Lower bounds to the Weizsäcker correction

Two rigorous lower bounds to T₂, the Weizs\"acker correction, have been derived: ${T}₂{≥}({{{π}}4/3{2}2/3}{24})×{}{({∫}{{ρ}}³({{→}}{r})d{{→}}{r})}1/3={T}₂B1[{ρ}]$ and ${T}₂>(1/72)<{r}^{{-}2}>={T}₂B2[{ρ}]$. The first bound is universal, while the second holds only for spherically symmetric bound systems. Numerical comparisons employing the Hartree-Fock atomic densities reveal that the bounds are not very tight; however, the ratios T₂T₂B1 and T₂T₂B2, though decreasing slowly with increasing Z, remain fairly constant for $Z=2$ through 24. The implications of these bounds in the variational context are discussed.