Organometallic neptunium(III) complexes

Studies of transuranic organometallic complexes provide a particularly valuable insight into covalent contributions to the metal–ligand bonding, in which the subtle differences between the transuranium actinide ions and their lighter lanthanide counterparts are of fundamental importance for the effective remediation of nuclear waste. Unlike the organometallic chemistry of uranium, which has focused strongly on UIII and has seen some spectacular advances, that of the transuranics is significantly technically more challenging and has remained dormant. In the case of neptunium, it is limited mainly to NpIV. Here we report the synthesis of three new NpIII organometallic compounds and the characterization of their molecular and electronic structures. These studies suggest that NpIII complexes could act as single-molecule magnets, and that the lower oxidation state of NpII is chemically accessible. In comparison with lanthanide analogues, significant d- and f-electron contributions to key NpIII orbitals are observed, which shows that fundamental neptunium organometallic chemistry can provide new insights into the behaviour of f-elements

Constant-angle surfaces in liquid crystals

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect

A topological classification of convex bodies

The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale functions on S^2 by exhausting all combinatorial possibilities: every 2-colored quadrangulation of the sphere is isomorphic to a suitably represented Morse-Smale complex associated with a function in M_C (and vice versa). We prove our claim by an inductive algorithm, starting from the path graph P_2 and generating convex bodies corresponding to quadrangulations with increasing number of vertices by performing each combinatorially possible vertex splitting by a convexity-preserving local manipulation of the surface. Since convex bodies carrying Morse-Smale complexes isomorphic to P_2 exist, this algorithm not only proves our claim but also generalizes the known classification scheme in [36]. Our expansion algorithm is essentially the dual procedure to the algorithm presented by Edelsbrunner et al. in [21], producing a hierarchy of increasingly coarse Morse-Smale complexes. We point out applications to pebble shapes.Comment: 25 pages, 10 figure

Strongly coupled binuclear uranium-oxo complexes from uranyl oxo rearrangement and reductive silylation

The most common motif in uranium chemistry is the d0f0 uranyl ion [UO2]21 in which the oxo groups are rigorously linear and inert. Alternative geometries, such as the cis-uranyl, have been identified theoretically and implicated in oxo-atom transfer reactions that are relevant to environmental speciation and nuclear waste remediation. Single electron reduction is now known to impart greater oxo-group reactivity, but with retention of the linear OUO motif, and reactions of the oxo groups to form new covalent bonds remain rare. Here, we describe the synthesis, structure, reactivity and magnetic properties of a binuclear uranium–oxo complex. Formed through a combination of reduction and oxo-silylation and migration from a trans to a cis position, the new butterfly-shaped Si–OUO2UO–Si molecule shows remarkably strong UV–UV coupling and chemical inertness, suggesting that this rearranged uranium oxo motif might exist for other actinide species in the environment, and have relevance to the aggregation of actinide oxide clusters.JRC.E.6-Actinides researc

Switchable pi-coordination and C-H metallation in small-cavity macrocyclic uranium and thorium complexes

New, conformationally restricted ThIV and UIV complexes, [ThCl2(L)] and [UI2(L)], of the small-cavity, dipyrrolide, dianionic macrocycle trans-calix[2]benzene[2]pyrrolide (L)2− are reported and are shown to have unusual κ5:κ5 binding in a bent metallocene-type structure. Single-electron reduction of [UI2(L)] affords [UI(THF)(L)] and results in a switch in ligand binding from κ5-pyrrolide to η6-arene sandwich coordination, demonstrating the preference for arene binding by the electron-rich UIII ion. Facile loss of THF from [UI(THF)(L)] further increases the amount of U–arene back donation. [UI(L)] can incorporate a further UIII equivalent, UI3, to form the very unusual dinuclear complex [U2I4(L)] in which the single macrocycle adopts both κ5:κ5 and η6:κ1:η6:κ1 binding modes in the same complex. Hybrid density functional theory calculations carried out to compare the electronic structures and bonding of [UIIII(L)] and [UIII2I4(L)] indicate increased contributions to the covalent bonding in [U2I4(L)] than in [UI(L)], and similar U–arene interactions in both. MO analysis and QTAIM calculations find minimal U–U interaction in [U2I4(L)]. In contrast to the reducible U complex, treatment of [ThCl2(L)] with either a reductant or non-nucleophilic base results in metallation of the aryl rings of the macrocycle to form the (L−2H)4− tetraanion and two new and robust Th–C bonds in the –ate complexes [K(THF)2ThIV(μ-Cl)(L−2H)]2 and K[ThIV{N(SiMe3)2}(L−2H)]

Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integro-difference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile-adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, \emph{Calathea ovandensis}. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates ``remember'' the past