The geometries of C-n (n = 2-30) clusters have been optimized with a genetic algorithm (GA) associated with simulated annealing (SA) method on the Brenner bond-order potential energy surface (PES). it showed that the geometries are linear when n is less than 6, single ring when n is at 6-12, double ring when n is equal to 13 or 14. Multi-ring structures start as n is greater than 14. C-28 is in a fullerene structure; while C-20 and C-21 are bowl- and cap-like, respectively. The other multi-ring structures were predicted to be planar. Further analysis indicated the stability of the non-planar open structures on the Brenner PES is related to the number of the triple bonds in the clusters. (C) 2002 Elsevier Science B.V. All rights reserved.