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

Semi-empirical valence bond surfaces for the homonuclear alkali trimers (M3) 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 1Σg+ and 3Σu+ states of the dimers (M2). Calculations were also carried out using an effective 3Σu+ 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 (2B2 symmetry) bound with respect to M2(1Σg+)+M(2S) 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 (2A1 symmetry) and a linear symmetric structure (2Σu+) lying above but very close to the minimum. The force constants of the 2Σu+, 2A1 and 2B2 structures, as well as the fundamental frequencies and zero point energies of vibration of the equilibrium 2B2 species, have also been calculated.