Lower bounds to the Weizsacker correction

Abstract

Two rigorous lower bounds to T₂, the Weizsacker correction, have been derived: T₂≥(π^4/32^2/3/24)×(∫³(r)dr)^1/3=T₂^B1[ρ] and T₂>(1/72)r-²=T₂^B2[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 T₂/T₂^B1 and T₂/T₂^B2, 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.