Dodecahedron- and Bowl-Shaped Structures C 20
- PDF / 346,424 Bytes
- 6 Pages / 420.48 x 639 pts Page_size
- 99 Downloads / 256 Views
DODECAHEDRON- AND BOWL-SHAPED STRUCTURES C20 ZDENEK SLANINA* AND LUDWIK ADAMOWICZ Department of Chemistry, The University of Arizona, Tucson, AZ 85721
ABSTRACT Purely carbonaceous aggregates C20 have been studied by the AM1 quantumchemical method. In addition to one dodecahedron-shaped structure possessing C', symmetry another three-dimensional species is revealed, viz. a bowl-shaped structure of Cs•, symmetry (and also one two-dimensional and two one-dimensional species). Temperature dependence of the relative stabilities of both three-dimensional structures is evaluated, showing that in the relevant temperature region the fullerenic species is prevailing. However, in a very high temperature region a relative-stability interchange has been predicted.
INTRODUCTION Fullerenes have been defined [1-3] as purely carbonaceous species C,, with n > 20, possessing a polyhedral shape built from five- and six-membered rings. Quite recently, in addition to the celebrated C60 and C70 [4-7] other fullerenes have been studied [3,8]. It has been pointed out [8-10] that the fullerenic isomerism can represent, at the conditions of the fullerenic preparations, an important phenomenon. Quantum chemical computations have widely been used [11-13] for descriptions of structural, spectral and energetical features of the unique species. This report deals with the smallest member of the fullerene family, C 20 , and compares its thermodynamic stability with another plausible structure built from the carbon rings though not closed into a cage. The quantum-chemical AM1 calculations [14] axe combined with thermodynamic treatment in the partition-function terms.
COMPUTATIONS Topological reasoning [1-3] proves that any fullerene always contains exactly f5 = 12 five-membered rings while the number f 6 of six-membered depends on the number of carbon atoms m: f6
= m/2 - 10.
(1)
Hence, the smallest fullerene, C20, is built just from 12 pentagons (and no hexagons). It violates however the isolated pentagon rule considerably so that a particular stability cannot be expected. In fact, the well known hydrocarbon dodecahedrane exhibits such a cage [15], derived from the polyhedron dodecahedron (Ih point group of symmetry). *
On a leave of absence from the Czechoslovak Academy of Sciences, Prague.
Mat. Res. Soc. Symp. Proc. Vol. 270. 01992 Materials Research Society
216
In our quantum-chemical AM1 [14] calculations, a local energy minimum of the dodecahedron shape (see the Figure) exhibited only the C1 symmetry, i.e. no symmetry element is present. It means that all the five-membered rings in the frame are somewhat distorted, apparently in order to compensate for the steric tension originated in the five-membered ring junctions. There is another three-dimensional (though not fullerenic) structure which should be treated in connection with C 2 0 , the structure related to the hydrocarbon corannulene [16]. The latter structure is composed of one five-membered and five six-membered rings arranged in a bowl-like shape (see the Figure). Our AM1 geom
Data Loading...
