An O(N) tight-binding study of carbon clusters up to C8640: the geometrical shape of the giant icosahedral fullerenes

We report an efficient implementation of the Li-Nunes-Vanderbilt conjugate gradient density matrix search method that exploits sparse matrix algorithms for storage and matrix operations. The scheme avoids the N3 diagonalization bottleneck and scales linearly with the systemʹs size. Benchmarks on large carbon systems indicate that the method becomes faster than diagonalization for small number of atoms (⩽250). Clusters containing thousands of atoms are studied with modest workstation computation resources. We also report geometry optimizations of very large icosahedral fullerenes (up to C8640) which clearly indicate that these clusters have a faceted (polyhedral) geometrical shape.