The structural and electronic properties of small sodium clusters are investigated using a distancehyphen;dependent extension of the tighthyphen;binding (Huuml;ckel) 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 pentagonalhyphen;based seeds (pentagonal bipyramids and icosahedral structures) are shown to play an increasing role beyondn=12. Optimized geometries of Nanclusters are obtained in the rangen=4ndash;21 and forn=34. In particular, Na20is found to haveC3symmetry, hardly prolate with all axial ratios almost equivalent, whereas Na34hasD5hsymmetry and consists of a doubly icosahedral seed of 19 atoms surrounded by a ring of 15 atoms. Stabilities, fragmentation channels, and onehyphen;electron orbital levels are derived for the lowest isomers and shown to be characterized by a regular oddndash;even alternation. The present results are in generally good correspondence with previous nucleihyphen;based calculations when available. The global shapes of clusters, as well as the shapehyphen;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.
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