Preparation of cyclopentadienes and diazocyclopentadienesvia cyclopentenolones and cyclopentenones

The structure and stereochemistry of the cyclopentenolones obtained by condensation of dialkyl ketones with benzil have been studied by NMR spectroscopy. These enolones were converted into cyclopentenones and cyclopentadienes. Alkyl-substituted cyclopentadienes required phenyllithium to effect their conversion by toluenesulphonyl azide into diazo-cyclopentadienes; otherwise piperidine sufficed as base catalyst.2,3,4-Triphenyldiazocyclopentadiene was simply procured by reaction of the condensation product of benzil and phenylacetone with toluenesulphonylhydrazone followed by alkali. Cyclohexyl- and methoxy-triphenylcyclopentadienes were prepared by photolytic decomposition of diazotriphenylcyclopentadiene in cyclohexane or methanol respectively.     

Sign changes in the prime number theorem

The Ramanujan Journal - Let V(T) denote the number of sign changes in $$\psi (x) - x$$ for $$x\in [1, T]$$ . We show that $$\liminf _{T\rightarrow \infty } V(T)/\log T\ge \gamma _{1}/\pi +...     

Triplet excition emissions of octafluoronaphthalene crystalline complexes with naphthalene and durene

The phosphorescence spectra of naphthalene-octafluoronaphthalene and durene-octafluoronaphthalene at 4.2 K reveal a localized exciton emission from octafluoronaphthalene, a weak intercomponent triplet-states quasi-resonance and a weak exciton-phonon coupling.     

Ligand dynamics and reactivity in trimetallic clusters

The general relationships between trinuclear cluster reactivity and the ligand dynamical processes in these systems are explored. Three specific mechanistic studies are presented: (1) the rate and stereochemistry of ligand addition to ₃-imidoyl complexes, (2) the factors influencing the rate of carbon-hydrogen bond activation in ₃-alkyne complexes, and (3) the origin of anomalously large kinetic deuterium isotope effect in metal to ligand and ligand to metal hydrogen transfer in trinuclear and binuclear complexes. In all three cases, the current state of the mechanistic studies are summarized and the possible rate of specific ligand dynamical processes in controlling the mechanism are put forth.