Bounds for rectilinear crossing numbers

A rectilinear drawing of a graph is one where each edge is drawn as a straight-line segment, and the rectilinear crossing number of a graph is the minimum number of crossings over all rectilinear drawings. We describe, for every integer k ≥ 4, a class of graphs of crossing number k, but unbounded rectilinear crossing number. This is best possible since the rectilinear crossing number is equal to the crossing number whenever the latter is at most 3. Further, if we consider drawings where each edge is drawn as a polygonal line segment with at most one break point, then the resulting crossing number is at most quadratic in the regular crossing number. © 1993 John Wiley & Sons, Inc.     

Unusually sharp dependence of water exchange rate versus lanthanide ionic radii for a series of tetraamide complexes

The tetraamide ligand, DOTA-tetra(glycine ethyl ester), forms complexes with the lanthanide(III) cations that exist in solution predominantly as the square antiprism structure with single, slowly exchanging inner-sphere water molecule. Variable-temperature 1H and 17O NMR studies revealed that the bound water lifetimes in these complexes were sharply dependent upon the ionic radius of Ln3+ cation. A novel lanthanide-induced shift technique was used to unmask the bound water 17O resonance of SmL3+ and YL3+ complexes from the bulk water resonance. The bound water lifetime (tauM298) was approximately 800 mus in the EuL3+ complex but became much shorter (several microseconds) for Ln3+ cations with larger and smaller ionic radii. This demonstrates that water exchange is exquisitely fine-tuned in this macrocyclic tetraamide system and that a variety of Ln3+ complexes meet with the exchange requirement, Deltaomega*tauM >/= 1, necessary for an efficient MT agent.     

Synthesis and structural characterization of acetatobis(triphenylphosphine)dicarbonylmanganese(I), (CH3CO2)Mn(CO)2[P(C6H5)3]2: An organometallic complex containing a chelating acetate ligand

The accidental but intriguing synthesis of acetatobis(triphenylphosphine)dicarbonylmanganese(I), (CH₃CO₂)Mn(CO)₂[P(C₆H₅)₃]₂, has been accomplished by the reaction of NaMn(CO)₅ with (CH₃)₃SiCl followed by the addition of triphenylphosphine and acetic acid. A three-dimensional single-crystal X-ray diffraction analysis has shown an octahedral-like molecule containing a symmetrically oxygen-chelating acetate group, the first such group to be reported in a metal carbonyl complex. The two triphenylphosphine ligands occupy mutually trans positions with the two carbonyl ligands possessing the remaining cis sites in the octahedral complex. The compound crystallizes with four molecules in a monoclinic unit cell of space group symmetry $\text{P}\text{2}{}_1\text{c}$ and of dimensions a = 17.744(2) Å, b = 9.692(1) Å, c = 20.004(2) Å, and β = 106.195(4)°. The relatively long MnO(acetate) bond lengths [2.066(6) and 2.069(7) Å] and the relatively short MnCO bond lengths [1.701(12) and 1.760(13) Å] and the relatively short MnP(C₆H₅)₃ bond lengths [2.260(3) and 2.275(3) Å], compared to the corresponding MnCO and MnP(C₆H₅)₃ bond lengths in other manganese carbonyl triphenylphosphine complexes, are rationalized on the basis that the acetate ligand in this molecule functions primarily as a σ-donor.     

Syntheses of seven-membered rings: ruthenium-catalyzed intramolecular [5+2] cycloadditions

The Ru-catalyzed intramolecular [5+2] cycloaddition of cyclopropylenynes is investigated with respect to the regio- and diastereoselectivity as well as the functional group compatibility of the reaction. Evidence for the mechanism as occurring through a ruthenacyclopentene intermediate is elucidated from 1) the study of the diastereoselectivity of the cycloaddition; 2) the effect of variation of substituents on the regioselectivity of cyclopropyl bond cleavage in 1,2-trans- and 1,2-cis-disubstituted cyclopropanes and 3) examples that clearly do not involve ruthenacyclohexene as intermediates as products still incorporate the cyclopropyl moiety. The scope and limitations of the Ru-catalyzed cycloaddition are discussed and compared with the Rh-catalyzed reaction. The potential power of this methodology towards natural product total synthesis is demonstrated by the formation of several polycyclic systems with the chosen reaction conditions and readily available cyclopropylenyne substrates.     

Evidence against the occurrence of artifacts due to carrier ampholyte-protein binding during isoelectric focusing.

The formation of irreversible complexes between carrier ampholyte components and proteins was investigated by gel filtration of mixtures of proteins and radioactively labelled ampholytes. Experiments were performed both with purified proteins (albumin, ferritin, beta-glucuronidase) and with a complex mixture of proteins (serum); in no case was binding of ampholytes to proteins detected. Thus the results argue against the occurrence in isoelectric focusing of proteins of artifacts due to such complex formation.     

The partial hydrogenation of small unsaturated molecules by osmium cluster compounds. The reaction of diispropylcarbodiimide with H2Os3(CO)10

The products (μ-H)[μ-η²-(CH₃)₂CHNHCNCH(CH₃)₂]Os₃(CO)₁₀, I, and (μ-H)- [μ-η²-(CH₃)₂CHNHCO]Os₃(CO)₉[CNCH(CH₃)₂], II have been obtained from the reaction of H₂Os₃(CO)₁₀ with diisopropylcarbodiimine. Both products have been investigated by infrared and ¹H NMR spectroscopies, and by single crystal X-ray diffraction analyses. For I: Space group, P2₁/c, a12.840(4), b  15.724(4), c 12.638(4) Å, β 106.91(2)°, V  2441(2) ų, Z4, ? calc  2.66 g/cc. For 2869 reflections, R  0.051 and R_w  0.052. I contains an N-hydrido, N-isopropylamidinyl ligand bridging one edge of a triangular cluster of three osmium atoms. It was apparently formed by the incorporation of one carbodiimide molecule into the coordination sphere of the cluster followed by the transfer of one hydride ligand to one of the nitrogen atoms. For II: Space group P2 ₁/n;a  13.936(7), b  12.146(2), c  15.509(6) Å, β  105.20(4)°, V  2533(3) Å, Z  4, ?calc  2.57 g/cc. For 3065 reflections, R  0.052 and R_w  0.057. II contains an N-hydrido, N-isopropylformamido ligand bridging one edge of a triangular cluster of three osmium atoms and an isopropylisocyanide ligand. The molecule appears to have been formed by the cleavage of an NCH(CH₃)₂ moeity from one carbodiimide molecule and the transfer of it together with one hydride ligand to the carbon atom of a carbonyl group. The resultant formamido ligand bridges an edge of the cluster. The remaining fragment of the carbodiimide molecule bonds to one of the metal atoms of the cluster as a terminal isocyanide ligand. When heated, I loses one mole of carbon monoxide and forms the new cluster complex (μ-H)[μ₃-η²-(CH₃)₂CHNHCNCH-(CH₃)₂]Os₃(CO)₉ III. On the basis of electron counting schemes, III is believed to contain a triply-bridging amidinyl ligand serving as a five electron donor. Most importantly, no II was formed from I indicating that it is not a precursor -to II. A mechanism for the formation of I and II is presented and discussed.     

The influence of chemical composition on models of Type Ia supernovae

Type Ia supernovae are bright stellar explosions distinguished by standardizable light curves that allow for their use as distance indicators for cosmological studies. Despite the highly successful use of these events in this capacity, many fundamental questions remain. Contemporary research investigates how properties of the progenitor system that follow from the host galaxy such as composition and age influence the brightness of an event with the goal of better understanding and assessing the intrinsic scatter in the brightness. We provide an overview of these supernovae and proposed progenitor systems, all of which involve one or more compact stars known as white dwarfs. We describe contemporary research investigating how the composition and structure of the progenitor white dwarf systematically influences the explosion outcome assuming the progenitor is a single white dwarf that has gained mass from a companion. We present results illustrating some of these systematic effects from our research.