E. Brendsdal

Molecular vibrations of footballene

Abstract A normal coordinate analysis has been carried out for C 60 “footballene”. A five-parameter force field was employed in order to calculate the vibrational frequencies. Results for the 10 Raman-active and 4 infrared-active frequencies are reported.

Corannulene as a member of circulenes: its topological properties and molecular vibrations

Abstract The polycyclic aromatic hydrocarbon C 20 H 10 corannulene or [5] circulene, is considered as a member of a class of [ n ]circulenes. The Kekule structure counts of [ n ]circulenes are expressed in terms of the Lucas numbers and by means of the matching polynomials of the cycles C n . For corannulene in particular, the Huckel molecular orbital energies are computed, and a normal coordinate analysis of molecular vibrations is performed. Some new enumeration results for coronoids belonging to the class of [n ] circulenes considered are reported.

Normal Coordinate Analysis of “Footballene” C60

Abstract An approximate force field previously developed for condensed aromatics is adapted to footballene, a C60 molecule of icosahedral symmetry. The 46 vibrational frequencies are calculated. For a general introduction to the interesting (hypothetical) C60 molecule called “footballene” it is referred to another paper in this issue [3], In the present work the reported symmetry coordinates [3] are used to calculate the assigned vibrational frequencies of footballene.

Symmetry coordinates of molecular vibrations of «footballene» C60

Abstract A complete set of the 174 symmetry coordinates for the C molecular model referred to as footballene is reported. The model is the truncated icosahedron (symmetry Ih ). Hence in addition to triple degeneracy also quadruple and quintuple degeneracies occur.

ENUMERATION OF POLYENE HYDROCARBONS: A COMPLETE MATHEMATICAL SOLUTION

Polyenoid systems (or polyenoids) are trees which can be embedded in a hexagonal lattice and represent CnHn+2 polyene hydrocarbons. Complete mathematical solutions in terms of summations and in terms of a generating function are deduced for the numbers of polyenoids when overlapping edges and/or vertices are allowed. Geometrically planar polyenoids (without overlapping vertices) are enumerated by computer programming. Thus the numbers of geometrically nonplanar polyenoids become accessible. Some of their numbers are confirmed by combinatorial constructions, a pen-and-paper method.

The Simplest Coronoids: Hollow Hexagons**

Hollow hexagons form a subclass of primitive coronoid systems. The macrocyclic aromatic hydrocarbon kekulene corresponds to a hollow hexagon. The hollow hexagons for given numbers of hexagonal units (h) were enumerated by computer aid, but also an analytical solution for the numbers of hollow hexagons was achieved. For the Kekulé structure counts (k) of a hollow hexagon a general formula is reported. Also the maximum and minimumK numbers are considered.

Condensed aromatics. XXIII: Cyclo[d.e.d.e.d.e.d.e.d.e.d.e]dodecakisbenzene (kekulene)

Abstract Some topological properties of coronoids are given. These systems have chemical counterparts in cycloarenes. For one of these molecules, viz. C 48 H 24 kekulene, the simple Huckel molecular orbital analysis has been performed and employed in the construction of a harmonic force field. Finally the set of calculated vibrational frequencies is reported.

Molecular vibrations and mean amplitudes of kekulene, including relevant historical glimpses

Abstract The interesting polycyclic aromatic hydrocarbon kekulene (C 48 H 24 ), a molecule with a hole, is suggested as a challenging subject for a gas electron diffraction investigation. The history of the synthesis of kekulene is reviewed briefly. A Huckel molecular orbital analysis of kekulene is reported, and some comments on the Coulson and Pauling bond orders are offered. The main topic is the normal coordinate analysis of kekulene with computations of the mean amplitudes and perpendicular amplitude correction coefficients which would be useful in the gas electron diffraction investigation.

Molecular vibrations of the smallest fullerene: C20 dodecahedron

Abstract The smallest fullerene, C 20 in the structure of the regular dodecahedron (symmetry I h ) is treated. The 36 Kekule structures are deduced. The Huckel molecular orbital energies are re-derived. A normal coordinate analysis is performed and includes a set of predicted vibrational frequencies, which contain one single infrared-active frequency (840 cm −1 ). Mean amplitudes of vibration and perpendicular amplitude correction coefficients are reported.

Computerized enumeration of staggered alkane conformers

Abstract An alkanoid is defined as a tree (in the graph-theoretical sense) which can be embedded in the diamond lattice. It corresponds to a staggered conformer of an alkane. A computer program for enumerating non-overlapping alkanoids is described. In these systems there is no pair of coalescing vertices. Results for the unbranched and branched alkanoids are given separately, and the symmetry groups of the systems are determined.