Atomization energies of the carbon clusters C_n (n = 2−10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods

Abstract

The thermochemistry of the carbon clusters C _n (n = 2−10) has been revisited by means of W4 theory and W3.2lite theory. Particularly, the larger clusters exhibit very pronounced post-CCSD(T) correlation effects. Despite this, our best calculated total atomization energies agree surprisingly well with the 1991 estimates obtained from scaled CCD(ST)/6-31G* data. Accurately reproducing the small singlet–triplet splitting in C₂ requires inclusion of connected quintuple and sextuple excitations. Post-CCSD(T) correlation effects in C₄ stabilize the linear form. Linear/cyclic equilibria in C₆, C₈, and C₁₀ are not strongly affected by connected quadruples, but they are affected by higher-order triples, which favor polyacetylenic rings but disfavor cumulenic rings. Near the CCSD(T) basis set limit, C₁₀ does undergo bond angle alternation in the bottom-of-the-well structure, although it is expected to be absent in the vibrationally averaged structure. The thermochemistry of these systems, and particularly the longer linear chains, is a particularly difficult test for density functional methods. Particularly for the smaller chains and the rings, double-hybrid functionals clearly outperform conventional DFT functionals for these systems. Among compound thermochemistry schemes, G4 clearly outperforms the other members of the Gn family. Our best estimates for total atomization energies at 0 K are: C₂() 144.07, C₂(³Π_u) 142.39, C₃() 315.83, C₄() 429.16, C₄(¹A_g) 430.09, C₅() 596.64, C₆() 717.19, C₆() 729.68, C₇() 877.45, C₈() 1001.86, C₈(¹A _g ) 1014.97, C₉() 1159.21, C₁₀() 1288.22, and C₁₀() 1355.54 kcal mol⁻¹.

Keywords:

• thermochemistry
• ab initio
• anharmonic force fields
• density functional theory

Acknowledgements

Research at Weizmann was funded by the Israel Science Foundation (grant 709/05), the Minerva Foundation (Munich, Germany), and the Helen and Martin Kimmel Center for Molecular Design. JMLM is the incumbent of the Baroness Thatcher Professorial Chair of Chemistry and a member ad personam of the Lise Meitner-Minerva Center for Computational Quantum Chemistry.