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

Carbon rings C-n and infinite chains C-infinity are investigated by molecular-orbital and band-structure calculations within the local-density approximation. Carbon rings C-4N (N less than or equal to 8) exhibit a substantial first-order Jahn-Teller distortion that leads to long/short (single/triple) bond alternation decreasing with increasing N. Rings C4N + 2 show no alternation (i.e., aromatic behavior is retained) until very large sizes (N greater than or equal to 20). For the infinite carbon chain uniform Brillouin-zone sampling within 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 0.070(a0) and 0.065a(0) for bond alternation and 0.021-0.090 millihartrees/atom for condensation energy. [S0163-1829(98)51836-X].