Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits

Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, limω→∞G-(q,ω). In two dimensions limω→∞G-(q,ω) is found to diverge as 1/q at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as 1/q2 in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches