Jet-discharge cavity ring-down spectroscopy of ionized polycyclic aromatic hydrocarbons: progress in testing the PAH hypothesis for the diffuse interstellar band problem.

Naphthalene cations (C10H+8) were produced in a slit jet coupled with an electronic discharge, and cavity ring down was used to obtain its absorption spectrum in the region 645-680 nm. Two of the strongest C10H+8 bands previously characterized by matrix isolation spectroscopy were found, both with a fractional blue shift of about 0.5%. This is the first gas-phase electronic absorption spectrum of an ionized polycyclic aromatic hydrocarbon (PAH). This work opens the way for a direct comparison of laboratory PAH spectra with the diffuse interstellar bands (DIB), the origin of which still constitutes an open problem in astrophysics.     

Closed-shell polycyclic aromatic hydrocarbon cations: a new category of interstellar polycyclic aromatic hydrocarbons

Density functional theory has been employed to calculate the harmonic frequencies and intensities of a range of polycyclic aromatic hydrocarbon (PAH) cations that explore both size and electronic structure effects on the infrared spectroscopic properties of these species. The sample extends the size range of PAH species considered to more than 50 carbon atoms and includes several representatives from each of two heretofore unexplored categories of PAH cations: (1) fully benzenoid PAH cations whose carbon skeleton is composed of an odd number of carbon atoms (C(odd) PAHs); and (2) protonated PAH cations (HPAH+). Unlike the radical electronic structures of the PAH cations that have been the subject of previous theoretical and experimental work, the species in these two classes have a 'closed'-shell electronic configuration. The calculated spectra of circumcoronene, C54H18, in both neutral and (radical) cationic form are also reported and compared with those of the other species. Overall, the C(odd) PAHs spectra are dominated by strong CC stretching modes near 1600 cm(-1) and display spectra that are remarkably insensitive to molecular size. The HPAH+ species evince a more complex spectrum consistent with the added contributions of aliphatic modes and their generally lower symmetry. Finally, for both classes of closed-shell cations, the intensity of the aromatic CH stretching modes is found to increase with molecular size far out of proportion with the number of CH groups, approaching a value more typical of neutral PAHs for the largest species studied.     

On some nonself mappings

Let X be a Banach space, let K be a non–empty closed subset of X and let T : K → X be a non–self mapping. The main result of this paper is that if T satisfies the contractive–type condition (1.1) below and maps ?K (?K the boundary of K) into K then T has a unique fixed point in K.