Extension of the Thomas-Fermi-Dirac-Weizsacker model: four-order gradient corrections to the kinetic energy

The authors present an accurate numerical solution of the variational equation resulting from the standard Thomas-Fermi-Dirac-Weizsacker energy functional plus four-order gradient terms of the kinetic energy. They show that the solution of the variational equation leads to kinetic energies that differ from estimates obtained by evaluation of the kinetic energy functional to fourth order with Hartree-Fock densities.