Ej. Bylaska et al., From small to large behavior: The transition from the aromatic to the Peierls regime in carbon rings, J CHEM PHYS, 113(15), 2000, pp. 6096-6106
Results of local density approximation (LDA) and Hartree-Fock (HF) calculat
ions for even numbered monocyclic rings are reported. Small C-n rings satis
fying n=4N+2 show aromatic stability with equal bond-length structures, whe
reas rings of size n=4N show antiaromatic destabilization with bond-length
alternation. For large rings a transition, the Peierls transition, from aro
matic and antiaromatic to nonaromatic behavior, takes place. Above the Peie
rls 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 nonar
omatic behavior depends on the electron-phonon coupling strength and theref
ore depends on the choice of ab initio method. HF predicts nonaromatic beha
vior for ring sizes n=14 and above. Fully optimized LDA results are present
ed up to n=42, which still has a cumulenic structure. Calculations based on
periodic infinite ring systems show that within LDA the onset of nonaromat
ic behavior does not occur until n=82. Experimental results suggest that ar
omatic behavior exists in these ring systems to at least n=22. The force co
nstant for in-plane angle bending may also be estimated from these calculat
ions 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 estim
ates. (C) 2000 American Institute of Physics. [S0021-9606(00)31339-3].