Lower bounds to the Weizsäcker correction

Two rigorous lower bounds to $T_2$, the Weizsäcker correction, have been derived: $T_2\ge \left(\frac{{\pi }^{\frac{4}{3}}{2}^{\frac{2}{3}}}{24}\right)\times {\left(\int {\rho }^3\left(\overrightarrow{\mathrm{r}}\right)d\overrightarrow{\mathrm{r}}\right)}^{\frac{1}{3}}=T_2^{B1\mathrm{}}\left[\rho \right]$ and $T_2>\left(\frac{1}{72}\right)<\mathrm{}{r}^{-2\mathrm{}}>=T_2^{B2\mathrm{}}\left[\rho \right]$. 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 $\frac{T_2}{T_2^{B1\mathrm{}}}$ and $\frac{T_2}{T_2^{B2\mathrm{}}}$, though decreasing slowly with increasing $Z$, remain fairly constant for $Z=2\mathrm{}$ through 24. The implications of these bounds in the variational context are discussed.