Differential geometry of edgeworth expansions in curved exponential family

Summary In order to construct a higher-order asymptotic theory of statistical inference, it is useful to know the Edgeworth expansions of the distributions of related statistics. Based on the differential-geometrical method, the Edgeworth expansions are performed up to the third-order terms for the joint distribution of any efficient estimators and complementary (approximate) ancillary statistics in the case of curved exponential family. The marginal and conditional distributions are also obtained. The roles and meanings of geometrical quantities are elucidated by the geometrical interpretation of the Edgeworth expansions. The results of the present paper provide an indispensable tool for constructing the differential-geometrical theory of statistics.     

A tin-complexation strategy for use with diverse acylation methods in the preparation of 1,9-diacyldipyrromethanes

The acylation of dipyrromethanes to form 1,9-diacyldipyrromethanes is an essential step in the rational synthesis of porphyrins. Although several methods for acylation are available, purification is difficult because 1,9-diacyldipyrromethanes typically streak extensively upon chromatography and give amorphous powders upon attempted crystallization. A solution to this problem has been achieved by reacting the 1,9-diacyldipyrromethane with Bu(2)SnCl(2) to give the corresponding dibutyl(5,10-dihydrodipyrrinato)tin(IV) complex. The reaction is selective for dipyrromethanes that bear acyl groups at both the 1- and 9-positions but otherwise is quite tolerant of diverse substituents. The diacyldipyrromethane-tin complexes are stable to air and water, are highly soluble in common organic solvents, crystallize readily, and chromatograph without streaking. Four methods (Friedel-Crafts, Grignard, Vilsmeier, benzoxathiolium salt) were examined for the direct 1,9-diacylation of a dipyrromethane or the 9-acylation of a 1-acyldipyrromethane. In each case, treatment of the crude reaction mixture with Bu(2)SnCl(2) and TEA at room temperature enabled facile isolation of multigram quantities of the 1,9-diacyldipyrromethane-tin complex. The diacyldipyrromethane-tin complexes could be decomplexed with TFA in nearly quantitative yield. Alternatively, use of a diacyldipyrromethane-tin complex in a porphyrin-forming reaction (reduction with NaBH(4), acid-catalyzed condensation with a dipyrromethane, DDQ oxidation) afforded the desired free base porphyrin in yield comparable to that obtained from the uncomplexed diacyldipyrromethane. The acylation/tin-complexation strategy has been applied to a bis(dipyrromethane) and a porphyrin-dipyrromethane. In summary, the tin-complexation strategy has broad scope, is compatible with diverse acylation methods, and greatly facilitates access to 1,9-diacyldipyrromethanes.     

9-Acylation of 1-acyldipyrromethanes containing a dialkylboron mask for the alpha-acylpyrrole motif

1,9-Diacyldipyrromethanes are important precursors to porphyrins, yet synthetic access remains limited owing to (1) poor conversion in the 9-acylation of 1-acyldipyrromethanes and (2) handling difficulties because acyldipyrromethanes typically streak upon chromatography and give amorphous powders upon attempted crystallization. A reliable means for converting a dipyrromethane to a 1-acyldipyrromethane-dialkylboron complex was recently developed, where the dialkylboron (BR(2)) unit renders the complex hydrophobic and thereby facilitates isolation. Herein a refined preparation of 1,9-diacyldipyrromethanes is presented that employs the 1-acyldipyrromethane-BR(2) complex as a substrate for 9-acylation. The dialkylboron unit provides protection for the alpha-acylpyrrole unit. 9-Acylation requires formation of the pyrrolyl-MgBr reagent and the presence of 1 equiv of a nonnucleophilic base to quench the proton liberated upon alpha-acylation. Reaction of the 1-acyldipyrromethane-BR(2) complex (1 equiv) with mesitylmagnesium bromide (2 equiv) followed by the addition of an acylating agent (S-2-pyridyl thioate or acid chloride, 1.1 equiv) gives the corresponding 1,9-diacyldipyrromethane-BR(2) complex. The acylation method afforded 1,9-diacyldipyrromethane-BR(2) complexes with limited or no chromatography in yields of 64-92%. The 1,9-diacyldipyrromethane-BR(2) complexes are stable to routine handling, are readily soluble in common organic solvents, crystallize readily, and can now be prepared in multigram quantities through use of stoichiometric quantities of reagents.     

Spectroscopic study of water-NaCl-benzene mixtures at high temperatures and pressures

Near-infrared and ultraviolet spectra of water-NaCl-benzene mixtures have been measured in the 473-573 K and 100-400 bar range and 373-498 K and 50-300 bar range, respectively. Concentrations of water in the benzene-rich phase and benzene in the water-rich phase were estimated from integrated intensities of the absorption bands. It is found that addition of NaCl in the aqueous phase suppresses transfer of water into the benzene-rich phase, and the relative decrease in water solubility in benzene exhibits good correlation with an increase in density of the aqueous NaCl solution relative to that of neat water. The salting-out constant for the water-NaCl-benzene system, which is estimated from a relative decrease in benzene solubility in the aqueous phase by addition of sodium chloride, increases significantly with increasing temperature. It is suggested that the effect of sodium chloride on the water-benzene mutual solubilities can be explained by ion-induced electrostriction of the aqueous phase.     

Structure of the jet-cooled 1-naphthol dimer studied by IR dip spectroscopy: cooperation between the pi-pi interaction and the hydrogen bonding

The structure of a jet-cooled 1-naphthol (1-NpOH) dimer was investigated by using resonant-enhanced two-photon ionization (R2PI) and ion-detected infrared (IR) dip spectroscopy. A geometrical optimization and a frequency calculation in (1-NpOH)2 were also performed at the MP2/cc-pVDZ level. Stable isomers in the MP2/cc-pVDZ calculation were classified into a structure dominated only by the pi-pi interaction and structures formed by cooperation between the pi-pi interaction and hydrogen bonding. On the basis of a comparison between the observed and calculated IR spectra, the geometry of (1-NpOH)2 was concluded to be a pi-pi stacking structure supported by hydrogen bonding.     

Lewis acidity/basicity of pi-electron systems: theoretical study of a molecular interaction between a pi system and a Lewis acid/base

Molecular interactions between pi systems having different pi-electron character (benzene, hexafluorobenzene, and borazine), and a Lewis acid/base (borane and ammonia) were theoretically studied. An attractive interaction between benzene, the electron-rich pi system, and borane was observed. On the other hand, repulsive interactions between benzene and ammonia was observed when the lone pair of nitrogen points toward the benzene ring. In contrast, an attractive interaction between hexafluorobenzene, an electron-deficient pi system, and ammonia was observed. Unexpectedly, a weak attractive interaction between hexafluorobenzene and borane was also observed. Borazine shows an interaction both to borane and ammonia. The attraction between the nitrogen atom of borazine and borane was larger than that between the boron atom of borazine and ammonia.     

Catalytic asymmetric synthesis of binaphthol derivatives by aerobic oxidative coupling of 3-hydroxy-2-naphthoates with chiral diamine-copper complex

Asymmetric aerobic oxidative coupling of 3-hydroxy-2-naphthoate with a copper complex prepared in situ from chiral diamine 3 and cuprous chloride as catalyst afforded binaphthol derivatives in good enantioselectivities up to 73% ee.     

Ruthenium-catalyzed oxidative cyanation of tertiary amines with molecular oxygen or hydrogen peroxide and sodium cyanide: sp3 C-H bond activation and carbon-carbon bond formation

Ruthenium-catalyzed oxidative cyanation of tertiary amines with molecular oxygen in the presence of sodium cyanide and acetic acid gives the corresponding alpha-aminonitriles, which are highly useful intermediates for organic synthesis. The reaction is the first demonstration of direct sp(3) C-H bond activation alpha to nitrogen followed by carbon-carbon bond formation under aerobic oxidation conditions. The catalytic oxidation seems to proceed by (i) alpha-C-H activation of tertiary amines by the ruthenium catalyst to give an iminium ion/ruthenium hydride intermediate, (ii) reaction with molecular oxygen to give an iminium ion/ruthenium hydroperoxide, (iii) reaction with HCN to give the alpha-aminonitrile product, H2O2, and Ru species, (iv) generation of oxoruthenium species from the reaction of Ru species with H2O2, and (v) reaction of oxoruthenium species with tertiary amines to give alpha-aminonitriles. On the basis of the last two pathways, a new type of ruthenium-catalyzed oxidative cyanation of tertiary amines with H2O2 to give alpha-aminonitriles was established. The alpha-aminonitriles thus obtained can be readily converted to alpha-amino acids, diamines, and various nitrogen-containing heterocyclic compounds.