 
Summary: How to Tell an Atom From an Electron Gas: A SemiLocal Index of Density
Inhomogeneity
John P. Perdew and Jianmin Tao
Department of Physics and Quantum Theory Group,
Tulane University, New Orleans, Louisiana 70118, USA
Rickard Armiento
Department of Physics, Royal Institute of Technology,
AlbaNova University Center, SE106 91 Stockholm, Sweden
(Dated: July 8, 2003)
From a global perspective, the density of an atom is strongly inhomogeneous and not at all like
the density of a uniform or nearlyuniform electron gas. But, from the semilocal or myopic
perspective of standard density functional approximations to the exchangecorrelation energy,
it is not so easy to tell an atom from an electron gas. We address the following problem: Given
the groundstate electron density n and orbital kinetic energy density in the neighborhood of
a point r, can we construct an "inhomogeneity index" w(r) which approaches zero for weakly
inhomogeneous densities and unity for stronglyinhomogeneous ones? The solution requires not
only the usual local ingredients of a metageneralized gradient approximation (n, n, 2
n,),
but also and 2
. The inhomogeneity index is displayed for atoms, and for model densities
