ALL-ELECTRON LOCAL AND GRADIENT-CORRECTED DENSITY-FUNCTIONAL CALCULATIONS OF NA-N DIPOLE POLARIZABILITIES FOR N=1-6

Sodium clusters represent an experimentally accessible and seemingly s imple system for studying the size dependence of the optical propertie s 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 t o reduce sodium to an effective one-electron atom or correlation effec ts were entirely neglected. The present study presents the results of correlated all-electron density-functional calculations of sodium-clus ter dipole polarizabilities for clusters through the hexamer. In parti cular, polarizabilities were calculated at the local-density-approxima tion- (LDA-) optimized geometries using the LDA functional, with the P erdew-Wang 1986 exchange plus the Perdew 1986 correlation (PW86x+P86c) gradient corrections, and with the Becke 1988 exchange plus the Perde w 1986 correlation (B88x+P86c) gradient corrections. The results are c ompared with the available experimental and ab initio theoretical valu es. Of the three exchange-correlation functionals presented in this pa per, the mean polarizabilities calculated using the B88x+P86c function al are in best agreement with the experimental values, with discrepanc ies between theory and experiment of only 3.5% for the atom and 5% for the dimer. Differences between the experimental and B88x+P86c optimiz ed dimer and trimer geometries are also significantly smaller than in the LDA case. However, there is little difference between mean polariz abilities calculated at the LDA-optimized, B88x+P86c optimized, and ex perimental geometries. In particular, this cannot explain the 11-22% d iscrepancies found here between the experimental polarizabilities for the trimer and higher-order clusters and those calculated at the LDA-o ptimized geometries using the B88x+P86c functional. It is suggested th at molecular motion may need to be taken into account before a complet ely satisfactory explanation of the experimental polarizabilities of t hese floppy molecules can be given.