Many-body approach to the electronic properties of clusters: Application to doubly charged Pb clusters.

Abstract

A many-body theoretical approach to the electronic properties of small clusters is presented. The nucleus of the theory is a realistic many-body Hamiltonian with intra-atomic and interatomic Coulomb interactions, which describes the dynamics of the valence electrons. The exact solution and several variational Ansa$iuml---tze (e.g., Hartree-Fock, Gutzwiller) are considered in order to quantify the importance of correlations to the electronic properties. As an application, the stability of doubly charged Pb clusters is studied. From the exact solution of the model we obtain, in agreement with experiment, that ${\mathrm{Pb}}_{3}^{2+}$ has a metastable ground state with isosceles geometry. While the Hartree-Fock approximation fails to account for the metastability, a simple spin-symmetrized Ansatz \ensuremath{\Vert}SSHF〉 yields a very good account of both the geometry and the energy barrier preventing dissociation. One concludes that both the metastability and structure of ${\mathrm{Pb}}_{3}^{2+}$ result mainly from antiferromagnetic quantum spin fluctuations. Furthermore, by introducing local correlations in \ensuremath{\Vert}SSHF〉, more than 99% of the exact binding energy is obtained for the whole range of interatomic distances. General implications and improvements necessary for the study of more complex systems are discussed.