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

• Published in: Physics and chemistry of liquids 2011-09, Vol.49 (5), p.693-697
• Main Authors: Krishtal, A., March, N.H., Alsenoy, C. Van
• Format: Article
• Language: English
• Subjects: electron density n; gradient quotient n′/n; Kinetics; orbital-free kinetic energy; Studies
• ISSN: 0031-9104; 1029-0451
• DOI: 10.1080/00319104.2010.518283

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)/n(r) depends, though non-locally, only on the single variable n′(r)/n(r), no high-order gradients entering for the spherical Be atom.