Allowed and forbidden d-d transitions in poly(3,5-dimethylpyrazolyl)methane complexes of nickel(II)

Absorption spectra of four nickel(II) complexes with poly(pyrazolyl)methane ligands are presented in the NIR-VIS-UV region and the band system corresponding to the lowest-energy spin-allowed and spin-forbidden transitions is analyzed. A quantitative theoretical model involving coupled electronic states provides precise energies for the lowest-energy triplet and singlet excited states and allows comparisons between complexes with a variable number of nitrogen and oxygen ligator atoms. Singlet energies between 12,840 and 13,000 cm(-1) are determined for heteroleptic complexes. These energies are in an intermediate range between those for homoleptic complexes with either nitrogen or oxygen ligator atoms with singlet states at approximately 12,000 and 14,000 cm(-1), respectively. The new theoretical approach is compared to the traditional ligand-field parameters obtained from the maxima of the broad, spin-allowed absorption bands.     

Reduction of diesters of 1,2-diols. Regioselective C-O bond cleavage of the anionic forms

The electrochemical reduction of benzoate diesters of glycols has been studied in acetonitrile and N,N-dimethylformamide as solvents. The reductions occur in two closely spaced one-electron steps, and it was found that the dianion diradicals decompose by one of two routes, depending on the substituents on the ethylene moiety: cleavage of two benzoates to produce alkene or formation of benzil by way of a postulated cyclic intermediate to produce also the dianion of the diol. These correspond to cleavage of the R-OC(O)Ar bonds and the RO-C(O)Ar bonds, respectively. When the radical formed by the former cleavage is a primary or secondary radical, the reaction is too slow to compete with the latter reaction that produces benzil. However, when that radical is either tertiary or benzylic, the former cleavage reaction is fast and no benzil is detected. The dianions of p-cyano- and p-nitrobenzoate esters are rather stable on the voltammetric time scale. However, the addition of lithium ions results in detectable formation of 4,4'-dicyanobenzil from four different p-cyanobenzoate diesters.     

Doubly transitive automorphism groups of block designs

If G is a doubly transitive group of automorphisms of a block design with λ = 1, then for any block Δ of the design and any point α in Δ, the set Δ?{α} is a block of imprimitivity for G_α. What are sufficient conditions for a doubly transitive but not doubly primitive permutation group G to be a group of automorphisms of a non-trivial block design with λ = 1 ? Can the design or the group G be identified if there is a nonidentity automorphism in G fixing every point of some block of the design? Both of these questions are investigated and some answers are given.     

Uniaxial and biaxial extensional viscosity measurements of dilute and semi-dilute solutions of rigid rod polymers

Effective uniaxial extensional and biaxial extensional viscosities of dilute and semi-dilute solutions of collagen, a rigid rod molecule, have been measured with an opposing jet apparatus. The concentration of collagen in the glycerin/water solvent ranged from 50 to 2300 ppm. The data agree quantitatively with a theory developed by Batchelor describing the extensional viscosity of perfectly aligned rigid rods. The viscosity measured for the dilute rigid rod solutions is independent of the rate of strain as predicted by Batchelor's theory. Data taken on the semi-dilute, strain-thinning solutions at strain rates sufficiently high to align the rods in the extension direction also agree with the predictions of Batchelor's theory. The measured viscosity of semi-dilute solutions at low strain rates agree qualitatively with a theory developed by Doi and Edwards describing the strain-thinning behavior of semi-dilute rigid rod solutions.     

Note on primitive permutation groups and a diophantine equation

It is shown that there are no transitive rank 3 extensions of the projective linear groups H, PSL(m,q) ? H ? PFL(m,q), for any prime power q and integer m ? 3. In the course of the proof the diophantine equation 5^m + 11 = x^p2, where m, x are positive integers, arose. As such equations can now be solved completely we had the choice of using number theory or geometry to complete the proof.     

Reaction of nitrenes with strained olefins. Preparation and reactions of some 6-azabicyclo[3.1.0]hexanes

A number of examples of the 6-azabicycIo[3.1.0]hexane ring system have been prepared by the oxidation of N-aminophthalimide or 3-amino-2-methyl-4-quinazoIone with lead tetraacetate in the presence of variously substituted cyclopentenes. Thus, 6-phthalimidyl-6-azabicyclo[3.1.0]hexane, dimethy 1–6-phthalimidyl-6-azabicyclo[3.1.0]-hexane-1,5-dicarboxylate, 2,3-benzo-6-phthalimidyl-6-azabicycIo[3.1.0]hexane and N-3-(2-methyl-4-quinazolyl)-6-azabicyclo [3.1.0]hexane were prepared for the first time. All of the new compounds were found to be stable in refluxing carbon tetrachloride and chlorobenzene. Refluxing 6-phthalimidyl-6-azabieyclo[3,1.0]hexane in acetic acid for 24 hours resulted in quantitative rearrangement to a phthalohydrazide, 8 .