Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Algorithms for flows over time with scheduling costs

Mathematical Programming - Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated...     

Screening of Three Transition Metal‐Mediated Reactions Compatible with DNA‐Encoded Chemical Libraries

The construction of DNA‐encoded chemical libraries (DECLs) crucially relies on the availability of chemical reactions, which are DNA‐compatible and which exhibit high conversion rates for a large number of diverse substrates. In this work, we present our optimization and validation procedures for three copper and palladium‐catalyzed reactions (Suzuki cross‐coupling, Sonogashira cross‐coupling, and copper(I)‐catalyzed alkyne‐azide cycloaddition (CuAAC)), which have been successfully used by our group for the construction of large encoded libraries.     

Redox‐Active Tetraruthenium Macrocycles Built from 1,4‐Divinylphenylene‐Bridged Diruthenium Complexes

Metallamacrocylic tetraruthenium complexes were generated by treatment of 1,4‐divinylphenylene‐bridged diruthenium complexes with functionalized 1,3‐benzene dicarboxylic acids and characterized by HR ESI‐MS and multinuclear NMR spectroscopy. Every divinylphenylene diruthenium subunit is oxidized in two consecutive one‐electron steps with half‐wave potential splittings in the range of 250 to 330 mV. Additional, smaller redox‐splittings between the +/2+ and 0/+ and the 3+/4+ and 2+/3+ redox processes, corresponding to the first and the second oxidations of every divinylphenylene diruthenium entity, are due to electrostatic effects. The lack of electronic coupling through bond or through space is explained by the nodal properties of the relevant molecular orbitals and the lateral side‐by‐side arrangement of the divinylphenylene linkers. The polyelectrochromic behavior of the divinylphenylene diruthenium precursors is retained and even amplified in these metallamacrocyclic structures. EPR studies down to T=4 K indicate that the dications 1‐H²⁺ and 1‐OBu²⁺ are paramagnetic. The dications and the tetracation of macrocycle 3‐H display intense (dications) or weak ( 3‐H⁴⁺ ) EPR signals. Quantum chemical calculations indicate that the four most stable conformers of the macrocycles are largely devoid of strain. Bond parameters, energies as well as charge and spin density distributions of model macrocycle 5‐H^Me were calculated for the different charge and spin states.     

Crystal structure of K[PtCl3(caffeine)] and its interactions with important nitrogen-donor ligands

The crystal structure of K[PtCl₃(caffeine)] was determined. The coordination geometry around platinum is square-planar formed by N9 of the caffeine ligand and three Cl^? ions. The bond lengths and angles of K[PtCl₃(caffeine)] were compared with those reported for [PtCl₃(caffeine)]^? and K[PtCl₃(theobromine)]. At the level of the statistical significance of the data we have compared, no differences in the bond distances and angles for any of these compounds were noticed. Weak interactions between K⁺ and Cl^? are responsible for the formation of 1-D polymeric chains in the crystal structure of the complex. The interactions of K[PtCl₃(caffeine)] with inosine (Ino) and guanosine-5′-monophosphate (5′-GMP) were studied by ¹H NMR spectroscopy at 295 K in D₂O in a molar ratio of 1 : 1. The results indicate formation of the reaction product [PtCl₃(Nu)] (Nu=Ino or 5′-GMP) with the release of caffeine from the coordination sphere of the starting complex. The higher stability of the bond between the Pt(II) ion and Ino or 5′-GMP compared to the stability of the platinum–caffeine bond is confirmed by density functional theory calculations (B3LYP/LANL2DZp) using as models 9-methylhypoxanthine and 9-methylguanine.