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 the one-body potential V(r) in terms of low-order derivatives of the idempotent Dirac density matrix built from a single Slater determinant of Kohn-Sham orbitals. Here, this is first combined with the study of Dawson and March [J. Chem. Phys. 81, 5850 (1984)] to express the single-particle kinetic energy density 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, by removing V(r), demonstrate that the ratio t(r)(r) depends, though non-locally, only on the single variable n'(r)(r), no high-order gradients entering for the spherical Be atom.