A Dicobalt Complex with an Unsymmetrical Quinonoid Bridge Isolated in Three Units of Charge: A Combined Structural, (Spectro)electrochemical,Magnetic and Spectroscopic Study

Quinonoid ligands are excellent bridges for generating redox‐rich dinuclear assemblies. A large majority of these bridges are symmetrically substituted, with examples of unsymmetrically substituted quinonoid bridges being extremely rare. We present here a dicobalt complex in its various redox states with an unsymmetrically substituted quinonoid bridging ligand. Two homovalent forms and one mixed‐valent form have been isolated and characterized by single crystal X‐ray diffraction. The complex displays a large comproportionation constant for the mixed‐valent state which is three orders of magnitude higher than that observed for the analogous complex with a symmetrically substituted bridge. Results from electrochemistry, UV/Vis/NIR spectroelectrochemistry, SQUID magnetometry, multi‐frequency EPR spectroscopy and FIR spectroscopy are used to probe the electronic structures of these complexes. FIR provides direct evidence of exchange coupling. The results presented here display the advantages of using an unsymmetrically substituted bridge: site specific redox chemistry, high thermodynamic stabilization of the mixed‐valent form, isolation and crystallization of various redox forms of the complex. This work represents an important step on the way to generating heterodinuclear complexes for use in cooperative catalysis.     

Fluorescent perylene diimide rotaxanes: spectroscopic signatures of wheel-chromophore interactions

[2]- and [3]-rotaxanes with a tetraphenoxy perylene diimide core were synthesized. Hydrogen bonding between the wheel and the imide changes the optical properties of the perylene chromophore: the absorption and fluorescence spectra are red-shifted. The decay times of the rotaxanes are shorter in comparison with that of the axle. Single molecule fluorescence measurements reveal relatively narrow distributions of emission maxima and decay times. The averages are in agreement with ensemble measurements. The observed red shifts make the perylene diimide a suitable chromophore for sensing the position of the wheel on the axle.     

A branch-and-cut algorithm based on semidefinite programming for the minimum <Emphasis Type="Italic">k</Emphasis>-partition problem

The minimum k-partition (MkP) problem is the problem of partitioning the set of vertices of a graph into k disjoint subsets so as to minimize the total weight of the edges joining vertices in the same partition. The main contribution of this paper is the design and implementation of a branch-and-cut algorithm based on semidefinite programming (SBC) for the MkP problem. The two key ingredients for this algorithm are: the combination of semidefinite programming with polyhedral results; and a novel iterative clustering heuristic (ICH) that finds feasible solutions for the MkP problem. We compare ICH to the hyperplane rounding techniques of Goemans and Williamson and of Frieze and Jerrum, and the computational results support the conclusion that ICH consistently provides better feasible solutions for the MkP problem. ICH is used in our SBC algorithm to provide feasible solutions at each node of the branch-and-bound tree. The SBC algorithm computes globally optimal solutions for dense graphs with up to 60 vertices, for grid graphs with up to 100 vertices, and for different values of k, providing a fast exact approach for k≥3.     

Developments for the direct determination of the g-factor of a single proton in a Penning trap

The measurement and comparison of the magnetic moment (or g-factor) of the proton and antiproton provide a stringent experimental test of the CPT-theorem in the baryonic sector (Quint et al., Nucl Instrum Methods Phys Res, B 214:207, 2004). We present an experimental setup for the first direct high-precision measurement of the g-factor of a single isolated proton in a double cylindrical Penning trap. The application of the continuous Stern-Gerlach effect to detect quantum jumps between the two spin states of the particle, together with a novel trap design specially developed for this purpose, offers the possibility of measuring the magnetic moment not only of a single proton but also of a single antiproton. It is aimed to achieve a relative uncertainty of 10^???9 or better. Preliminary results including mass spectra of particle clouds as well as single proton preparation and detection are shown.     

Universal deformation rings and dihedral 2-groups

Let k be an algebraically closed field of characteristic 2,and let W be the ring of infinite Witt vectors over k. Supposethat D is a dihedral 2-group. We prove that the universal deformationring R(D, V) of an endo-trivial kD-module V is always isomorphicto W [/2x/2]. As a consequence, we obtain a similar result formodules V with stable endomorphism ring k belonging to an arbitrarynilpotent block with defect group D. This confirms, for suchV, conjectures on the ring structure of the universal deformationring of V that had previously been shown for V belonging tocyclic blocks or to blocks with Klein four defect groups.     

Catching proteins in liquid helium droplets

An experimental approach is presented that allows for the incorporation of large mass-to-charge ratio selected ions in liquid helium droplets. It is demonstrated that droplets can be efficiently doped with a mass-to-charge ratio selected amino acid as well as with the much bigger m ≈ 12,000 amu protein cytochrome C in selected charge states. The sizes of the ion-doped droplets are determined via electrostatic deflection. Under the experimental conditions employed, the observed droplet sizes are very large and range, depending on the incorporated ion, from 101? helium atoms for protonated phenylalanine to 1012 helium atoms for cytochrome C. As a possible explanation, a simple model based on the size and internal energy dependence of the pickup efficiency is given.