Harmonic maps with torsion

In this article we introduce a natural extension of the well-studied equation for harmonic maps between Riemannian manifolds by assuming that the target manifold is equipped with a connection that is metric but has non-vanishing torsion. Such connections have already been classified in the work of Cartan(1924).The maps under consideration do not arise as critical points of an energy functional leading to interesting mathematical challenges. We will perform a first mathematical analysis of these maps which we will call harmonic maps with torsion.     

Hierarchically Structured Allotropes of Phosphorus from Data-Driven Exploration

The discovery of materials is increasingly guided by quantum-mechanical crystal-structure prediction, but the structural complexity in bulk and nanoscale materials remains a bottleneck. Here we demonstrate how data-driven approaches can vastly accelerate the search for complex structures, combining a machine-learning (ML) model for the potential-energy surface with efficient, fragment-based searching. We use the characteristic building units observed in Hittorf's and fibrous phosphorus to seed stochastic (“random”) structure searches over hundreds of thousands of runs. Our study identifies a family of hierarchically structured allotropes based on a P8 cage as principal building unit, including one-dimensional (1D) single and double helix structures, nanowires, and two-dimensional (2D) phosphorene allotropes with square-lattice and kagome topologies. These findings yield new insight into the intriguingly diverse structural chemistry of phosphorus, and they provide an example for how ML methods may, in the long run, be expected to accelerate the discovery of hierarchical nanostructures.     

Multiple Site Hydrogen Isotope Labelling of Pharmaceuticals

Radiolabelling is fundamental in drug discovery and development as it is mandatory for preclinical ADME studies and late-stage human clinical trials. Herein, a general, effective, and easy to implement method for the multiple site incorporation of deuterium and tritium atoms using the commercially available and air-stable iridium precatalyst [Ir(COD)(OMe)]₂ is described. A large scope of pharmaceutically relevant substructures can be labelled using this method including pyridine, pyrazine, indole, carbazole, aniline, oxa-/thia-zoles, thiophene, but also electron-rich phenyl groups. The high functional group tolerance of the reaction is highlighted by the labelling of a wide range of complex pharmaceuticals, containing notably halogen or sulfur atoms and nitrile groups. The multiple site hydrogen isotope incorporation has been explained by the in situ formation of complementary catalytically active species: monometallic iridium complexes and iridium nanoparticles.