TY - JOUR

T1 - Bridging density-functional and many-body perturbation theory

T2 - Orbital-density dependence in electronic-structure functionals

AU - Ferretti, Andrea

AU - Dabo, Ismaila

AU - Cococcioni, Matteo

AU - Marzari, Nicola

PY - 2014/5/27

Y1 - 2014/5/27

N2 - Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schlüter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

AB - Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schlüter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

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U2 - 10.1103/PhysRevB.89.195134

DO - 10.1103/PhysRevB.89.195134

M3 - Article

AN - SCOPUS:84902151929

VL - 89

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 19

M1 - 195134

ER -