From small to large behavior: The transition from the aromatic to the Peierls regime in carbon rings

Results of local density approximation (LDA) and Hartree–Fock (HF) calculations for even numbered monocyclic rings are reported. Small $Cn$ rings satisfying $n=4N+2$ show aromatic stability with equal bond-length structures, whereas rings of size $n=4N$ show antiaromatic destabilization with bond-length alternation. For large rings a transition, the Peierls transition, from aromatic and antiaromatic to nonaromatic behavior, takes place. Above the Peierls transition, both $n=4N$ and $n=4N+2$ rings show bond-length alternation and no differences in stability. The critical size for the transition to nonaromatic behavior depends on the electron-phonon coupling strength and therefore depends on the choice of ab initio method. HF predicts nonaromatic behavior for ring sizes $n=14$ and above. Fully optimized LDA results are presented up to $n=42,$ which still has a cumulenic structure. Calculations based on periodic infinite ring systems show that within LDA the onset of nonaromatic behavior does not occur until $n=82.$ Experimental results suggest that aromatic behavior exists in these ring systems to at least $n=22.$ The force constant for in-plane angle bending may also be estimated from these calculations and was found to be 0.022 kcal mol⁻¹ deg⁻² per atom, not a strong function of size beyond $n=22,$ and in good agreement with experimental estimates.