Localized-density-matrix method and its application to carbon nanotubes

The localized-density-matrix method (Yokojima, S.; Chen, G. H. Chem. Phys. Lett. 1998, 292, 379) is employed to simulate the optical responses of very large carbon nanotubes and polyacetylene oligomers containing 10 000 carbo n atoms. The Pariser-Parr-Pople Hamiltonian is used to describe the pi elec trons in these systems, and the time-dependent Hartree-Fock approximation i s employed to calculate the linear optical responses. In the calculation, t he fast multipole method or the cell multipole method is employed to evalua te the effects of Coulomb interaction. It is illustrated that the computati onal time scales linearly with the system size for carbon nanotubes while h igh accuracy is achieved.