Lower bounds to the dynamic dipole polarizability of beryllium

Hylleraas and Weinhold lower bounds to the frequency dependent dipole polarizability of beryllium atom in the ground state are computed by using exponentially correlated Gaussian wave functions. While Hylleraas approach requires the knowledge of the exact unperturbed wave function Ψ(0), the Weinhold formulae account for the errors in the approximated zero-order wave function Ψ̃(0) as measured by the overlap 〈Ψ(0)|Ψ̃(0)〉. Accurate unperturbed wave functions employed in this calculations give, as a by-product, the lowest up to date variational energies of the 21S, 31S, and 41S states.