Structural properties of sodium microclusters (n=4–34) using a Monte Carlo growth method

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Abstract
The structural and electronic properties of small sodium clusters are investigated using a distance‐dependent extension of the tight‐binding (Hückel) model and a Monte Carlo growth algorithm for the search of the lowest energy isomers. The efficiency and advantages of the Monte Carlo growth algorithm are discussed and the building scheme of sodium microclusters around constituting seeds is explained in details. The pentagonal‐based seeds (pentagonal bipyramids and icosahedral structures) are shown to play an increasing role beyond n=12. Optimized geometries of Nan clusters are obtained in the range n=4–21 and for n=34. In particular, Na20 is found to have C3 symmetry, hardly prolate with all axial ratios almost equivalent, whereas Na34 has D5h symmetry and consists of a doubly icosahedral seed of 19 atoms surrounded by a ring of 15 atoms. Stabilities, fragmentation channels, and one‐electron orbital levels are derived for the lowest isomers and shown to be characterized by a regular odd–even alternation. The present results are in generally good correspondence with previous nuclei‐based calculations when available. The global shapes of clusters, as well as the shape‐induced fine structure splitting of the spherical electronic jellium shell are found, with a few exceptions, to be also consistent with the ellipsoidal or spheroidal versions of the jellium model.