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

TL;DR

This study revisits the thermochemistry of carbon clusters Cn (n=2--10) using advanced computational methods, revealing the importance of post-CCSD(T) effects and evaluating the accuracy of various density functional and compound thermochemistry schemes.

Contribution

The paper provides highly accurate atomization energies for Cn clusters using W4 and related theories, and compares the performance of different density functional and thermochemistry methods.

Findings

Post-CCSD(T) effects are significant for larger clusters.

Double-hybrid functionals outperform conventional DFT for small chains and rings.

G4 thermochemistry scheme yields the most reliable atomization energies.

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 1991 estimates obtained from scaled CCD(ST)/6-31G* data. Accurately reproducing the small singlet-triplet splitting in C$_2$ requires inclusion of connected quintuple and sextuple excitations. Post-CCSD(T) correlation effects in C$_4$ stabilize the linear form. Linear/cyclic equilibria in C$_6$, C$_8$, and C$_{10}$ are not strongly affected by connected quadruples, but they are affected by higher-order triples, which favor polyacetylenic rings but disfavor cumulenic ones. Near the CCSD(T) basis set limit, C$_{10}$ 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 convential DFT functionals for these systems. Among compound thermochemistry schemes, G4 clearly outperforms the other members of the G$n$ family. Our best estimates for total atomization energies at 0 K should be reliable to 1 kJ/mol up to C$_5$ inclusive, and to better than 1 kcal/mol up to C$_9$ inclusive.