Photoabsorption spectra of small Na clusters: TDHF and BSE versus CI and experiment

Time-dependent Hartree-Fock (TDHF) and Bethe-Salpeter equation (BSE) methods are benchmarked against configuration interaction (CI) calculations of excitation energies and photoabsorption cross-sections for small closed shell sodium clusters with up to six atoms in several low-energy configurations. The mean absolute deviation of lowest excitation energies of each symmetry in these clusters for TDHF or BSE calculations from CI results is about 0.1 eV. The Thomas-Reiche-Kuhn (TRK) sum rule is satisfied to within numerical accuracy for both TDHF and BSE calculations, however, the Tamm-Dancoff approximations applied to either method for these systems yield optical cross-sections which grossly violate the TRK sum rule. TDHF and BSE calculations for photoabsorption cross-sections of ${\mathrm{Na}}₈$ and ${\mathrm{Na}}₂₀$ clusters are compared to experiment and found to be in good agreement. A feature in the cross-section of ${\mathrm{Na}}₂₀$ above 4 eV is found to be caused by a large density of optical transitions rather than an incipient volume plasmon with a short lifetime.