  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, Im [\alpha(w)], and the dipole strength function, S(w), of C60
and Na8, compared to previous calculations and to experiment. We also show how
to calculate the integrated frequency-dependent second order non-linear
polarizability for the case of a step function electric field,
\gamma_{step}(w), and present results for C60.
