On signed graphs and gramians

Let A be a symmetric matrix with entries (0, 1, -1) and ¹(A) its smallest eigenvalue. We consider the question of how closely A–¹(A)I can be approximated by a gramian KK ^T , where each entry in K is 0, 1, or -1.This work was supported (in part) by the U.S. Army Research Office under Contract DAAG 29-74-C-0007.     

High-frequency and -field electron paramagnetic resonance of high-spin manganese(III) in tetrapyrrole complexes

High-field and -frequency electron paramagnetic resonance (HFEPR) spectroscopy has been used to study three complexes of high spin Manganese(III), 3d4, S = 2. The complexes studied were tetraphenylporphyrinatomanganese(III) chloride (MnTPPCI), phthalocyanatomanganese(III) chloride (MnPcCl), and (8,12-diethyl-2,3,7,13,17,18-hexamethylcorrolato)manganese(III) (MnCor). We demonstrate the ability to obtain both field-oriented (single-crystal like) spectra and true powder pattern HFEPR spectra of solid samples. The latter are obtained by immobilizing the powder, either in an n-eicosane mull or KBr pellet. We can also obtain frozen solution HFEPR spectra with good signal-to-noise, and yielding the expected true powder pattern. Frozen solution spectra are described for MnTPPCl in 2:3 (v/v) toluene/CH2Cl2 solution and for MnCor in neat pyridine (py) solution. All of the HFEPR spectra have been fully analyzed using spectral simulation software and a complete set of spin Hamiltonian parameters has been determined for each complex in each medium. Both porphyrinic complexes (MnTPPCl and MnPcCl) are rigorously axial systems, with similar axial zero-field splitting (zfs): D approximately -2.3 cm(-1), and g values quite close to 2.00. In contrast, the corrole complex, MnCor, exhibits slightly larger magnitude, rhombic zfs: D approximtely -2.6 cm(-1), absolute value(E) approximately 0.015 cm(-1), also with g values quite close to 2.00. These results are discussed in terms of the molecular structures of these complexes and their electronic structure. We propose that there is a significant mixing of the triplet (S = 1) excited state with the quintet (S= 2) ground state in Mn(III) complexes with porphyrinic ligands, which is even more pronounced for corroles.     

The electronic structure of FeV-cofactor in vanadium-dependent nitrogenase

The electronic structure of the active-site metal cofactor (FeV-cofactor) of resting-state V-dependent nitrogenase has been an open question, with earlier studies indicating that it exhibits a broad S = 3/2 EPR signal (Kramers state) having g values of ∼4.3 and 3.8, along with suggestions that it contains metal-ions with valencies [1V³⁺, 3Fe³⁺, 4Fe²⁺]. In the present work, genetic, biochemical, and spectroscopic approaches were combined to reveal that the EPR signals previously assigned to FeV-cofactor do not correlate with active VFe-protein, and thus cannot arise from the resting-state of catalytically relevant FeV-cofactor. It, instead, appears resting-state FeV-cofactor is either diamagnetic, S = 0, or non-Kramers, integer-spin (S = 1, 2 etc.). When VFe-protein is freeze-trapped during high-flux turnover with its natural electron-donating partner Fe protein, conditions which populate reduced states of the FeV-cofactor, a new rhombic S = 1/2 EPR signal from such a reduced state is observed, with g = [2.18, 2.12, 2.09] and showing well-defined ⁵¹V (I = 7/2) hyperfine splitting, a_iso = 110 MHz. These findings indicate a different assignment for the electronic structure of the resting state of FeV-cofactor: S = 0 (or integer-spin non-Kramers state) with metal-ion valencies, [1V³⁺, 4Fe³⁺, 3Fe²⁺]. Our findings suggest that the V³⁺ does not change valency throughout the catalytic cycle.

Active site FeV-cofactor of the V-nitrogenase and the EPR spectrum of the reduced cofactor showing ⁵¹V-hyperfine coupling.     

Synthesis of (r)- and (s)-1-formyl-6,7,8,9-tetrahydro- N,N-(dipropyl)-3H-benz[e]indol-8-amines: Potent and orally active 5-ht1a receptor agonists

An efficient synthesis of the potent and orally active 5-HT_1A agonists, (R)-(+)- and (S)-(-)-1-formyl-6,7,8,9-tetrahydro-N,N-dipropyl-3H-benz[e]indol-8-amines 1a and 1b , is described. This synthesis was accomplished in twelve steps from commercially available 1,5,6,7-tetrahydro-4H-indol-4-one ( 5 ). The key step involved a regio-controlled Friedel-Crafts acylation of 1-(p-toluenesulfonyl)indol-4-acetyl chloride with ethylene to yield a versatile synthon, 3-(p-toluenesulfonyl)-6,7,8,9-tetrahydro-3H-benz[e]indol-8-one ( 10 ). Subsequent coupling of this ketone with chiral α-methylbenzylamine under reductive amination conditions yielded a mixture of diastereomers. These diastereomers were efficiently separated by either chromatography or fractional recrystallization of the derived hydrochloride salts. Debenzylation of the pure diastereomers was followed by alkylation and formylation to yield (R)-(+)- and (S)-(-)-enantiomers 1a and 1b with >99% purity.     

Synthesis and structural characterization of integrally oxidized, metal-free phthalocyanine compounds: [H(2)(pc)][IBr(2)] and [H(2)(pc)](2)[IBr(2)]Br.C(10)H(7)Br

The first integrally oxidized metal-free phthalocyanine compounds have been synthesized by chemical oxidation. Phthalocyanine (H(2)(pc), pc = phthalocyaninato) was oxidized with IBr to afford the compounds [H(2)(pc)][IBr(2)] (1) and [H(2)(pc)](2)[IBr(2)]BrAC(10)H(7)Br (2), whose structures were determined by means of single-crystal X-ray diffraction methods: [H(2)(pc)][IBr(2)], P2(1)/c, a = 8.0272(9) A, b = 21.258(2) A, c = 18.1439(2) A, beta = 113.975(2) degrees, V = 2828.8(5) A(3), T = 153 K, Z = 4; [H(2)(pc)](2)[IBr(2)]Br.C(10)H(7)Br, P, a = 8.4724(6) A, b = 13.5794(10) A, c = 13.8403(10) A, alpha = 90.854(1) degrees, beta = 103.417(1) degrees, gamma = 97.049(1)E degrees, V = 1535.61(19) A(3), T = 153 K, Z = 1. The extended structure of [H(2)(pc)][IBr(2)] comprises slipped columns of pc rings stacked along the a axis in adjacent columns at approximately 70 degrees to one another. IBr(2-) ions occupy the interstitial columns. The extended structure of [H(2)(pc)](2)[IBr(2)]Br.C(10)H(7)Br comprises slant stacks of pc rings along the crystallographic a axis with IBr(2-) ions, Br(-) ions, and disordered 1-bromonaphthalene molecules in the adjacent, parallel columns. The overall reaction for the formation of 1 is 2H(2)(pc) + 4IBr --> 2[H(2)(pc)][IBr(2)] + I(2), and the overall reaction for the formation of 2 (not including solvent) is 2H(2)(pc) + 3IBr --> [H(2)(pc)](2)Br[IBr(2)] + I(2).     

The number oft-wise balanced designs

We prove that the number oft-wise balanced designs of ordern is asymptotically , provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by and above by for constants c₂>c₁>0.     

Optimal partitions having disjoint convex and conic hulls

LetA ¹,,A ⁿ be distinctk-dimensional vectors. We consider the problem of partitioning these vectors intom sets so as to maximize an objective which is a quasi-convex function of the sum of vectors in each set. We show that there exists an optimal partition whose sets have (pairwise) disjoint conic hulls. We also show that if the number of vectors in each of the sets is constrained, then a weaker conclusion holds, namely, there exists an optimal partition whose sets have (pairwise) disjoint convex hulls. The results rely on deriving necessary and sufficient conditions for a point to be an extreme point of a corresponding polytope.Research of this author was partially supported by NSF Grant ECS-83-10213 and by a Grant for the Promotion of Research at the Technion.     

Photophysics of ruthenium(II) complexes with 2-(2′-pyridyl) pyrimidine and 2,2′-bipyridine ligands in fluid solution

The photophysics of three complexes of the form Ru(bpy)₃₋(pypm)²⁺ (where bpy2,2′-bipyridine, pypm 2-(2′-pyridyl)pyrimidine and P=1, 2 or 3) was examined in H₂O, propylene carbonate, CH₃CN and 4:1 (v/v) C₂H₅OH---CH₃OH; comparison was made with the well-known photophysical behavior of Ru(bpy)₃²⁺. The lifetimes of the luminescent metal-to-ligand charge transfer (MLCT) excited states were determined as a function of temperature (between −103 and 90 °C, depending on the solvent), from which were extracted the rate constants for radiative and non-radiative decay and ΔE, the energy gap between the MLCT and metal-centered (MC) excited states. The results indicate that ^*Ru(bpy)₂(pypm)²⁺ decays via a higher lying MLCT state, whereas ^*Ru(pypm)₃²⁺ and ^*Ru(pypm)₂(bpy)²⁺ decay predominantly via the MC state.