Jg. Guan et al., ALL-ELECTRON LOCAL AND GRADIENT-CORRECTED DENSITY-FUNCTIONAL CALCULATIONS OF NA-N DIPOLE POLARIZABILITIES FOR N=1-6, Physical review. B, Condensed matter, 52(3), 1995, pp. 2184-2200
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.