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

Romuald Poteau (1) , Fernand Spiegelmann (1)

1 LPQ - Laboratoire de Physique Quantique

A distance-dependent extension of the Huckel 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 Na2 and Na&. 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 (Na3-Na8), 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 Na9-Na». Larger clusters in the range Na» — Na&6i are examined with restricted symmetry constraints (icosahedra, cuboctahedra, and cubic clusters). Beyond n =147, the cuboctahedral structure is preferred.

Domaines: Chimie théorique et/ou physique

Romuald Poteau, Fernand Spiegelmann. Distance-dependent Hückel-type model for the study of sodium clusters. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 1992, 45 (4), pp.1878-1888. ⟨10.1103/PhysRevB.45.1878⟩. ⟨hal-01755301⟩