A study of accurate exchange-correlation functionals through adiabatic connection

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial generalized gradient approximation (GGA) functionals, this has culminated into the recently proposed SCAN (strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals-the GGA hybrid functionals B3LYP and PBE0 and the meta-GGA functional SCAN-from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as αV_ee with α varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference T_c between the interacting and the non-interacting kinetic energy for the same density.