Local density functional approximations and conjectured bounds for momentum moments

Self consistent field wave functions of good, and in many cases of near Hartree–Fock, quality are used to test local density functional approximations to momentum moments for 122 linear molecules. Heuristic corrections to the local density functionals are suggested. The modified functionals for the kinetic energy and mean momentum have median errors less than 0.6% and maximum errors less than 1.7% on this large sample of 122 molecules. Moreover, the functionals correctly approach the Thomas–Fermi limit for large N, and should be competitive with gradient expansions. No counter examples were found for some previously conjectured [J. Chem. Phys. 85, 958 (1986)] bounds; serious efforts to prove them rigorously are invited.