Development of bond-length alternation in very large carbon rings: LDA pseudopotential results

Abstract

Carbon rings ${\mathrm{C}}_{n}$ and infinite chains ${\mathrm{C}}_{\ensuremath{\infty}}$ are investigated by molecular-orbital and band-structure calculations within the local-density approximation. Carbon rings ${\mathrm{C}}_{4N}$ $(Nl~8)$ exhibit a substantial first-order Jahn-Teller distortion that leads to long/short (single/triple) bond alternation decreasing with increasing $N.$ Rings ${\mathrm{C}}_{4N+2}$ show no alternation (i.e., aromatic behavior is retained) until very large sizes $(Ng~20).$ For the infinite carbon chain uniform Brillouin-zone sampling with an even number of points ${N}_{s}$ gives bond alternation. An odd number of sampling points gives no bond alternation for less than ${N}_{s}=41.$ In the large ${N}_{s}$ limit even and odd sampling lead to an upper and lower bound of ${0.070a}_{0}$ and ${0.065a}_{0}$ for bond alternation and 0.021--0.090 millihartrees/atom for condensation energy.