Time-dependent local-density approximation in real time

We study the dipole response of atomic clusters by solving the equations of the time-dependent local-density approximation in real time. The method appears to be more efficient than matrix or Green’s function methods for large clusters modeled with realistic ionic pseudopotentials. As applications of the method, we exhibit results for sodium and lithium clusters and for ${\mathrm{C}}_{60}$ molecules. The calculated Mie resonance in ${\mathrm{Na}}_{147}$ is practically identical to that obtained in the jellium approximation, leaving the origin of the redshift unresolved. The pseudopotential effects are strong in lithium and act to broaden the Mie resonance and give it a substantial redshift, confirming earlier studies. There is also a large broadening due to Landau damping in the calculated ${\mathrm{C}}_{60}$ response, again confirming earlier studies. © 1996 The American Physical Society.