Premium
Consequences for exchange energy density functional of exponentially decaying nature of atomic electron densities
Author(s) -
Liu Shubin,
Parr Robert G.
Publication year - 1999
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(19990115)20:1<2::aid-jcc3>3.0.co;2-2
Subject(s) - density functional theory , electron , electron density , simple (philosophy) , exponential function , local density approximation , thomas–fermi model , hybrid functional , chemistry , physics , atomic physics , quantum mechanics , mathematics , mathematical analysis , philosophy , epistemology
A simple model is studied for the atomic exchange energy density functional, which is based on the exponential decaying feature of the density and the Fermi–Amaldi model for exchange correlation. The model is exact for hydrogen‐like atoms. It is shown to provide a reasonable approximation for many‐electron atoms. The local exchange energy density and potential are expressed as universal functions of r , ρ( r ), and |∇ρ( r )|, and go beyond the generalized gradient approximation (GGA) framework in which E x [ρ]=∫ e x (ρ, ∇ρ) d r . The conclusion reached previously by Gill and Pople ( Phys. Rev. A 1993, 47, 2383), that the general atomic exchange functional cannot be of the GGA form, is supplemented by the more optimistic conclusion that it could well have the form E x [ρ]=∫ e x ( r , ρ, ∇ρ) d r . © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 2–11, 1999