Synthesis of the P-sulfide derivatives of 3-phosphabicyclo[3.1.0]hexanes and 1,2-dihydrophosphinines

Several 3-phosphabicyclo[3.1.0]hexane 3-oxides have been transformed into the corresponding sulfides by reaction with phosphorus pentasulfide. The 3-phenyl derivative could also be prepared by deoxygenation of the oxide followed by reaction with elemental sulfur. Opening of the cyclopropane ring in phosphabicyclohexane sulfides afforded mixtures of 3- and 5-methyl-1,2-dihydro-phosphinine-1-sulfides. Because of better yields, preparation of these products by thionation of the dihydrophosphinine oxides is more appropriate. The new phosphorus heterocycles have been characterized by ³¹P, ¹³C, and ¹H NMR and mass spectral data.     

Detection of small amounts of H2O in CO2‐rich fluid inclusions using Raman spectroscopy

Raman spectroscopic analysis at low (−100 °C) or high (100–200 °C) temperature is shown to be effective for detecting small amounts of H₂O in CO₂‐rich fluid inclusions from the deep lithosphere, which have previously been thought to be water‐free. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of Silolide Dianions via Reduction of Dichlorosiloles: Important Role of the Solvent

The reduction of 1,1-dichloro-2,5-bistrimethylsilyl-3,4-diphenylsilole to silolide dianion by alkali metals was investigated. As previously demonstrated, the outcome of the reaction depends strongly on the applied alkali metal, solvent, reaction conditions, and substituent pattern. We showed that lithium is a powerful reducing agent in THF or DME solvents, the reaction is even faster than the same reaction with sodium. The X-ray structures of the corresponding dilithio and disodium silolide dianion were investigated, interestingly recrystallization of the dilithio salt results in a coordination polymer. In order to support the synthetic work DFT calculations were performed.     

Reconfiguration of connected graph partitions

Motivated by recent computational models for redistricting and detection of gerrymandering, we study the following problem on graph partitions. Given a graph $G$ and an integer $k\ge 1$, a $k$-district map of $G$ is a partition of $V\left(G\right)$ into $k$ nonempty subsets, called districts, each of which induces a connected subgraph of $G$. A switch is an operation that modifies a $k$-district map by reassigning a subset of vertices from one district to an adjacent district; a 1-switch is a switch that moves a single vertex. We study the connectivity of the configuration space of all $k$-district maps of a graph $G$ under 1-switch operations. We give a combinatorial characterization for the connectedness of this space that can be tested efficiently. We prove that it is PSPACE-complete to decide whether there exists a sequence of 1-switches that takes a given $k$-district map into another; and NP-hard to find the shortest such sequence (even if a sequence of polynomial lengths is known to exist). We also present efficient algorithms for computing a sequence of 1-switches that take a given $k$-district map into another when the space is connected, and show that these algorithms perform a worst-case optimal number of switches up to constant factors.     

Quantum Nuclear Delocalization and its Rovibrational Fingerprints

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complex . The equilibrium structure of is planar and T-shaped, one He atom solvating the quasi-linear He−H⁺−He core. The dynamical structure of , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bent chomophore, but freely orbits the central proton, forming a three-dimensional torus around the chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.