Laurent series expansions in density functional theory

Abstract

It is shown that various energy functionals in density functional theory, including the total correlation functional E c[ ϱ], its kinetic-energy component T c[ ϱ], and its electron-electron repulsion component V c[ ϱ], can be expanded to good accuracy in Laurent series in terms of a common set of homogeneous functionals of different specific degrees in coordinate scaling: …, (1 + n), …, 2, 1, 0, −1, − 2, …, (1 - n), … From the asymptotic behavior of the Kohn-Sham effective potential, it is further argued that the local approximation to such Laurent series requires a complete truncation of the Taylor-like component of the Laurent series, and the remaining series are combinations of functionals 〈 ϱ κ 〈 homogeneous in ϱ of degrees k = 4/3, 5/3, 2, 7/3, …, (4 + n)/3, …. Numerical results on atoms confirm the soundness of this theory. Several exact integro-differential relations are derived within the adiabatic connection formulation.