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 carbon atoms. The Pariser-Parr-Pople Hamiltonian is used to describe the pi electrons in these systems, and the time-dependent Hartree-Fock approximation is employed to calculate the linear optical responses. In the calculation, the fast multipole method or the cell multipole method is employed to evaluate the effects of Coulomb interaction. It is illustrated that the computational time scales linearly with the system size for carbon nanotubes while high accuracy is achieved.