene)-1,3,5-triazine ( 1 ) coordinates all three coinage metal(I) ions in a 1:1 tridentate coordination mode. The C₃-symmetric coordination in both solid state and solution is stabilised by an uncommon cation–π interaction between the triazine core and the metal cation. Intramolecular dynamic behaviour was observed by variable-temperature NMR spectroscopy. The borane adduct of 1 , 1BH₃ , displays four accessible oxidation states, suggesting complexes of 1 to be intriguing candidates for redox-switchable catalysis. Complexes 1Cu , 1Ag , and 1Au display a more complicated electrochemical behaviour, and the electrochemical mechanism was studied by temperature-resolved UV/Vis spectroelectrochemistry and chemical oxidation.     

Quantum Interference Line Shifts of Broad Dipole‐Allowed Transitions

High‐resolution laser spectroscopy serves the purpose of determining the energy difference between states of atoms and molecules with the best possible accuracy. Therefore, one may face the problem of finding the center of a symmetric line within a small fraction of the line width, or one needs to extract the energy difference from an asymmetric line without a uniquely defined center. Multiplets of atomic resonance lines are subject to mutual line pullings and give rise to asymmetric line distortions due to quantum interference. This paper reviews the treatment of these distortions for dipole‐allowed one‐photon transitions. Specific examples are given for hydrogen and helium spectroscopy.     

Directed C−H Halogenation Reactions Catalysed by PdII Supported on Polymers under Batch and Continuous Flow Conditions

A new generation of N-heterocyclic carbene palladium(II) complexes containing vinyl groups in different positions in the backbone of the N-heterocycle have been developed. The fully characterised monomers were copolymerised with divinylbenzene to fabricate robust polymer supported NHC-Pd^II complexes and these polymers were applied as heterogeneous catalysts in directed C−H halogenation of arenes with a pyridine-type directing group. The catalysts demonstrated medium-high catalytic activity with up to 90 % conversion and 100 % selectivity in chlorination. They are heterogeneous and recyclable (at least six times) with no significant leaching of palladium in batch mode catalysis. The best catalyst was also applied under continuous flow conditions where it disclosed an exceptional activity (90 % conversion) and 100 % selectivity for the mono-halogenated product for at least six days, with no leaching of palladium, no loss of activity and an ability to maintain the original oxidation state of Pd^II.     

Photoinduced Charge Transfer in a Conformational Switching Chlorin Dimer–Azafulleroid in Polar and Nonpolar Media

In the present study, a biomimetic reaction center model, that is, a molecular triad consisting of a chlorin dimer and an azafulleroid, is synthesized and its photophysical properties are studied in comparison with the corresponding molecular dyad, which consists only of a chlorin monomer and an azafulleroid. As evidenced by ¹H NMR, UV/Vis, and fluorescence spectroscopy, the chlorin dimer–azafulleroid folds in nonpolar media into a C₂‐symmetric geometry through hydrogen bonding, resulting in appreciable electronic interactions between the chlorins, whereas in polar media the two chlorins diverge from contact. Femtosecond transient absorption spectroscopy studies reveal longer charge‐separated states for the chlorin dimer–azafulleroid; ≈1.6 ns in toluene, compared with the lifetime of ≈0.9 ns for the corresponding chlorin monomer–azafulleroid in toluene. In polar media, for example, benzonitrile, similar charge‐separated states are observed, but the lifetimes are inevitably shorter: 65 and 73 ps for the dimeric and monomeric chlorin–azafulleroids, respectively. Nanosecond transient absorption and singlet oxygen phosphorescence studies corroborate that in toluene, the charge‐separated state decays indirectly via the triplet excited state to the ground state, whereas in benzonitrile, direct recombination to the ground state is observed. Complementary DFT studies suggest two energy‐minima conformations, that is, a folded chlorin dimer–azafulleroid, which is present in nonpolar media, and another conformation in polar media, in which the two hydrophobic chlorins wrap the azafulleroid. Inspection of the frontier molecular orbitals shows that in the folded conformation, the HOMO on each chlorin is equivalent and is shared owing to partial π–π overlap, resulting in delocalization of the conjugated π electrons, whereas the wrapped conformation lacks this stabilization. As such, the longer charge‐separated lifetime for the dimer is rationalized by both the electron donor–acceptor separation distance and the stabilization of the radical cation through delocalization. The chlorin folding seems to change the photophysical properties in a manner similar to that observed in the chlorophyll dimer in natural photosynthetic reaction centers.