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

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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.