Relevance of the Slowly Varying Electron Gas to Atoms, Molecules, and Solids

John P. Perdew, Lucian A. Constantin, Espen Sagvolden, Kieron Burke
2006 Physical Review Letters  
Under a certain scaling, the electron densities of finite systems become both large and slowly-varying, so that the gradient expansions of the density functionals for the Kohn-Sham kinetic and exchange energies become asymptotically exact to order $\nabla^2$. Neutral atoms of large $Z$ scale similarly, but a cusp correction at the nucleus requires generalizing the gradient expansion for exchange, producing the wrong gradient coefficient in the slowly-varying limit. Meta-generalized gradient
more » ... alized gradient approximations (meta-GGA's) recover both the slowly-varying and large-$Z$ limits. GGA correlation energies of large-Z atoms are found to be accurate.
doi:10.1103/physrevlett.97.223002 pmid:17155798 fatcat:v54nzzltqzborj25yt3mectsue