Calculation of the optical response of atomic clusters using time-dependent density functional theory and local orbitals

We report on a general method for the calculation of the frequency-dependent optical response of clusters based upon time-dependent density functional theory (TDDFT). The implementation is done using explicit propagation in the time domain and a self-consistent program that uses a linear combination of atomic orbitals (LCAO). Our actual calculations employ the SIESTA program, which is designed to be fast and accurate for large clusters. We use the adiabatic local density approximation to account for exchange and correlation effects. Results are presented for the imaginary part of the linear polarizability, $\mathrm{Im}\ensuremath{\alpha}(\ensuremath{\omega}),$ and the dipole strength function, $S(\ensuremath{\omega}),$ of ${\mathrm{C}}_{60}$ and ${\mathrm{Na}}_{8},$ and compared to previous calculations and to experiment. We also develop a method for the calculation of the integrated frequency-dependent second-order nonlinear polarizability for the case of a step function electric field, ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\gamma}}}_{\mathrm{step}}(\ensuremath{\omega}),$ and present results for ${\mathrm{C}}_{60}.$