A pseudo-hamiltonian model for small alkali metal clusters

The dissociation energies and equilibrium geometries of the molecules Na₃, Na₃ ⁺, K₃ and K₃ ⁺ are calculated using a simple model hamiltonian. The model was previously developed by Roach and Baybutt to explain an anomalous feature in the bonding of alkali metal diatomics. For polyatomics it is convenient to introduce a small gaussian expansion of Slater orbitals, and this also allows the use of an improved method of evaluating integrals over the core volumes. Although Na₃ and K₃ are only predicted to be metastable (like H₃), their calculated ionization potentials are in quite good agreement with experiment. The failure of the model for the other alkali metals is discussed.