Hydrodynamic tensor density functional theory with correct susceptibility

摘要

In a previous work the authors developed a family of orbital-free tensor equations for the density functional theory[J.Chem.Phys.124,024105(2006)].The theory is a combination of the coupled hydrodynamic moment equation hierarchy with a cumulant truncation of the one-body electron density matrix.A basic ingredient in the theory is how to truncate the series of equation of motion for the moments.In the original work the authors assumed that the cumulants vanish above a certain order(N).Here the authors.show how to modify this assumption to obtain the correct susceptibilities.This is done for N=3,a level above the previous study.At the desired truncation level a few relevant terms are added,which,with the right combination of coefficients,lead to excellent agreement with the Kohn-Sham Lindhard susceptibilities for an uninteracting system.The approach is also powerful away from linear response,as demonstrated in a nonperturbative study of a jellium with a repulsive core,where excellent matching with Kohn-Sham simulations is obtained,while the Thomas-Fermi and von Weiszacker methods show significant deviations.In addition,time-dependent linear response studies at the new N=3 level demonstrate the author's previous assertion that as the order of the theory is increased new additional transverse sound modes appear mimicking the random phase approximation transverse dispersion region.