Smaller Carbon Clusters: Linear, Cyclic, Polyhedral
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At same stages both small carbon clusters and fullerenes have been suggested as potential candidates responsible for the astrophysical spectroscopic patterns known as [28,291 diffuse interstellar bands, this problem being closely related to the form in which carbon is present in the interstellar space. Very recently, however, a convincing experimental evidence has been supplied [30] that the diffuse bands could be generated by highly unsaturated hydrocarbons, e.g., C6 H or C8 H, which can be understood as simple derivatives of the carbon clusters themselves. This report thus presents results from on-going computations not only of carbon aggregates, especially C12 , but also on C8 H. COMPUTATIONS The computations were partly carried out with the Gaussian 90 [31] and partly with the Gaussian 92 [32] program packages. For the sake of consistency with the previous studies the standard 6-31G* basis set was applied and the electron correlation was treated through all-electron second order Moller-Plesset (MP2=FULL) perturbation treatment. Open shell species were computed using the related unrestricted approach. The C 12 and *
On a leave of absence from the Academy of Sciences of the Czech Republic, Prague. 163 Mat. Res. Soc. Symp. Proc. Vol. 359 01995 Materials Research Society
C 13 systems have however been treated with the frozen-core MP2 option (MP2=FC/631G*). The geometry optimization was carried out in internal coordinates restricted to the smallest possible set of optimized variables. The energy gradient was constructed analytically, force-constant matrix numerically or analytically, depending on memory and software resources. Hence, it supplied a check of the types of the stationary points found and their vibrational spectra as well. RESULTS AND DISCUSSION Table I surveys the computed energetics for the linear and cyclic C,, clusters for n = 6 - 13. (In fact, some additional computations are needed, especially for the linear Cio, Ci 1 , and C 13 structures in order to clarify if we deal with real minimum-energy structures.) While the C7 and C 9 cyclic structures are slightly higher in energy than the related linear forms, C1 1 cycle is located considerably below the corresponding linear structure, and the C 13 cycle again closer, but still being the ground state. This fairly agrees with the findings from ion chromatography [3] where two well resolved peaks were found for n = 7 - 10, but not for n = 11 - 20. Entropy calculations, which are also in progress, can influence the stability interrelationships, especially at higher temperatures. As linear structures are typically favored [30] by this contribution, we could explain the very recent results [27] on infrared laser spectroscopy of the linear C 13 through this factor. The C 12 system has received rather limited attention by now, and therefore we have studied it in a detail. Two clear minimum-energy structures have been established, the D6h planar cycle and triplet linear species (Figure 1), the cycle being the system ground state (Table I). There are two type
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