Chemical potential for harmonically interacting particles in a harmonic potential

The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin-½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.     

Triphenyl verdazyl radicals’ reactivity with alkyne carboxylates as a synthetic route to 1-(phenyldiazenyl)isoquinoline-3,4-dicarboxylates

A series of 1-(phenyldiazenyl)isoquinoline-3,4-dicarboxylates are synthesized by a unique reaction of triphenyl verdazyl radical with di-substituted electron deficient alkyne carboxylates. This transformation allows for the quick synthesis of this class of compounds in just three steps starting from a hydrazone. A radical mechanism that is consistent for the substitution patterns observed in the series of compounds made is proposed. The final product is obtained by a subsequent retro-Diels-Alder reaction.     

A Facile Syntheses of 6-Bicyclo[3.2.1]octanones

Copper oxide-catalyzed decomposition of 1-diazoacetyl-1-methyl-3-methylenecyclohexanes produces strained tricycles whose reduction or hydrolysis affords 6-bicyclo[3.2.1]octanones.     

SR XRF and micro-PIXE studies on ancient metallurgy of thirteen Dacian gold bracelets

A thorough microscopic investigation by SR XRF and micro-PIXE brings insight into the probable techniques used in the manufacture of thirteen Dacian gold bracelets, one of the most spectacular archaeological finds ever on the territory of Romania.     

2-Oxocephems. Synthesis and Properties of 7-Acylamino-2-oxocephem-4-carboxylic Acids

A synthesis of (6 R, 7 R)-7-acylamino-2-oxocephem-4-carboxylic acids from penicillins is reported based on the formation of the 2-oxocephem system in an intramolecular Wittig condensation. An interesting steric effect of the acylamino grouping on the course of this key step was used to advantage. Some physical and biological properties of this new type of Δ³-cephem are described.     

Theoretical invstigations of the electronic states of porphyrins. I. Basis set development and predicted spectrum of pyrrole

A new minimum basis set was developed for use in computing excitation energies of large molecules. It is particularly suited to calculating ionization potentials and Rydberg transitions. Pyrrole excitation energies and oscillator strengths calculated with this basis set are compared to larger basis set ab initio and semiempirical results. The 6-eV band in the experimental spectrum is predicted to be the result of three Rydberg absorptions, with no underlying (π, π*) absorption. The calculations also provide an explanation for the observed N? H stretch in the 6-eV region.     

Determination of rotational barriers of carbon?carbon bonds in 2-arylpiperidines

Carbon-carbon sp³-sp² rotational barriers of 3,3-dimethyl-2-(3,4,5-trimethoxyphenyl)-4-piperidones and their ethylene ketals have been evaluated using nmr techniques. The conformation of 1 hydrochloride has been studied by NOE determinations. Values found for the hydrochlorides of the title compounds are discussed in terms of equilibria with free bases and nitrogen inversion.     

A theorem of Cohen on parapolar spaces

We give an elementary proof of a critical lemma of Arjeh Cohen used in his fundamental paper giving an axiomatic characterization of Grassmann spaces of finite singular rank.