Abstract
A distance-dependent extension of the Hückel 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 and . 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 (–), 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 –. Larger clusters in the range – are examined with restricted symmetry constraints (icosahedra, cuboctahedra, and cubic clusters). Beyond n=147, the cuboctahedral structure is preferred.
- Received 30 September 1991
DOI:https://doi.org/10.1103/PhysRevB.45.1878
©1992 American Physical Society