TY - JOUR

T1 - Piecewise linearity of approximate density functionals revisited

T2 - Implications for frontier orbital energies

AU - Kraisler, Eli

AU - Kronik, Leeor

PY - 2013/3/19

Y1 - 2013/3/19

N2 - In the exact Kohn-Sham density-functional theory, the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies that do not exhibit this piecewise-linear behavior. As a result, the ionization potential theorem, equating the highest occupied eigenvalue with the ionization potential, is grossly disobeyed. Here, we show that, contrary to conventional wisdom, most of the required piecewise linearity of an arbitrary approximate density functional can be restored by careful consideration of the ensemble generalization of density-functional theory. Furthermore, the resulting formulation introduces the desired derivative discontinuity to any approximate exchange-correlation functional, even one that is explicitly density dependent. This opens the door to calculations of the ionization potential and electron affinity, even without explicit electron removal or addition. All these advances are achieved while neither introducing empiricism nor changing the underlying functional form. The power of the approach is demonstrated on benchmark systems using the local density approximation as an illustrative example.

AB - In the exact Kohn-Sham density-functional theory, the total energy versus the number of electrons is a series of linear segments between integer points. However, commonly used approximate density functionals produce total energies that do not exhibit this piecewise-linear behavior. As a result, the ionization potential theorem, equating the highest occupied eigenvalue with the ionization potential, is grossly disobeyed. Here, we show that, contrary to conventional wisdom, most of the required piecewise linearity of an arbitrary approximate density functional can be restored by careful consideration of the ensemble generalization of density-functional theory. Furthermore, the resulting formulation introduces the desired derivative discontinuity to any approximate exchange-correlation functional, even one that is explicitly density dependent. This opens the door to calculations of the ionization potential and electron affinity, even without explicit electron removal or addition. All these advances are achieved while neither introducing empiricism nor changing the underlying functional form. The power of the approach is demonstrated on benchmark systems using the local density approximation as an illustrative example.

UR - http://www.scopus.com/inward/record.url?scp=84875237836&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.110.126403

DO - 10.1103/PhysRevLett.110.126403

M3 - Article

AN - SCOPUS:84875237836

SN - 0031-9007

VL - 110

JO - Physical Review Letters

JF - Physical Review Letters

IS - 12

M1 - 126403

ER -