A Computational Study on a Strategy for Isolating a Stable Cyclopentadienyl Cation

A computational study has been carried out to examine the feasibility of generating a simple monocyclic cyclopentadienyl cation that may be sufficiently stable to isolate and handle at ambient temperatures. Using judicious placement of electron‐withdrawing groups (CF₃) about the ring we have identified a derivative that may approach the stability of isolobal (and isolatable) borole rings, as evaluated by HOMO–LUMO and singlet–triplet gaps. These Cp⁺ derivatives may therefore be an attractive target for synthetic isolation.     

Weak-heap sort

A data structure called aweak-heap is defined by relaxing the requirements for a heap. The structure can be implemented on a 1-dimensional array with one extra bit per data item and can be initialized withn items using exactlyn–1 data element compares. Theoretical analysis and empirical results indicate that it is a competitive structure for sorting. The worst case number of data element comparisons is strictly less than (n–1) logn+0.086013n and the expected number is conjectured to be approximately (n–0.5)logn–0.413n.     

Operational Research and the Behavioural Sciences

Operational research has set for itself the general goal of providing solutions to management problems. In view of this the authors assert that operational research has paid scant attention to work in the behavioural sciences in devising its approaches to problems. This omission can be serious. It can also be remedied, at least in part, and it is the purpose of this article to lay a foundation for such a remedy.     

Are N-heterocyclic carbenes "better" ligands than phosphines in main group chemistry? A theoretical case study of ligand-stabilized E2 molecules, L-E-E-L (L = NHC, phosphine; E = C, Si, Ge, Sn, Pb, N, P, As, Sb, Bi)

A theoretical examination of the L-E-E-L class of molecules has been carried out (E = group 14, group 15 element; L = N-heterocyclic carbene, phosphine), for which Si, Ge, P, and As-NHC complexes have recently been synthesized. The focus of this study is to predict whether it is possible to stabilize the elusive E(2) molecule via formation of L-E-E-L beyond the few known examples, and if the ligand set for this class of compounds can be extended from the NHC to the phosphine class of ligands. It is predicted that thermodynamically stable L-E-E-L complexes are possible for all group 14 and 15 elements, with the exception of nitrogen. The unknown ligand-stabilized Sn(2) and Pb(2) complexes may be considered attractive synthetic targets. In all cases the NHC complexes are more stable than the phosphines, however several of the phosphine derivatives may be isolable. The root of the extra stability conferred by the NHC ligands over the phosphines is determined to be a combination of the NHCs greater donating ability, and for the group 15 complexes, superior π acceptor capability from the E-E core. This later factor is the opposite as to what is normally observed in transition metal chemistry when comparing NHC and phosphine ligands, and may be an important consideration in the ongoing "renaissance" of low-valent main group compounds supported by ligands.     

Homoleptic pnictogen-chalcogen coordination complexes

The synthesis and structural characterization of dicationic selenium and tellurium analogues of the carbodiphosphorane and triphosphenium families of compounds are reported. These complexes, [Ch(dppe)][OTf](2) [Ch = Se, Te; dppe = 1,2-bis(diphenylphosphino)ethane; OTf = trifluoromethanesulfonate], are formed using [Ch](2+) reagents via a ligand-exchange protocol and represent extremely rare examples of homoleptic pnictogen → chalcogen coordination complexes. The corresponding arsenic compounds were also prepared, [Ch(dpAse)][OTf](2) [Ch = Se, Te; dpAse = 1,2-bis(diphenylarsino)ethane], exhibiting the first instance of an arsenic → chalcogen dative bond. The electronic structures of these unique compounds were determined and compared to previously reported chalcogen dications.     

Quantum spin liquid in frustrated one-dimensional LiCuSbO4

A quantum magnet, LiCuSbO4, with chains of edge-sharing spin-1/2 CuO6 octahedra is reported. While short-range order is observed for T<10 K, no zero-field phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high-field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with q=(0.47±0.01)π/a and places an upper limit of 70 μeV on any spin gap. Exact diagonalization of 16-spin easy-plane spin-1/2 chains with competing ferro- and antiferromagnetic interactions (J1=-75 K, J2=34 K) accounts for the T>2 K data.     

Structural and magnetic properties of Pr18Li8Fe5−xMxO39 (M=Ru, Mn, Co)

A polycrystalline sample of Pr₁₈Li₈Fe₄RuO₃₉ has been synthesized by a solid state method and characterized by neutron powder diffraction, magnetometry and Mössbauer spectroscopy; samples of Pr₁₈Li₈Fe_5−xMn_xO₃₉ and Pr₁₈Li₈Fe_5−xCo_xO₃₉ (x=1, 2) have been studied by magnetometry. All these compounds adopt a cubic structure (space group , a₀∼11.97 Å) based on intersecting 〈111〉 chains made up of alternating octahedral and trigonal-prismatic coordination sites. These chains occupy channels within a Pr-O framework. The trigonal-prismatic site in Pr₁₈Li₈Fe₄RuO₃₉ is occupied by Li⁺ and high-spin Fe³⁺. The remaining transition-metal cations occupy the two crystallographically-distinct octahedral sites in a disordered manner. All five compositions adopt a spin-glass-like state at 7 K (Pr₁₈Li₈Fe₄RuO₃₉) or below.     

On global domination critical graphs

A dominating set of a graph G=(V,E) is a subset S⊆V such that every vertex not in S is adjacent to at least one vertex of S. The domination number of G is the cardinality of a smallest dominating set. The global domination number, γ_g(G), is the cardinality of a smallest set S that is simultaneously a dominating set of both G and its complement . Graphs for which γ_g(G−e)>γ_g(G) for all edges e∈E are characterized, as are graphs for which γ_g(G−e)<γ_g(G) for all edges e∈E whenever is disconnected. Progress is reported in the latter case when is connected.     

Partitioning a graph into alliance free sets

A strong defensive alliance in a graph G=(V,E) is a set of vertices A⊆V, for which every vertex v∈A has at least as many neighbors in A as in V−A. We call a partition A,B of vertices to be an alliance-free partition, if neither A nor B contains a strong defensive alliance as a subset. We prove that a connected graph G has an alliance-free partition exactly when G has a block that is other than an odd clique or an odd cycle.