Some rules forS(-2k) dipole sums?

Stieltjes conditions and the ratio test provide necessary but not sufficient conditions onS(-2k) dipole sums. If the dipole sums are accurate the associated n, n –1] Padé approximant provides a better representation of (), the frequency-dependent dipole polarizability, than a truncated series expression and, in addition, should bound () below. It is shown how constraints on the dipole sums effect the form of the 2,1] Padé approximant and an additional constraint is derived that ensures the analyticity of the approximant on 0 < ₁. There then follows a discussion of the reliability of available literature dipole sum values for small molecules containing H, C, N and O.