Semi-empirical valence bond potential energy surfaces for homonuelear alkali trimers

Abstract

Semi-empirical valence bond surfaces for the homonuclear alkali trimers (M ₃) have been obtained by evaluating the Coulomb and exchange integrals in the London equation, respectively, as half the sum and difference of new reliable analytical potential energy curves for the ¹Σ _{g ⁺} and ³Σ _{u ⁺} states of the dimers (M ₂). Calculations were also carried out using an effective ³Σ _{u ⁺} universal diatomic function which was chosen to reproduce the experimentally known binding energy of Li₃. The ground state equilibrium structures of those trimers are predicted to be an obtuse triangle (² B ₂ symmetry) bound with respect to M ₂(¹Σ _{g ⁺} )+M(² S) and ordered Li₃>Na₃>K₃>Rb₃>Cs₃ according to their stabilities. The surfaces are found to be extremely flat with two saddle points, an acute isosceles triangle (² A ₁ symmetry) and a linear symmetric structure (²Σ _{u ⁺} ) lying above but very close to the minimum. The force constants of the ²Σ _{u ⁺} , ² A ₁ and ² B ₂ structures, as well as the fundamental frequencies and zero point energies of vibration of the equilibrium ² B ₂ species, have also been calculated.

Additional information

Notes on contributors

V.M.F. Morais

Work carried out as part of an M.Sc. degree in Theoretical Chemistry at the University of Oporto.