Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Determination of flux from a saddle field fast-atom bombardment gun

The flux or beam density (equivalent current/area) of xenon atoms striking the sample target from a saddle field fast-atom bombardment (FAB) gun has been compared with that from a cesium ion gun mounted on the same instrument. A shielded Faraday cup mounted on the end of a solids probe was used to measure directly the flux of the Cs⁺ beam. Samples of methylene blue in glycerol solution were then exposed to the ion beam at different fluxes and the extents of reduction were measured. The extent of reduction varied linearly with flux up to a value of about 1.16 × 10¹³ particles s^?1 cm^?2 (1.85 μ cm^?2); above this level, the reduction effect appeared to saturate. FAB spectra were obtained from the same dye solution by using varying settings of the FAB gun. By comparing the extents of reduction of the dye from the two guns, the flux from the atom gun could be estimated. Observation of luminescence from a CsI-coated target allowed estimation of the area of the atom beam. The atom beam “equivalent current” could then be calculated by multiplying the flux times the area. It was noted that for given settings, the flux from the atom gun depended on the physical condition of the gun electrodes. With new electrodes, a flux ≥ 1.16 × 10¹³ particles s^?1 cm^?2 was obtained with nominal gun emission currents of 0.60–1.0 mA. Electrodes used extensively, but freshly cleaned, provided a flux of ～ 8 × 10¹² particles s^?1 cm^?2 at nominal emission currents of 0.40–1.0 mA. With dirty electrodes this flux could only be achieved at the highest (1.0 mA) emission current. This decline in performance occurs over a matter of months as a result of contamination and erosion of the electrodes during use. Such behavior can adversely affect spectral reproducibility even when nominal FAB gun voltage and emission current are carefully reproduced.     

Accurate quantum calculation of the bound and resonant rovibrational states of Li-(H2)

In a recent paper [B. Poirier, Chem. Phys. 308, 305 (2005)] a full-dimensional quantum method for computing the rovibrational dynamics of triatomic systems was presented, incorporating three key features: (1) exact analytical treatment of Coriolis coupling, (2) three-body "effective potential," and (3) a single bend angle basis for all rotational states. In this paper, these ideas are applied to the Li-(H2) electrostatic complex, to compute all of the rovibrational bound state energies, and a number of resonance energies and widths, to very high accuracy (thousandths of a wave number). This application is very challenging, owing to the long-range nature of the interaction and to narrow level spacings near dissociation. Nevertheless, by combining the present method with a G4 symmetry-adapted phase-space-optimized representation, only modest basis sizes are required for which the matrices are amenable to direct diagonalization. Several new bound levels are reported, as compared with a previous calculation [D. T. Chang, G. Surratt, G. Ristroff, and G. I. Gellene, J. Chem. Phys. 116, 9188 (2002)]. The resonances exhibit a clear-cut separation into shape and Feshbach varieties, with the latter characterized by extremely long lifetimes (microseconds or longer).     

Factors influencing the autoxidation of fatty acids: effect of olefin geometry of the nonconjugated diene

Autoxidations of cis,cis, cis,trans, and trans,trans nonconjugated octadecadienoates and pentadecadienes were carried out in the presence of alpha-tocopherol to investigate the effect of olefin geometry on this oxidation process and provide insight into the factors that influence the autoxidation of fatty acids. We have found that as the trans character of the diene increases, the amount of O(2) trapping at the central (bis-allylic) position of the pentadienyl radical also increases. In addition, the rate constant for beta-fragmentation (k(beta) approximately 10(6) s(-1)) of the bis-allylic peroxyl radical decreased on going from the cis,cis to the trans,trans diene. We have also found that for the cis,trans nonconjugated dienes, there is a preference for trapping of the pentadienyl radical by O(2) at the transoid end, generating the cis,trans conjugated hydroperoxide as the major product.     

Secondary bonding interactions in biomimetic [2Fe-2S] clusters

A series of synthetic [2Fe-2S] complexes with terminal thiophenolate ligands and tethered ether or thioether moieties has been prepared and investigated in order to provide models for the potential interaction of additional donor atoms with the Fe atoms in biological [2Fe-2S] clusters. X-ray crystal structures have been determined for six new complexes that feature appended Et (1(C)), OMe (1(O)), or SMe (1(S)) groups, or with a methylene group (2(C) ), an ether-O (2(O)), or an thioether-S (2(S)) linking two aryl groups. The latter two systems provide a constrained chelate arrangement that induces secondary bonding interactions with the ether-O and thioether-S, which is confirmed by density functional theory (DFT) calculations that also reveal significant spin density on those fifth donor atoms. Structural consequences of the secondary bonding interactions are analyzed in detail, and effects on the spectroscopic and electronic properties are probed by UV-vis, M?ssbauer, and (1)H NMR spectroscopy, as well by SQUID measurements and cyclic voltammetry. The potential relevance of the findings for biological [2Fe-2S] sites is considered.     

Fluxional processes in diamagnetic and paramagnetic allyl dicarbonyl and 2-methylallyl dicarbonyl molybdenum histidinato complexes as revealed by spectroscopic data and density functional calculations

This work describes a detailed study on the structure and dynamics of pseudooctahedral low-valent complexes of the type [Mo(His-N(epsilon)-R)(eta-2-R'-allyl)(CO)(2)] (His=N(delta),N,O-L-histidinate; R=H, R'=H (1); R=C(2)H(4)CO(2)Me, R'=H (2); R=H, R'=Me (3); R=C(2)H(4)CO(2)Me, R'=Me (4)). These diamagnetic 18-electron complexes were comprehensively characterized spectroscopically and by X-ray crystallography. In the solid state, the (substituted) allyl ligand is in an endo position in all compounds, but it is trans to the His-N(delta) atom in 1 and 2, whereas it is trans to the carboxylate O atom for the 2-Me-allyl compounds 3 and 4. In solution, both isomers are present in a solvent-dependent equilibrium. The third isomer (allyl trans to His-NH(2)) is not spectroscopically observed in solution. This is in agreement with the results from density functional (DFT) computations (BPW 91 functional) for 1 and 3, which predict a considerably higher energy (+6.3 and +5.9 kJ mol(-1), respectively) for this isomer. A likely path for isomerization is calculated, which is consistent with the activation energy determined by variable temperature NMR measurements. At least for 3, the preferred path involves several intermediates and a rotation of the 2-Me-allyl ligand. For the paramagnetic 17-electron congeners, DFT predicts the exo isomer of 3(+) with the 2-Me-allyl ligand trans to the carboxylate O atom to be by far the most stable isomer. For 1(+), an endo-exo equilibrium between the isomers with the allyl ligand trans to the carboxylate O atom is suggested. These suggestions are confirmed by EPR spectroscopy on the electrochemically generated species, which show signals for one- (4) and two- (2) metal-containing compounds. The appearance of the EPR spectra may be rationalized by inspection of the SOMOs from DFT calculations of the species in question. The notion of a metal-centered oxidation is also substantiated by IR spectroelectrochemistry and by UV/Vis spectra of the 17-electron complexes. Upon depleting the metal of electron density, the stretching vibrations of the carbonyl ligands shift more than 100 cm(-1) to higher wavenumbers, and the carbonyl vibration of the metal-coordinated carboxylate shifts by about 50 cm(-1). A color change from yellow to green upon oxidation is observed visually and quantified by the appearance of a new band at 622 nm (2(+)) and 546 nm (4(+)), respectively.