All-electron local and gradient-corrected density-functional calculations ofNandipole polarizabilities forn=1–6

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Abstract
Sodium clusters represent an experimentally accessible and seemingly simple system for studying the size dependence of the optical properties of metal clusters. Nevertheless, with the exception of the atom and dimer, previous ab initio calculations have either been restricted to correlated calculations in which pseudopotentials were used in order to reduce sodium to an effective one-electron atom or correlation effects were entirely neglected. The present study presents the results of correlated all-electron density-functional calculations of sodium-cluster dipole polarizabilities for clusters through the hexamer. In particular, polarizabilities were calculated at the local-density-approximation- (LDA-) optimized geometries using the LDA functional, with the Perdew-Wang 1986 exchange plus the Perdew 1986 correlation (PW86x+P86c) gradient corrections, and with the Becke 1988 exchange plus the Perdew 1986 correlation (B88x+P86c) gradient corrections. The results are compared with the available experimental and ab initio theoretical values. Of the three exchange-correlation functionals presented in this paper, the mean polarizabilities calculated using the B88x+P86c functional are in best agreement with the experimental values, with discrepancies between theory and experiment of only 3.5% for the atom and 5% for the dimer. Differences between the experimental and B88x+P86c optimized dimer and trimer geometries are also significantly smaller than in the LDA case. However, there is little difference between mean polarizabilities calculated at the LDA-optimized, B88x+P86c optimized, and experimental geometries. In particular, this cannot explain the 11–22 % discrepancies found here between the experimental polarizabilities for the trimer and higher-order clusters and those calculated at the LDA-optimized geometries using the B88x+P86c functional. It is suggested that molecular motion may need to be taken into account before a completely satisfactory explanation of the experimental polarizabilities of these floppy molecules can be given.