C 60 and the icosahedral group Ih: Simplification methods and group-theoretical applications

Group-theoretical methods are used to induce “global” distortions of C ₆₀ from basis function(s) of a single “local” distortion in two cases: (1) The 60 vibrational modes arising from radial displacements of carbon atoms are found in terms of basis functions of A′, the one-dimensional symmetric representation of C_s; (2) The 24 vibrational modes arising from tangential displacements of hypothetical atoms placed at pentagon centers are found in terms of basis functions of E ₁, the vector irreducible representation of C_5v . The induction process is simplified by an icon notation (v) or (vμ) which uniquely labels the operations in I_h if μ,v = 0, 1, 2, 3, 4 and under/over lining of a digit is included. These icons describe the transformations IUS^vTS^μ of Felix Kline referred to a five-fold z-axis and two-fold x-axis and serve to label and “distinguish” symmetrically equivalent points of the truncated icosahedron.     

Decay of high-energy astrophysical neutrinos

Existing limits on the nonradiative decay of one neutrino to another plus a massless particle (e.g., a singlet Majoron) are very weak. The best limits on the lifetime to mass ratio come from solar neutrino observations and are tau/m greater, similar 10(-4) s/eV for the relevant mass eigenstate(s). For lifetimes even several orders of magnitude longer, high-energy neutrinos from distant astrophysical sources would decay. This would strongly alter the flavor ratios from the phi(nu(e)):phi(nu(mu)):phi(nu(tau))=1:1:1 expected from oscillations alone and should be readily visible in the near future in detectors such as IceCube.     

Elastically driven ferromagnetic resonance in nickel thin films

Surface acoustic waves (SAWs) in the GHz frequency range are exploited for the all-elastic excitation and detection of ferromagnetic resonance (FMR) in a ferromagnetic-ferroelectric (Ni/LiNbO(3)) hybrid device. We measure the SAW magnetotransmission at room temperature as a function of frequency, external magnetic field magnitude, and orientation. Our data are well described by a modified Landau-Lifshitz-Gilbert approach, in which a virtual, strain-induced tickle field drives the magnetization precession. This causes a distinct magnetic field orientation dependence of elastically driven FMR that we observe in both model and experiment.     

Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors

The two-photon absorption coefficient is calculated from perturbation theory for direct-gap zincblende semiconductors using exact nonparabolic energies and matrix elements. The enhancement due to exciton effects is included. The results are compared to experiment and to other theories including the tunneling or Keldysh theory.     

Sensory principles of higher plants

Plants respond to a broad variety of stimuli from the interior of their body and from the outside environment. A revolution in our knowledge of the sensory capabilities of plants took place during the last decade, thanks to the consequent application of the tools of molecular genetics and the focusing of most work, in a world-wide effort, on a single, representative, higher plant: Arabidopsis thaliana. This review concentrates on the complete sensory periphery of higher plants, with focus placed on the principles rather than the details, and such systems that have been functionally identified unambiguously. Higher plants are no less fascinating, no less complex, and no less sensitive than animals, even man, with respect to their sensory capabilities. Plants constantly monitor their environment and their interior situation by using a stunning array of sensory systems, that are mostly different from those of animals or man.     

Unsaturated dodecahedranes--in quest of the C20H14 1,4,16-triene and C20H12 1,4,10(14),16-tetraene, and their cations and anions

The highly pyramidal, highly strained 1,4,16-dodecahedratriene (4) and C20H12 1,4,10(14),16-dodecahedratetraene (5) are cage olefins with an intriguing "inner life". For 5 DFT calculations give information about the energetic and geometrical consequences of one-/two-electron oxidation and reduction. Attempts to prepare 4 and 5 through thermal retro[2+2]/[4+2]cycloaddition strategies proved unsuccessful. Still, the C20H14/C20H12 cage cations and anions are liberated upon electron impact or gas-discharge ionization of their thermally extremely stable tris-/tetrakisanthraceno-anellated derivatives. Mass-selection (photoelectron (PE) characterization) of the anions failed, however, due to the very small anion intensity, the preferential formation of hydrogen-poor ions, and minor cage disruption.     

Der zweistufige Carbanion-Mechanismus der Fragmentierung von 3-Aminopropylbenzoaten. Fragmentierungs-Reaktionen. 25. Mitteilung

The unsubstituted and p-substituted benzoates 2b – 2e of 3-dimethylamino-2,2bis(p-nitrophenyl)-propanol ( 2a ) undergo quantitative fragmentation in 80% ethanol yielding 1,1-bis(p-nitrophenyl)-ethylene ( 5 ) besides formaldehyde and dimethylamine, the hydrolysis products of the imonium ion 3 . The corresponding alcohol 2a , however, yields 2,2-bis(p-nitrophenyl)-ethanol ( 9 ) in addition to fragmentation products. Conversely, no fragmentation is observed with the benzoates 6b – 6e of 3-dimethylamino-2,2-diphenylpropanol ( 6a ) which lack electronwithdrawing substituents in the β-phenyl groups. These results are in agreement with a two-step carbanion mechanism (Scheme 2) involving the ionization of the aminoalkohol 2a and its esters 2b – 2e to the imonium ion 3 and the carbanions 4a – 4e . The latter undergo competitive cleavage, recombination and protonation to 5 , 2 and 9 , respectively, depending on the nucleofugal activity of –X. These conclusions are supported by the first-order rate constants for the benzoates 2b – 2e which differ merely by a factor of three. Since the p-substituents in the benzoate groups have only a minor effect on the reaction rate the bonds to the nucleofugal groups are not appreciably broken in the rate determining step.