Sigmatropic rearrangements in 5-allyloxytetrazoles

Mechanisms of thermal isomerization of allyl tetrazolyl ethers derived from the carbocyclic allylic alcohols cyclohex-2-enol and 3-methylcyclohex-2-enol and from the natural terpene alcohol nerol were investigated. In the process of the syntheses of the three 1-aryl-5-allyloxytetrazoles, their rapid isomerization to the corresponding 1-aryl-4-allyltetrazol-5-ones occurred. The experiments showed that the imidates rearrange exclusively through a [3,3']-sigmatropic migration of the allylic system from O to N, with inversion. Mechanistic proposals are based on product analysis and extensive quantum chemical calculations at the DFT(B3LYP) and MP2 levels, on O-allyl and N-allyl isomers and on putative transition state structures for [1,3']- and [3,3']-sigmatropic migrations. The experimental observations could be only explained on the basis of the MP2/6-31G(d,p) calculations that favoured the [3,3']-sigmatropic migrations, yielding lower energies both for the transition states and for the final isomerization products.     

Vibrational spectra and structure of 1-phenyltetrazole and 5-chloro-1-phenyltetrazole: A combined study by low temperature matrix isolation and solid state FTIR spectroscopy and DFT calculations

Infrared spectra of 1-phenyltetrazole (C₇N₄H₆) and 5-chloro-1-phenyltetrazole (C₇N₄H₅Cl) isolated in argon matrixes (T=8 K) and in the solid state (at room temperature) were studied. DFT(B3LYP)/6-31G* calculations predict the minimum energy conformation of 1-phenyltetrazole as being non-planar, with the two rings (phenyl and tetrazole) twisted by 29°. For 5-chloro-1-phenyltetrazole, the optimized dihedral angle between the two rings is larger (48°). The theoretically calculated IR spectra of both compounds fit well the spectra observed experimentally. This allowed a reliable assignment of observed IR absorption bands.     

Critical visibility and outward rays

The notion ofclear visibility has appeared recently in the literature concerning the geometry of starshaped sets. A somewhat converse notion, that ofcritical visibility, is explored here. As a by-product it is proved that the points of local nonconvexity of a closed connected set S determine the nontrivial portions of the boundary of the star of a point in S. Paragraph 4 is devoted to the study of the concepts ofoutward ray through a boundary point andinner stem of that point. A new characterization of the convex kernel of a starshaped set results from this study, and Krasnoselsky-type theorems are obtained in the planar case.     

Rotational isomers of methyl trans-cinnamate: A Raman study

The Raman and infrared spectra of methyl trans-cinnamate were measured as a function of temperature in the liquid and solid phases. The temperature dependence of the band intensities established the presence of two conformers in the liquid phase (the s-cis and s-trans forms, with CC CO dihedral angles equal to 0° and 180°, respectively; ΔH_{(s-trans)-(s-cis)} = 3.43 ± 0.84 kJ mol⁻¹) and led to the conclusion that the thermodynamically most stable s-cis form is the only form present in the solid.