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Distance-dependent Hückel-type model for the study of sodium clusters

1992; American Physical Society; Volume: 45; Issue: 4 Linguagem: Inglês

10.1103/physrevb.45.1878

1095-3795

Romuald Poteau, F. Spiegelmann,

Advanced Physical and Chemical Molecular Interactions

A distance-dependent extension of the H\"uckel model is proposed and applied to sodium clusters. It consists primarily of a two-band monoelectronic formulation expressed in an s+p basis set. The s+p Hamiltonian is reduced into an s-only Hamiltonian by means of quasidegenerate perturbation theory, with the p band treated perturbatively. The parametrization is taken from accurate calculations of ${\mathrm{Na}}_{2}$ and ${\mathrm{Na}}_{4}$. This formulation allows a very quick determination of the potential-energy surfaces, and the use of the Monte Carlo simulated-annealing technique for determining the stable isomers of clusters. For the smallest clusters (${\mathrm{Na}}_{3}$--${\mathrm{Na}}_{8}$), the model provides stabilities and geometries in very good agreement with previous studies involving more sophisticated calculations (ab initio configuration-interaction or density-functional theory). Optimization results without constraint are also presented for clusters in the range ${\mathrm{Na}}_{9}$--${\mathrm{Na}}_{19}$. Larger clusters in the range ${\mathrm{Na}}_{55}$--${\mathrm{Na}}_{561}$ are examined with restricted symmetry constraints (icosahedra, cuboctahedra, and cubic clusters). Beyond n=147, the cuboctahedral structure is preferred.