Ab initio study of small He cluster ions He n + ,n=2, 3, 4, 5, and low-lying Rydberg states of He4

SCF and CEPA calculations are applied to study the structure of small He cluster ions, He _n ⁺ ,n=2, 3, 4, 5 and some low-lying Rydberg states of He₄. The effect of electron correlation upon the equilibrium structures and binding energies is discussed. He ₃ ⁺ has a linear symmetric equilibrium geometry with a bond length of 2.35a ₀ and a binding energyD _e =0.165 eV with respect to He ₂ ⁺ +He (experimentally:D ₀=0.17 eV which corresponds toD _e ≈0.20 eV). He ₄ ⁺ is a very floppy molecular ion with several energetically very similar geometrical configurations. Our CEPA calculations yield a T-shaped form with a He ₃ ⁺ centre (R _e = 2.35a ₀) and one inductively bound He atom (4.39a ₀ from the central He atom of He ₃ ⁺ ) as equilibrium structure. Its binding energy with respect to He ₃ ⁺ +He is 0.031 eV. A linear symmetric configuration consisting of a He ₂ ⁺ centre with a bond length of 2.10a ₀ and two inductively bound He atoms (4.20a ₀ from the centre of He ₂ ⁺ ) is only 0.02–0.03 eV higher in energy. We expect that in larger He cluster ions structures with He ₂ ⁺ and He ₃ ⁺ centres andn?2 orn?3 inductively bound He atoms have nearly the same energies. In He₄ a low-lying metastable Rydberg state (³ Π symmetry for linear He ₄ ^* ,³ B ₁ for the T-shaped form) exists which is slightly stronger bound with respect to He ₃ ^* +He than the corresponding ion.