Influence of the exchange-correlation potential in density-functional calculations on polarizabilities and absorption spectra of alkali-metal clusters

All-electron calculations in large basis sets of excitation energies, oscillator strengths, and polarizabilities of small alkali-metal clusters of Li, Na, and K, with up to eight atoms, are performed using time-dependent density-functional theory. It is shown that the use of the recently developed statistical average of orbital potentials (SAOP) exchange-correlation (chic) potential [P.R.T. Schipper et al., J. Chem. Phys. 112, 1344 (2000)] leads to polarizabilities of these alkali-metal clusters which are 10-15% larger than polarizabilities calculated with the re potential of the local-density approximation (LDA). The lower LDA polarizabilities (in comparison to the SAOP) are shown to originate from differences in the low-lying excitation energies, which are determined by the re potential in the molecular inner and valence region. In spite of such differences, both SAOP and LDA results are shown to provide reliable assignments of the experimental absorption spectra, with typical errors in peak positions of only 0.1-0.2 eV, or even less.