Results of local density approximation (LDA) and Hartree-Fock (HF) calculations for even numbered monocyclic rings are reported. Small C-n 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.