Isomers of Polyenes Attached to Benzene

A polyene graph is a tree that can be embedded in a hexagonal lattice. Systems of polyene graphs attached to one hexagon are considered. Overlapping edges and/or vertices (geometrically nonplanar systems) are allowed. A complete mathematical solution is presented in terms of a generating function for the numbers of isomers of the systems in question. The corresponding geometrically planar systems, referred to as styrenoids, are enumerated by computer programming. Finally, in the Appendix, the generating function is given for the numbers of free polyene graphs

Enumeration and Classification of Double Coronoid Hydrocarbons Appendix: Triple Coronoids

An enumeration of double coronoids (polyhexes with two heles) is performed, both by hand and by computer. The numbers 15123 and 125760 for the systems with h = 17 and h = 18, respectively, are reported for the first time. Here h denotes the number of hexagons. The generated systems are classified in different ways. In this connection the strata of corona hale constellations are defined, depending on the proximity of the holes. As appendix, a first enumeration of triple coronoids is reported

GRAPH-THEORETICAL STUDIES ON FLUORANTHENOIDS AND FLUORENOIDS - ENUMERATION OF SOME CATACONDENSED SYSTEMS

Precise definitions are given for some classes of molecular graphs with one pentagon and otherwise hexagons: the monopentapolyhexes. The fluoranthenoid and fluorenoid systems belong to monopentapolyhexes. Complete mathematical solutions, using combinatorial summations on the one hand and generating functions on the other hand, are given for the numbers of catacondensed simply connected monopentapolyhexes (catafluorenoids and the corresponding helicenic systems). Generating functions and numerical values are included

The crossover from propagating to strongly scattered acoustic modes of glasses observed in densified silica

Spectroscopic results on low frequency excitations of densified silica are presented and related to characteristic thermal properties of glasses. The end of the longitudinal acoustic branch is marked by a rapid increase of the Brillouin linewidth with the scattering vector. This rapid growth saturates at a crossover frequency Omega_co which nearly coincides with the center of the boson peak. The latter is clearly due to additional optic-like excitations related to nearly rigid SiO_4 librations as indicated by hyper-Raman scattering. Whether the onset of strong scattering is best described by hybridization of acoustic modes with these librations, by their elastic scattering (Rayleigh scattering) on the local excitations, or by soft potentials remains to be settled.Comment: 14 pages, 6 figures, to be published in a special issue of J. Phys. Condens. Matte

Infrared Emission from Interstellar Dust. I. Stochastic Heating of Small Grains

We present a method for calculating the infrared emission from a population of dust grains heated by starlight, including very small grains for which stochastic heating by starlight photons results in high temperature transients. Because state-to-state transition rates are generally unavailable for complex molecules, we consider model PAH, graphitic, and silicate grains with realistic vibrational mode spectra and realistic radiative properties. The vibrational density of states is used in a statistical-mechanical description of the emission process. Unlike previous treatments, our approach fully incorporates multiphoton heating effects, important for large grains or strong radiation fields. We discuss how the "temperature" of the grain is related to its vibrational energy. By comparing with an "exact" statistical calculation of the emission process, we determine the conditions under which the "thermal" and the "continuous cooling" approximations can be used to calculate the emission spectrum. We present results for the infrared emission spectra of PAH grains of various sizes heated by starlight. We show how the relative strengths of the 6.2, 7.7, and 11.3um features depend on grain size, starlight spectrum and intensity, and grain charging conditions. We show results for grains in the "cold neutral medium", "warm ionized medium", and representative conditions in photodissociation regions. Our model results are compared to observed ratios of emission features for reflection nebulae and photodissociation regions, the Milky Way, normal spiral galaxies, and starburst galaxies.Comment: Submitted to ApJ. 42 pages, 18 figures, Late

Raman scattering in C_{60} and C_{48}N_{12} aza-fullerene: First-principles study

We carry out large scale {\sl ab initio} calculations of Raman scattering activities and Raman-active frequencies (RAFs) in ${\rm C}_{48}{\rm N}_{12}$ aza-fullerene. The results are compared with those of ${\rm C}_{60}$. Twenty-nine non-degenerate polarized and 29 doubly-degenerate unpolarized RAFs are predicted for ${\rm C}_{48}{\rm N}_{12}$. The RAF of the strongest Raman signal in the low- and high-frequency regions and the lowest and highest RAFs for ${\rm C}_{48}{\rm N}_{12}$ are almost the same as those of ${\rm C}_{60}$. The study of ${\rm C}_{60}$ reveals the importance of electron correlations and the choice of basis sets in the {\sl ab initio} calculations. Our best calculated results for ${\rm C}_{60}$ with the B3LYP hybrid density functional theory are in excellent agreement with experiment and demonstrate the desirable efficiency and accuracy of this theory for obtaining quantitative information on the vibrational properties of these molecules.Comment: submitted to Phys.Rev.