Structure and Vibrations of Small Carbon Clusters from Coupled-Cluster Calculations

The vibrational spectrum of the linear carbon clusters C 2 −C 9 and of cyclic C 4, C 6, C 8, and C 10 has been investigated using the augmented coupled-cluster, CCSD(T), method and correlation-consistent basis sets. Particular emphasis is placed on assignment of bands in matrix infrared spectra of trapped graphite vapor. The relative energetics of linear and cyclic isomers of C 6, C 8, and C 10 were investigated at the CCSD(T) level using basis sets of [4s3p2d1f] quality. Our best calculations predict that the ground state structure of C 6 is a cumulenic D 3 h ring and that of C 8 a polyacetylenic C 4 h ring. Linear states are close in energy (13 ± 2 and 8 ± 2 kcal/mol, respectively), and both forms should be observable. The ground state structure of cyclic C 10 clearly has D 5 h rather than D 10 h symmetry, at least for the r e geometry. A linear regression of computed CCSD(T)/[3s2p1d] harmonic frequencies vs observed fundamentals for the previously assigned stretching frequencies of linear C n clusters has a very high correlation coefficient (up to r = 0.99975 at 10 data points). From the regression line and the calculated frequencies, band origins for linear C 8 are predicted at 2063 ± 18 and 1711 ± 14 cm -1 (99% confidence intervals) and ancillary bands for linear C 9 at 2093 ± 18 and 1604 ± 16 cm -1 . From the calculated infrared-active CCSD(T) frequencies for the cyclic clusters and anharmonicity considerations, we suggest that bands near 1695, 1818, and 1915 or 1921 cm -1 belong to cyclic C 6, C 8, and C 10, respectively, while bands near 1590 and 1715 cm -1 are probably due to linear C 9 and C 8, respectively. Finally, a broad feature at 2070−2090 cm -1, which upon deconvolution appears to consist of three bands, is suggested to contain bands of both linear C 8 and C 9 .