Imaginary-frequency polarizability and van der Waals force constants of two-electron atoms, with rigorous bounds

Variational functionals of Braun and Rebane for the imaginary-frequency polarizability α (iω) have been generalized by the method of Gramian inequalities to give rigorous upper and lower bounds, valid even when the true (but unknown) unperturbed wavefunction must be represented by a variational approximation. Using these formulas in conjunction with flexible variational trial functions we have computed tight error bounds for α (iω) and the associated two- and three-body van der Waals interaction constants of the ground 1 1S and metastable 2 1,3S states of He and Li+. These bounds generally establish the ground-state properties to within a fraction of a percent and metastable properties to within a few percent, permitting a comparative assessment of competing theoretical methods at this level of accuracy. Unlike previous ’’error bounds’’ for these properties, the present results have a completely a priori theoretical character, with no empirical input data.