The differentiation operator in the space of uniformly convergent Dirichlet series

Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fréchet space of all Dirichlet series that are uniformly convergent in all half-planes for each . The properties of the formal inverse of the differentiation are also investigated.     

On the Structure of Intermediates in Enyne Gold(I)-Catalyzed Cyclizations: Formation of trans-Fused Bicyclo[5.1.0]octanes as a Case Study

The nature of cyclopropyl gold(I) carbene-type intermediates has been reexamined as part of a mechanistic study on the formation of cis- or trans-fused bicyclo[5.1.0]octanes in a gold(I)-catalyzed cascade reaction. Benchmark of DFT methods together with QTAIM theory and NBO analysis confirms the formation of distinct intermediates with carbenic or carbocationic structures in the cycloisomerizations of enynes.     

Intermediates of N-Heterocyclic Carbene (NHC) Dimerization Probed in the Gas Phase by Ion Mobility Mass Spectrometry: C−H⋅⋅⋅:C Hydrogen Bonding Versus Covalent Dimer Formation

N-Heterocyclic carbenes (NHCs, :C ) can interact with azolium salts ( C−H⁺ ) by either forming a hydrogen-bonded aggregate ( CHC⁺ ) or a covalent C−C bond ( CCH⁺ ). In this study, the intramolecular NHC–azolium salt interactions of aromatic imidazolin-2-ylidenes and saturated imidazolidin-2-ylidenes have been investigated in the gas phase by traveling wave ion mobility mass spectrometry (TW IMS) and DFT calculations. The TW IMS experiments provided evidence for the formation of these important intermediates in the gas phase, and they identified the predominant aggregation mode (hydrogen bond vs. covalent C−C) as a function of the nature of the interacting carbene–azolium pairs.     

Charge-Transfer versus Charge-Separated Triplet Excited States of [ReI(dmp)(CO)3(His124)(Trp122)]+ in Water and in Modified Pseudomonas aeruginosa Azurin Protein

A computational investigation of the triplet excited states of a rhenium complex electronically coupled with a tryptophan side chain and bound to an azurin protein is presented. In particular, by using high-level molecular modeling, evidence is provided for how the electronic properties of the excited-state manifolds strongly depend on coupling with the environment. Indeed, only upon explicitly taking into account the protein environment can two stable triplet states of metal-to-ligand charge transfer or charge-separated nature be recovered. In addition, it is also demonstrated how the rhenium complex plus tryptophan system in an aqueous environment experiences too much flexibility, which prevents the two chromophores from being electronically coupled. This occurrence disables the formation of a charge-separated state. The successful strategy requires a multiscale approach of combining molecular dynamics and quantum chemistry. In this context, the strategy used to parameterize the force fields for the electronic triplet states of the metal complex is also presented.     

Tailoring a Dress to Single Protein Molecules: Proteins Can Do It Themselves through Localized Photo-Polymerization and Molecular Imprinting

Molecularly imprinted polymer nanoparticles (MIP NPs) are antibody-like recognition materials prepared by a template-assisted synthesis. MIP NPs able to target biomolecules, like proteins, are under the spotlight for their great potential in medicine, but efficiently imprinting biological templates is still very challenging. Here we propose generating a molecular imprint in single NPs, by photochemically initiating the polymerization from individual protein templates. In this way, each protein molecule tailors itself its own “polymeric dress”. For this, the template protein is covalently coupled with a photoinitiator, Eosin Y. Irradiated with light at 533 nm, the Eosin moiety acts as an antenna and transfers energy to a co-initiator (an amine), which generates a radical and initiates polymerization. As a result, a polymer network is forming only around the very template molecule, producing cross-linked NPs of 50 nm, with single binding sites showing high affinity (K_D 10⁻⁹ m ) for their biological target, and selectivity over other proteins.     

Control over the Self‐Assembly Modes of PtII Complexes by Alkyl Chain Variation: From Slipped to Parallel π‐Stacks

We report the self‐assembly of a new family of hydrophobic, bis(pyridyl) Pt^II complexes featuring an extended oligophenyleneethynylene‐derived π‐surface appended with six long (dodecyloxy ( 2 )) or short (methoxy ( 3 )) side groups. Complex 2 , containing dodecyloxy chains, forms fibrous assemblies with a slipped arrangement of the monomer units (d_Pt???Pt≈14 Å) in both nonpolar solvents and the solid state. Dispersion‐corrected PM6 calculations suggest that this organization is driven by cooperative π–π, C?H???Cl and π–Pt interactions, which is supported by EXAFS and 2D NMR spectroscopic analysis. In contrast, nearly parallel π‐stacks (d_Pt???Pt≈4.4 Å) stabilized by multiple π–π and C?H???Cl contacts are obtained in the crystalline state for 3 lacking long side chains, as shown by X‐ray analysis and PM6 calculations. Our results reveal not only the key role of alkyl chain length in controlling self‐assembly modes but also show the relevance of Pt‐bound chlorine ligands as new supramolecular synthons.