From small to large behavior: The transition from the aromatic to the Peierls regime in carbon rings Eric J. Bylaska William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory. P.O. Box 999, Richland, Washington 99352 Ryoichi Kawai Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 John H. Weare Department of Chemistry, University of California, San Diego, La Jolia, California 92093 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 alternations 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. Published in Journal of Chemical Physics 113 (2000), 6096. |