Towards an exact orbital-free single-particle kinetic energy density for the inhomogeneous electron liquid in the Be atom

摘要

Holas and March (Phys. Rev. A51, 2040 (1995)) wrote the gradient of theone-body potential V(r) in terms of low-order derivatives of the idempotentDirac density matrix built from a single Slater determinant of Kohn-Shamorbitals. Here, this is first combined with the study of Dawson and March (J.Chem. Phys. 81, 5850 (1984)) to express the single-particle kinetic energydensity of the Be atom ground-state in terms of both the electron density n(r)and potential V(r). While this is the more compact formulation, we then, byremoving V(r), demonstrate that the ratio t(r)/n(r) depends, thoughnon-locally, only on the single variable n'(r)/n(r), no high-order gradientsentering for the spherical Be atom.