Partitioning Boolean lattices into chains of subsets

We prove that the Boolean lattice of all subsets of an n-set can be partitioned into chains of size four if and only if n9.Research supported in part by N.S.F. grant DMS-8401281.Research supported in part by N.S.F. grant DMS-8406451.     

Thermodynamics of the dissociation of 2-aminopyridinium ion in synthetic seawater and a standard for pH in marine systems

Buffer solutions composed of 2-aminopyridinium chloride and 2-aminopyridine in synthetic seawater are useful as a supplement to buffers of Tris (pH 8.2) and Bis (pH 8.8) in standardizing measurements of hydrogen ion concentration (pm _H or pH(SWS)) in oceanography. The dissociation constant of 2-amino-pyridinium ion over the range of salinities (S) from 30 to 40 has now been determined from the emf of cells without liquid junction at eight temperatures (T) from 278.15 to 313.15 K. The results fit the equation pK=2498.31/T–15.3274+2.4050 lnT+S(0.012928–2.9417×10^–5T) with a standard deviation of 0.0023. Thermodynamic constants for the dissociation process and standard reference values of pm _H and pH(SWS) were derived from the data. The pm _H of the buffer consisting of 2-aminopyridinium chloride and 2-aminopyridine (each 0.04 molal) in synthetic seawater of salinity 35 varies from 7.356 at 278.15 K to 6.601 at 313.15 K.     

Synthesis and structural, spectroscopic and magnetic studies of two new polymorphs of Mn(SeO3)·H2O

Two new manganese(II) selenite polymorphs with formula Mn(SeO₃)·H₂O have been synthesized by slow evaporation from an aqueous solution. The crystal structure of both compounds (1) and (2) have been solved from X-ray diffraction data. The structure of (1) was determined from single-crystal X-ray diffraction techniques. The compound crystallizes in the Ama2 space group, with a=5.817(1), b=13.449(3), and Z=4. The structure of (2) has been solved from X-ray powder diffraction data. This phase crystallizes in the P2₁/n space group with unit-cell parameters of a=4.921(3), b=13.121(7), , β=90.03(2)° and Z=4. Both polymorphs exhibit a layered structure formed by isolated sheets of MnO₆ octahedra and (SeO₃)²⁻ trigonal pyramids in the (010) plane. These layers, which contain one manganese and selenium atom crystallographically independent, are formed by octahedra linked between them through the selenite oxoanions. The difference of both compounds consists in the stacking of the layers along the b-axis. The IR spectra show the characteristic bands of the selenite anion. Studies of luminescence performed at 6 K and diffuse reflectance spectroscopy have been carried out for both phases. The Dq and Racah (B and C) parameters, from luminescence and diffuse reflectance spectroscopy, are Dq=705, B=750, for (1) and Dq=720, B=745, for (2). The ESR spectra of both compounds are isotropic with g-values of 1.99(1). Magnetic measurements indicate the presence of antiferromagnetic couplings in both phases. The J-exchange parameters have been estimated by fitting the experimental magnetic data to a model for square-planar lattice. The values obtained are J/k=-0.83, −0.91 K and J^′/k=-0.97, −1.20 K, for polymorphs (1) and (2), respectively.     

Reactions of Molecules with Two Equivalent Functional Groups. 5. Anomalous Reactivity of 1,10-Cyclooctadecanedione. Crystal and Molecular Structures of cis,cis-1,10-Diphenyl-1,10-cyclooctadiene and the Stereoisomers of 1,10-Diphenyl-1,10-cyclooctadecanediol(1)

The reaction of the title diketone (3) with phenyl Grignard produces (with rate constant k(1)) the conjugate base (6-M) of 10-hydroxy-10-phenylcyclooctadecanone (6), which is subsequently converted (with rate constant k(2)) to the conjugate base of the title diol, as a mixture of the cis (7, 55%) and trans (8, 45%) isomers. The ratio k(2)/k(1), 2.2 +/- 0.4, indicates that the carbonyl group in 6-M is 4.4 times as reactive as each carbonyl in 3. Competition experiments further demonstrate that the relative rates (per carbonyl) for addition of phenylmagnesium bromide to 3, 10-methylenecyclooctadecanone (11), and cyclopentadecanone (12) are 1.0:0.60:1.92. Possible reasons for this order of reactivity are discussed. Diols 7 and 8 undergo facile double dehydration to form the title diene 13, which is predicted by molecular mechanics calculations to be the most stable of the four possible symmetrical diene isomers. The structures of 7, 8, and 13 were secured by single-crystal X-ray studies.     

Surface chemistry studies of (CdSe)ZnS quantum dots at the air-water interface

Trioctylphosphine oxide- (TOPO-) capped (CdSe)ZnS quantum dots (QDs) were prepared through a stepwise synthesis. The surface chemistry behavior of the QDs at the air-water interface was carefully examined by various physical measurements. The surface pressure-area isotherm of the Langmuir film of the QDs gave an average diameter of 4.4 nm, which matched very well with the value determined by transmission electron microscopy (TEM) measurements if the thickness of the TOPO cap was counted. The stability of the Langmuir film of the QDs was tested by two different methods, compression/decompression cycling and kinetic measurements, both of which indicated that TOPO-capped (CdSe)ZnS QDs can form stable Langmuir films at the air-water interface. Epifluorescence microscopy revealed the two-dimensional aggregation of the QDs in Langmuir films during the early stage of the compression process. However, at high surface pressures, the Langmuir film of QDs was more homogeneous and was capable of being deposited on a hydrophobic quartz slide by the Langmuir-Blodgett (LB) film technique. Photoluminescence (PL) spectroscopy was utilized to characterize the LB films. The PL intensity of the LB film of QDs at the first emission maximum was found to increase linearly with increasing number of layers deposited onto the hydrophobic quartz slide, which implied a homogeneous deposition of the Langmuir film of QDs at surface pressures greater than 20 mN.m(-1).     

Über Pterinchemie. 79. Mitteilung. 13C-und 15N-NMR.-spektroskopische Untersuchungen an der (6RS)-5, 10-Methylen-5, 6, 7, 8-tetrahydro-L-folsäure; eindeutiger Beweis ihrer Struktur

¹³C- and ¹⁵N-NMR.-Spectroscopic Studies on (6RS)-5, 10-Methylene-5, 6, 7, 8-tetrahydro-L -folic Acid; Unequivocal Proof of thier Structure The existence of a 5, 10-methylene bridge in the title compound has been established with the help of ¹⁵N-NMR, and ¹³C-NMR. spectroscopy. The simultaneous coupling of ¹³C(11) with ¹⁵N(5) and ¹⁵N(10) proves that C(11) must be bound as a methylene bridge to both N-atoms. Some other aspects of the NMR. spectra of the compound are discussed. Synthesis of the title product with the label ¹⁵N is described.     

Myoglobin-CO substate structures and dynamics: multidimensional vibrational echoes and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.     

Deoxy-nitrosugars 12th communication Synthesis of isosteric mono-phosphonate analogues of β-and α-D-fructose 2,6-bisphosphate

A synthesis of the isosteric mono-phosphonate analogues 2a and 19 of the β-and α-D -fructose 2,6-bisphosphate, respectively, is described. Chain elongation of the 1-deoxy-1-nitro-D -arabinose 3 (Scheme 1) by a Henry reaction with paraformaldehyde followed by protection of the resulting alcohol (methoxymethyl ether) and a radical-chain substitution by nitromethane anion gave the key intermediates, the gluco-anhydroalditol 6 and the manno-anhydroalditol 7 . These products equilibrated under basic conditions. Conversion of 7 to the aldehyde 9 , Abramov reaction of 9 with diphenyl phosphite followed by deoxygenation according to Barton gave the phosphonate 11 (Scheme 2). Selective hydrogenolysis of 11 , phosphorylation and deprotection gave 2 which was converted to the tetrasodium salt 2a . Similarly, 6 was transformed into the isosteric phosphonate analogue 19 of the α-D -fructose 2,6-bisphosphate (Scheme 3).     

Uranium-sulfilimine chemistry. The preparation of Cp2*UCl2(HNSPh2) and its hydrolysis with HNSPh2 · H2O

The reaction of Cp₂*UCl₂ with HNSPh₂ produces Cp₂*UCl₂(HNSPh₂), which is the first structurally characterized complex of a sulfilimine. The hydrolysis of Cp₂*UCl₂(HNSPh₂) with HNSPh₂ · H₂O yields a tetrauranium cluster whose heavy atom structure has been determined by x-ray diffraction and which is formulated as a U^IV/U^V complex: [Cp*(Cl)(HNSPh₂)U(μ₃-O)(μ₂-O)₂U(Cl)(HNSPh₂)₂]₂.     

Fragmentation of Homoallylic Alkoxides. Preparation of 1-(3′-cyclopentenyl)-2-alkanones from 2-substituted bicyclo[2.2.1]hept-5-en-2-ols

The potassium 2-substituted bicyclo[2.2.1]hept-5-en-2-alkoxides derived from alcohols 2–9 at 30° in hexamethylphosphoric triamide (HMPA) afford 1-(3′-cyclopentenyl)-2-alkanones 10–19 via heterolytic C(1), C(2)-allylic bond cleavage in the substrate alkoxide followed by intramolecular protonation of the resultant transient allylic anion.