Carbon rings (Formula presented) and infinite chains (Formula presented) are investigated by molecular-orbital and band-structure calculations within the local-density approximation. Carbon rings (Formula presented) exhibit a substantial first-order Jahn-Teller distortion that leads to long/short (single/triple) bond alternation decreasing with increasing (Formula presented) Rings (Formula presented) show no alternation (i.e., aromatic behavior is retained) until very large sizes (Formula presented) For the infinite carbon chain uniform Brillouin-zone sampling with an even number of points (Formula presented) gives bond alternation. An odd number of sampling points gives no bond alternation for less than (Formula presented) In the large (Formula presented) limit even and odd sampling lead to an upper and lower bound of (Formula presented) and (Formula presented) for bond alternation and 0.021-0.090 millihartrees/atom for condensation energy. © 1998 The American Physical Society.
