How tight is the Lieb-Oxford bound?

摘要

Density-functional theory requires ever better exchange-correlation(xc)functionals for the ever more precise description of many-body effects on electronic structure.Universal constraints on the xc energy are important ingredients in the construction of improved functionals.Here we investigate one such universal property of xc functionals:the Lieb-Oxford lower bound on the exchange-correlation energy,E_(xc)[n]>=-C/d~3rn~(4/3),where C<=C_(LO)= 1.68.To this end,we perform a survey of available exact or near-exact data on xc energies of atoms,ions,molecules,solids,and some model Hamiltonians(the electron liquid,Hooke's atom,and the Hubbard model).All physically realistic density distributions investigated are consistent with the tighter limit C<= 1.For large classes of systems one can obtain class-specific(but not fully universal)similar bounds.The Lieb-Oxford bound with C_(LO)= 1.68 is a key ingredient in the construction of modern xc functionals,and a substantial change in the prefactor C will have consequences for the performance of these functionals.